This article was downloaded by: [Michigan State University] On: 19 March 2013, At: 06:27 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Advances in Physics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tadp20 Ultrathin oxide films and interfaces for electronics and spintronics Manuel Bibes a b , Javier E. Villegas a b & Agnès Barthélémy a b a Unité Mixte de Physique CNRS/Thales, 1 Avenue Fresnel, Campus de l'Ecole Polytechnique, 91767, Palaiseau, France b Université Paris-Sud, 91405, Orsay, France Version of record first published: 06 Jan 2011. To cite this article: Manuel Bibes , Javier E. Villegas & Agnès Barthélémy (2011): Ultrathin oxide films and interfaces for electronics and spintronics, Advances in Physics, 60:1, 5-84 To link to this article: http://dx.doi.org/10.1080/00018732.2010.534865 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and- conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
Transcript
This article was downloaded by: [Michigan State University]On: 19 March 2013, At: 06:27Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Advances in PhysicsPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tadp20
Ultrathin oxide films and interfaces forelectronics and spintronicsManuel Bibes a b , Javier E. Villegas a b & Agnès Barthélémy a ba Unité Mixte de Physique CNRS/Thales, 1 Avenue Fresnel, Campusde l'Ecole Polytechnique, 91767, Palaiseau, Franceb Université Paris-Sud, 91405, Orsay, FranceVersion of record first published: 06 Jan 2011.
To cite this article: Manuel Bibes , Javier E. Villegas & Agnès Barthélémy (2011): Ultrathin oxidefilms and interfaces for electronics and spintronics, Advances in Physics, 60:1, 5-84
To link to this article: http://dx.doi.org/10.1080/00018732.2010.534865
PLEASE SCROLL DOWN FOR ARTICLE
Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden.
The publisher does not give any warranty express or implied or make any representationthat the contents will be complete or accurate or up to date. The accuracy of anyinstructions, formulae, and drug doses should be independently verified with primarysources. The publisher shall not be liable for any loss, actions, claims, proceedings,demand, or costs or damages whatsoever or howsoever caused arising directly orindirectly in connection with or arising out of the use of this material.
Advances in PhysicsVol. 60, No. 1, January–February 2011, 5–84
REVIEW ARTICLE
Ultrathin oxide films and interfaces for electronics and spintronics
Manuel Bibes*, Javier E. Villegas and Agnès Barthélémy
Unité Mixte de Physique CNRS/Thales, 1 Avenue Fresnel, Campus de l’Ecole Polytechnique, 91767Palaiseau, France and Université Paris-Sud, 91405 Orsay, France
(Received 15 February 2010; final version received 17 August 2010 )
Oxides have become a key ingredient for new concepts of electronic devices. To a large extent,this is due to the profusion of new physics and novel functionalities arising from ultrathinoxide films and at oxide interfaces. We present here a perspective on selected topics within thisvast field and focus on two main issues. The first part of this review is dedicated to the useof ultrathin films of insulating oxides as barriers for tunnel junctions. In addition to dielectricnon-magnetic epitaxial barriers, which can produce tunneling magnetoresistances in excessof a few hundred percent, we pay special attention to the possibility of exploiting the multi-functional character of some oxides in order to realize ‘active’ tunnel barriers. In these, theconductance across the barrier is not only controlled by the bias voltage and/or the electrodesmagnetic state, but also depends on the barrier ferroic state. Some examples include spin-filteringeffects using ferro- and ferrimagnetic oxides, and the possibility of realizing hysteretic, multi-state junctions using ferroelectric barriers. The second part of this review is devoted to novelstates appearing at oxide interfaces. Often completely different from those of the correspond-ing bulk materials, they bring about novel functionalities to be exploited in spintronics andelectronics architectures. We review the main mechanisms responsible for these new properties(such as magnetic coupling, charge transfer and proximity effects) and summarize some of themost paradigmatic phenomena. These include the formation of high-mobility two-dimensionalelectron gases at the interface between insulators, the emergence of superconductivity (or fer-romagnetism) at the interface between non-superconducting (or non-ferromagnetic) materials,the observation of magnetoelectric effects at magnetic/ferroelectric interfaces or the effects ofthe interplay and competing interactions at all-oxide ferromagnetic/superconducting interfaces.Finally, we link up the two reviewed research fields and emphasize that the tunneling geometryis particularly suited to probe novel interface effects at oxide barrier/electrode interfaces. Weclose by giving some directions toward tunneling devices exploiting novel oxide interfacialphenomena.
PACS: 72.25.Mk Spin transport interfaces; 73.40.Gk Tunneling; 73.40.Rw Metal-insulator-metalstructures; 74.78.-w Superconducting films and law dimensional structures; 77.55.Nv Multifer-roic/magnetoelectric films; 77.80.bn Strain and interface effects
1. Introduction 72. Functional oxides as tunnel barriers 9
2.1. Introduction to tunneling and spin-dependent tunneling 92.1.1. Simple models of electron tunneling 92.1.2. The role of the density of states and spin-dependent tunneling 102.1.3. Tunneling through crystalline barriers 12
3. Novel functionalities at oxide interfaces 413.1. Introduction to oxide interface physics 413.2. High-mobility interfaces 43
3.2.1. The LaAlO3/SrTiO3 system 433.2.1.1 General properties 433.2.1.2 Origin of the electron gas: polar catastrophe 463.2.1.3 Origin of the electron gas: extrinsic doping 473.2.1.4 Field-effect device perspectives 48
3.2.2. Other SrTiO3-related systems 493.3. Superconductivity at interfaces 49
3.3.1. Interplay between superconductivity and ferromagnetism at cuprate/manganite interfaces 49
3.3.1.1 Basic properties and proximity effects 503.3.1.2 Charge transfer effects 513.3.1.3 Spin injection and diffusion effects 533.3.1.4 Magnetic coupling 54
3.3.2. Superconductivity at the interfaces between non-superconducting oxides 543.3.3. Other systems 56
3.4. Magnetic effects at interfaces 573.4.1. Predicted states at correlated oxide interfaces 583.4.2. Novel magnetic phases at manganite interfaces 623.4.3. Hints of magnetism at LaAlO3/SrTiO3 interfaces 64
3.5. Polar and ferroelectric interfaces 653.6. Magnetoelectric effects at interfaces 66
4. Conclusions and perspectives 68Acknowledgements 70References 71
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1. Introduction
Oxide materials are ubiquitous in nature and their impressive range of functional properties isstarting to make them ubiquitous in technological applications as well. The transport propertiesof oxides span from superconductivity to high-mobility metallicity, semiconducting propertiesand insulating behavior. They may also show ferroic behavior, i.e. an hysteretic dependence ofan order parameter with an external stimulus below a critical temperature (often coined the Curietemperature) being ferroelectric, ferromagnetic, or both (in multiferroics).An additional specificityof oxides is that compounds showing these functional properties crystallize in a limited numberof structural families, notably in the perovskite structure.
Most of these properties have been known for decades and a basic understanding of theirphysics has been achieved through theoretical developments and studies of bulk samples, eithersingle crystals or ceramics [1]. The progress in thin-film deposition techniques (by sputtering,pulsed laser deposition and molecular beam epitaxy) in the 1980s and 1990s [2] has made itpossible to grow thin layers with epitaxial relationships with the underlying substrates, showingsometimes crystalline quality as good as that of single crystals. The epitaxial strain induced bythe substrates appeared as a new powerful handle to tune the film’s properties, or even inducephase transformations to states different from those found in the bulk [3]. Using multiple targetdeposition setups, it was also possible to combine different oxides from the same structural familyinto heterostructures and exploit several functionalities in the same samples.
Further progress enabled the control of thin-film growth at the unit-cell level, using in-situreal-time reflection high-energy electron diffraction (RHEED) monitoring [4]. Films as thin as afew unit cells could then be grown, individually or combined in small-period superlattices. Strongdeviations from the properties of thicker films were often observed and thickness reduction thusappeared as another handle to tailor film functionalities.
When an ultrathin insulating film is sandwiched between two metallic electrodes, a tunneljunction is formed [5]. If one uses metals and insulators from the same structural family, sayperovskite, fully epitaxial junctions may be defined. In principle, both the barrier thicknessand the barrier/electrode interfaces can be controlled at the unit-cell level. The earliest fullyepitaxial tunnel junctions based on oxide materials used half-metallic mixed-valence mangan-ites [6] as electrodes and a 6-nm-thick SrTiO3 film as tunnel barriers, as reported by Lu etal. in 1996 [7]. SrTiO3 is a dielectric and diamagnetic compound, isostructural to many othersimple functional and multifunctional perovskites such as ferroelectric BaTiO3 or multiferroicBiFeO3. Replacing SrTiO3 by such functional compounds in tunnel junctions would bring noveldevice possibilities, not achievable with the materials used in current complementary metaloxide semiconductor (CMOS) technology (e.g. Si or III–Vs, conventional metals and simpledielectrics [8]).
We dedicate the first part of this review to the physics and properties of tunnel junctionsintegrating different types of functional oxides as barriers. We will briefly recall the mecha-nisms of quantum mechanical tunneling and spin-dependent tunneling, and then present howthe barrier material may have a notable influence on the tunneling and spin-dependent tunnel-ing transport. The barrier materials will be classified according to their functionalities. First,tunnel junctions based on simple diamagnetic-dielectric barriers will be presented, with empha-sis on the interesting tunneling physics arising from wave-function symmetry filtering whenusing epitaxial barriers. Two important materials will be discussed, namely MgO and SrTiO3.Then, we will introduce the concept of spin filtering and review the work on junctions basedon ferromagnetic insulating barriers (low-temperature Eu chalcogenides and oxides such asBiMnO3 and spinel ferrites). Next, we will get onto the nascent field of tunnel junctions withferroelectric barriers (ferroelectric tunnel junctions), recalling the physics underlying the occur-rence of electroresistance in such devices and emphasizing the issue of critical thickness for
ferroelectricity. This first part will end with a section on multiferroics, compounds in whichat least two primary ferroic orders coexist in the same phase [9], and address their poten-tial as tunnel barriers. We will describe in detail the work on BiFeO3 ultrathin films, presentresults on La0.1Bi0.9MnO3-based tunnel junctions and discuss the interest of rare-earth manganitemultiferroics.
As will be discussed, the tunnel current depends sensitively on the density of states at theinterface between the barrier and the electrodes, and can thus be used as a probe of the interfacialproperties. This resonates with the flurry of interface phenomena that were recently reported inoxide heterostructures, so that tunnel junctions appear as very appropriate architectures to exploitsuch novel interface effects in practical devices. Before developing these concepts, we will recallhow the tremendous progress in oxide growth and the control of interfaces at the unit-cell level hasmade possible the investigation of the consequences of the discontinuity between two differentmaterials and of the ensuing symmetry breakdown and electronic or atomic reconstruction in oxideheterostructures. As conjectured theoretically, they may result in unexpected effects and exoticground states. In view of the range of functionalities shown by oxide materials (see Figure 1 forsimple 3D transition metal perovskite oxides), the number of interfacial combinations is almostinfinite. Phases with no equivalent in the bulk have been reported, and more will certainly follow.Akey ingredient for this is the fact that the phase diagrams of these materials are strongly dependenton doping (see Figure 1) so that small changes in the carrier concentration lead to huge changesin the physical properties (e.g. from superconducting to insulating, or from antiferromagnetic toferromagnetic). Moreover, this strong phase competition can be tuned by external stimuli (e.g.magnetic and/or electric field, strain, light illumination and so on). Consequently, the engineeringof interfacial phases is now emerging as a route of choice to circumvent material issues in severalfields, such as the design of artificial room-temperature multiferroics with both large magnetizationand polarization, or room-temperature superconductors.
The second part of this review will be devoted to the burgeoning field of oxide interfaces. Aftera short introductory section, we will discuss high-mobility metallic interfaces starting with the
paradigmatic interface system LaAlO3/SrTiO3.A brief comparison with n-type, doped SrTiO3 sur-faces and ultrathin films will be given. The second interface property that we will discuss is super-conductivity. We will cover proximity effects in cuprate/manganite interfaces and the occurrence ofsuperconductivity at interfaces between non-superconducting oxides, and on LaAlO3/SrTiO3 andcuprates. Next, we will get onto magnetic effects at interfaces with focus on theoretical predictionsof novel states between two correlated insulating perovskites and then cover experimental resultson interfaces between manganites. Hints of magnetism in the LaAlO3/SrTiO3 system will alsobe discussed and critiqued. In the last section of this part, we will review novel magnetoelectriceffects that arise at interfaces, usually between a ferroelectric and a magnetic material.
Finally, we will summarize the state of the art in the use of oxide barriers for spintronics andthe progress in oxide interface physics. We will give perspectives for these two aspects of theexpanding field of oxide electronics and highlight some important issues that will have be to beaddressed in the near future.
2. Functional oxides as tunnel barriers
2.1. Introduction to tunneling and spin-dependent tunneling
2.1.1. Simple models of electron tunneling
In solid-state physics, electron tunneling is a quantum mechanical effect by which an electricalcurrent may flow from one metallic electrode, across a thin insulating barrier, into another metallicelectrode. A simple way to understand how tunneling is possible is by considering an electronwave that encounters a potential step. Though most of the intensity is reflected at the potential step,a portion decays exponentially through the barrier. For sufficiently thin barriers (typically a fewnanometers thick), some intensity remains on the other side of the potential step, and therefore theelectron will have a finite probability of being found on the other side of the tunnel barrier [12].
The current across the structure is given by the product of the density of states (DOS, η) in theelectrodes, multiplied by the square of the tunneling matrix elements M (that can be identified tothe transmission coefficient T (E) ≡ |M|2) and the thermal occupation probability of the statesinvolved:
I1→2(V ) =∫ +∞
−∞η1(E)η2(E + eV )|M|2f (E)[1 − f (E + eV )] dE. (1)
For identical non-magnetic electrodes and a dielectric diamagnetic barrier, the current densityJ can be expressed as given by Simmons [13] who calculated the tunneling matrix elements inthe Wentzel–Kramers–Brillouin (WKB) approximation:
J (V ) = J0
d2
(φ − eV
2
)exp
[−Ad
√φ − eV
2
]
− J0
d2
(φ + eV
2
)exp
[−Ad
√φ + eV
2
], (2)
where A = 4π√
2m�� and J0 = e/2π� are constants with m� being the electron effective mass,d the barrier thickness, φ the barrier height and eV the applied bias.
Importantly, the tunnel current thus depends exponentially on the barrier thickness, the squareroot of the effective mass and the square root of the barrier height. A consequence is that evensmall changes in any of these three parameters will have a strong influence on the tunnel current.
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Another important feature is that at a moderate voltage, the tunnel current density has the generalform
J ∝ αV + βV 3 (3)
so that the conductance G = dI/dV is a parabolic function of the voltage.When the applied bias voltage becomes larger than φ/e, tunneling is no longer direct; this is
the Fowler–Nordheim regime in which the current density may be described by
J = e3V 2
16π2d2�φexp
(−πd
√m�φ3/2
2√
2e�V
). (4)
In the direct (elastic) tunneling case of Equation (1), the final state of an electron tunnelingfrom the Fermi level in the first electrode is a state at an energy eV above the Fermi level inthe second electrode. However, in non-idealized cases, the electron may be able to interact withphonons or, when the ultrathin insulator separating the electrodes is not perfect, with defect stateswithin the bandgap of the insulator. The electron may loose energy in the process and tunnelingbecomes inelastic. In this assisted-tunneling regime the voltage dependence of the current ismodified and contains signatures of the inelastic processes (tunneling can thus even be used as atool for studying vibrational modes, e.g. of the barrier material [5]). The physics of defect-assistedtunneling is very rich, especially when spin-dependent processes come into play (see later). Wedo not review these effects here but we just point out the model of Glazman and Matveev [14,15]for assisted tunneling via two or more localized states that predicts a V4/3 dependence of theconductance G. Importantly, when tunneling is assisted by defects, the conductance of the junctionstrongly decreases as temperature decreases (for the latter case, G ∝ T 4/3), while it only decreasesslightly when tunneling is direct [16]. For more details on defect-assisted tunneling, the readermay consult [5].
2.1.2. The role of the density of states and spin-dependent tunneling
In his approach of direct tunneling, Simmons neglects any effect of the DOS on the tunnel current.Indeed, for tunnel junctions based on simple metals with broad s bands such as Al, Pb or Sn,these DOS effects are negligible. It is only through the investigation of tunnel junctions withsuperconducting electrodes (e.g. Al, Pb or Sn but at very low temperatures) that the role of DOSwas demonstrated. Below the critical temperature, the opening of a quasi-particle gap resultsin strong DOS variations close to the Fermi level that are readily visible in I (V ) and G(V )
curves [17].When ferromagnetic metals are used as electrodes, their non-equivalent DOS for spin-up and
spin-down states bring about novel physical effects. Let us assume that the spin is conserved duringthe tunnel process so that the total tunnel current is the sum of the currents for spin-up and spin-down (in analogy with Mott’s two-current model for diffusive transport [18]).Then the conductanceof a magnetic tunnel junction (MTJ, a trilayer in which two ferromagnetic electrodes sandwicha diamagnetic-dielectric tunnel barrier) in the parallel (P) and antiparallel (AP) configurations ofthe electrodes’ magnetization is simply proportional to the product of the DOS of the electrodes(see Figure 2):
GP ∝ G↑↑ + G↓↓ ∝ N1↑N2↑ + N1↓N2↓, (5)
GAP ∝ G↑↓ + G↓↑ ∝ N1↑N2↓ + N1↓N2↑, (6)
where N1↑(↓) and N2↑(↓) are the DOS of the two FM electrodes at the Fermi level for majority spinelectrons (↑) (respectively for minority spin electrons (↓)). Thus, the tunnel resistance is different
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in the P and AP states, which defines the tunnel magnetoresistance effect (TMR). This leads toJullière’s expression of the TMR ratio [19]:
TMR = RAP − RP
RP= GP − GAP
GAP= 2P 1
spinP2spin
1 − P 1spinP
2spin
, (7)
where Pspin is the spin polarization of the electrodes defined (in the simplest approach) as
P ispin = Ni↑ − Ni↓
Ni↑ + Ni↓. (8)
The first TMR experiment (at low temperature) dates back to 1975 [19] but it is only in1995 [20,21] with the observation of large and reproducible TMR effects at room temperaturein Fe/Al2O3/Fe and Co/Al2O3/CoFe (represented in Figure 3) respectively, that the research onTMR took off. Non-volatile magnetic random access memories (MRAMs) [22] based on the TMReffect, i.e. arrays of MTJs, have been commercialized since 2007 [23].
The inspection of the Jullière formula naturally leads one to search for materials with a highPspin in order to increase the TMR. Materials with a spin polarization of 100% are called half-metals [25]: they are metallic for one spin direction and insulating for the other. In other words,at the Fermi level, their DOS is finite for one spin direction and zero (or in practice vanishinglysmall) for the other. For reviews on half-metals, the reader is referred to [26,27]. The achievementof large TMR ratios using half-metallic electrodes is however not straightforward. Indeed, amongthe dozens of compounds that have been predicted to be half-metallic from ab initio calculations,very few have yielded good MTJ performance. Besides some Heussler and half-Heussler alloys[28], many half-metals are oxides: CrO2, Fe3O4 [29,30,31], mixed-valence manganites [6,32]and double-perovskites [33]. So far, MTJs based on CrO2 [34,35] or Fe3O4 [36,37] have shownlow TMR, typically less than 50%, compared to their predicted half-metallic nature. In contrast,optimized junctions based on half-metallic manganite electrodes such as La2/3Sr1/3MnO3 (LSMO)or La2/3Ca1/3MnO3 (LCMO) do exhibit TMR values of several hundred percent [38,39,24,40,41],corresponding within the Jullière model to Pspin of up to 95% [24]. An example of such a largeTMR is displayed in Figure 3(b). Importantly, the TMR of manganite-based MTJs is only largeat low temperature and vanishingly small at 300 K [42]. MTJs based on oxide electrodes arediscussed in detail in Ref. [43].
R
H
Parallel Antiparallel
Figure 2. Schematic description of the tunnel current in a magnetic tunnel junction with two identical,positively spin-polarized electrodes. In the parallel state (left), a strong current is carried by the spin-upchannel, resulting in a large total current and a low resistance. In the antiparallel state, the current is ratherweak in both spin channels, resulting in a weak total current and a high resistance. Consequently, the junctionresistance is expected to show two states as magnetic field is swept, as shown in the right panel. Note thesimilarity with the experimental curves of Figure 3.
The development of half-metallic electrodes for MTJs was initially motivated by the predicteddirect relationship between the spin polarization of the electrodes and the TMR value, expressedin the Jullière formula of Equation (7). In this scheme, the barrier plays no role, aside frommagnetically decoupling the electrodes and generating the potential step that electrons must tunnelthrough. In other words, the tunnel matrix elements |M| of Equation (1) are the same for alldirections, i.e.
T (E) ≡ |M|2 ∝ exp
(−d
√2m�
�(φ − eV )
). (9)
Nevertheless, it is natural to expect that, because the potential barrier is not generated by avacuum space between the electrodes but by a thin insulating material, the crystalline structureof the insulator, its physical properties (including functional ones such as ferromagnetism orferroelectricity) and the chemical bonding between the insulator and the electrodes will stronglyinfluence |M|. When the insulator is dielectric, diamagnetic and amorphous as in the case ofaluminum oxide barriers – that were virtually the only barriers available until the late 1990s –it may be fair to consider that |M| only depends on the basic barrier parameters, namely height,mass and thickness. However, in all other cases, the nature of the barrier will be the key to thebehavior of the junction.
In a crystalline conductor, electrons at the Fermi level traveling along a given crystallographicdirection exist in several states with different symmetries. When they reach the interface witha crystalline insulator, their wave-functions will penetrate it (metal-induced gap states (MIGS))and decay over different lengths depending on their symmetry and the crystalline structure ofthe insulator. This can be expressed by transmission coefficients depending on symmetry-specificdecay parameters κ , i.e. T (E) ∝ exp −2dκi , with i being the different possible wave-functionsymmetries. Just as the band structure of a material can be calculated for propagating Bloch states
(with real wave-vector), it can also be computed for evanescent states (with complex wave-vector),which produces its complex band structure [44].
Before addressing the physics of junctions based on functional barriers, we review in the nextsection the properties of junctions based on diamagnetic dielectrics, with special focus on thoseintegrating epitaxial barriers.
2.2. Dielectric and diamagnetic oxides
Historically, the barrier of MTJs was traditionally made of an amorphous or nanocrystalline mate-rial – mostly aluminum oxide (Al2O3) – with which the maximum room-temperature TMR peaksat 50 or 70% for Co75Fe25 [45] or amorphous Co60Fe20B20 [46] electrodes respectively. Recenttheoretical and experimental work performed on semi-epitaxial and epitaxial MTJs has provided abetter understanding of the spin-polarized tunneling phenomenon as well as a powerful approachto achieve very large TMR ratio by choosing specifically the electrode/barrier combination. Thislast approach will be presented in the following sections, with emphasis on MgO and SrTiO3.
2.2.1. MgO
MgO has a simple rock-salt structure with a lattice parameter 4.203 Å. The bulk optical bandgapis 7.8 eV. In 2001, ab initio calculations on MgO-based tunnel junctions have demonstrated that arealistic description of the band structures of the electrodes and the barrier is necessary to allow afull understanding of the spin-polarized tunneling in the case of epitaxial or semi-epitaxial tunneljunctions and started the race to records of magnetoresistance exploiting the symmetry filteringof the MgO barrier [47,48]. An intuitive description of these theoretical results [49], in the caseof large tunnel barrier thicknesses, i.e. when the tunnel current is primarily carried by stateswith wave-vector perpendicular to the interface (k‖ = 0) is the following. If one considers theband structure of b.c.c. Fe in the H direction shown in Figure 4(a) (corresponding to electronspropagating perpendicularly to the interface), one can see that at the Fermi level states of �1
(spd-like character), �5 (pd) and �2′ (d) symmetries coexist for the majority spin electrons. Onthe contrary, in the minority spin band structure, �1 symmetry is absent. As mentioned earlier, theBloch states of electrons of symmetry � coming from an Fe electrode will decay with differentrates in the crystalline MgO barrier. Considering the ab initio calculations of the complex bandstructure of MgO (Figure 4b), one can see that the decay rate �1 is much smaller than �5 whichis smaller than �2′ at the Fermi level. It follows that the evanescent states of symmetry �1 willbe less attenuated than those of symmetry �5 or �2′ . To have a complete picture, one has also toconsider the coupling of the Bloch states in the electrodes to the evanescent states in the barrier.In the case of Fe/MgO, since the MgO cubic cell is rotated by π /4 with respect to that of the Fe,Bloch states of �1 and �5 symmetries in the Fe electrodes decay as evanescent states with �1
(respectively �5) symmetry in MgO, whereas states with �2 and �2′ symmetries will decay asevanescent states of �2′ and �2 symmetries, respectively.
In fine, considering the different symmetries of the Bloch states in the electrodes, the trans-mission coefficient at the interface and the different decay rates of the evanescent states insidethe barrier in Fe-b.c.c.(001)/MgO/Fe-b.c.c.(001) tunnel junctions, Butler et al. [47] calculated thetunneling DOS in the parallel and antiparallel configuration of the magnetizations in this largethickness regime (see Figure 5). Consequently, in the parallel configuration, the tunneling is gov-erned by �1 states of majority spin with small decay rate that results in a high conductance state.In the antiparallel configuration, since for an injected �1 state none of the minority Bloch statesin the collecting electrode have the correct symmetry, the current is only due to the transmissionof �5 and �2 states with large decay rates and hence the conductance is small.
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This symmetry filtering is very efficient and should result in TMR ratios as large as severalthousand per cent in this large-thickness regime. In the low-thickness regime, the description isless intuitive since contributions of k‖ �= 0 and contributions from interfacial resonance statesbecome significant and will affect the conductance in the minority spin channel and thereby themagnetoresistance [47,48,51]. The nature of the bonding at the interface has also been predictedto strongly affect the conductance. Zhang and Butler [52] have investigated this influence inFe/FeOx /MgO/Fe tunnel junctions and found an order of magnitude drop in the TMR relatedto the reduced coupling between the incident majority spin Bloch state of �1 symmetry withthe MgO evanescent states of the same symmetry due to the presence of an FeO layer at theinterface. Nevertheless, Tusche et al. [53] predict a strong enhancement of the TMR (7790% ateight monolayers of MgO) when FeO layers are at both interfaces due to a fully coherent tunneling.In the case of asymmetric tunnel junction, the TMR drops to several tens of percent (74% at sixmonolayers) and is predicted to oscillate with the MgO thickness.
Experimentally, after the pioneering work of Bowen et al. [54] who reported a TMR of 60% inepitaxial Fe/MgO/Fe junctions, TMR values in excess of 200% were reported by Parkin et al. [55]andYuasa et al. [56]. There have also been reports of very large TMR in Co/MgO/Co (410% [50]),CoFe/MgO/CoFe (290% [55]) and CoFeB/MgO/CoFeB (1144% at low temperature and 604% atroom temperature [57]). This last result is reported in Figure 6(c).
In Co/MgO/Co tunnel junctions, the TMR depends weakly on temperature but more stronglyon bias compared to case of Fe/MgO/Fe. This has been ascribed to the influence of the bandstructure of b.c.c. Co [50,59]. In Fe/MgO/Fe MTJs, Yuasa et al. [58] also reported oscillations ofthe TMR as a function of the MgO thickness (Figure 6b) and interpreted them as the signatureof interferences between evanescent waves of different symmetry (different metal-induced gapstates), expected in a coherent tunnel regime. The general increase of the TMR with the MgO
thickness is also predicted by theory and attributed to the progressive decrease in the minorityspin channel of the nonzero momentum component in the layer plane. Tiusan et al. [60] studiedthe bias dependence of (001)Fe/MgO/Fe and (001)Fe/Pd/MgO/Fe epitaxial tunnel junctions. Forsmall MgO thickness, they found a TMR sign change at +0.2V for Fe/MgO/Fe and ascribed itto the existence of a sharp resonant interface state at the Fe/MgO interface. When Pd is insertedbelow the bottom Fe electrode, the coupling of this interface state with the Bloch states of theelectrode is strongly affected and the inversion disappears. In the same spirit, when carbon isinserted at the bottom interface between Fe and MgO, the TMR decreases more rapidly and canbe reversed through the bonding between Fe and carbon which affects the propagation of the �1
symmetry in the majority spin channel without affecting the interfacial resonance of Fe in theminority one [61]. Such experiments demonstrate the possibility to engineer the bias dependence.
The work on MgO-based MTJs has been mostly based on transition metal electrodes with b.c.c.structure. Few results have been reported on MgO-based tunnel junctions with other electrodematerials. For instance, there was a report in 2006 on the TMR of MTJs with a MgO barrier andtop and bottom Co2FeAl0.5Si0.5 full-Heusler electrodes. A maximum TMR effect of 175% at roomtemperature has been obtained for a 2 nm MgO barrier [62].
This very successful combination of theoretical and experimental work performed on MgO-based tunnel junctions has allowed a better understanding of the symmetry filtering phenomenapresent in epitaxial and semi-epitaxial tunnel junctions. This has opened new routes to engineer theresistance area (RA) product, TMR amplitude and bias dependence and obtain high-performanceMTJs. In addition, this progress has opened the investigation of other, more complex epitaxialinsulating oxides as tunnel barriers, including perovskites such as SrTiO3.
2.2.2. SrTiO3
SrTiO3 crystallizes in the perovskite structure ABO3 with an ideal cubic symmetry and a unit-cell parameter of a = 3.905Å. SrTiO3 is a band insulator with a bandgap of 3.2 eV [63,64]. Thevalence band is formed by O 2p states and the conduction band by Ti t2g states (see the bandstructure in Figure 7a). Contrary to the case of MgO, the states at the top of the valence band donot have the same symmetry as those at the bottom of the conduction band [65], which will haveimportant implications for tunneling. The complex band structure of SrTiO3 has been calculatedby Bowen et al. [66] and Velev et al. [67] and is reproduced in Figure 7(b). In contrast to whathappens in MgO, the hierarchy of decaying states is not simple and depends on the energy. While�2 and �2′ states decay very fast, both �1 and �5 states have rather slow decaying rates, and the κ
loops corresponding to these two symmetries intersect at energies close to EF and thus accessiblein tunneling experiments.
STO was introduced as a tunnel barrier in LSMO/STO/LSMO MTJs [7,68,69,70,24]. Aspreviously mentioned, these junctions have shown very large TMR ratios (see Figure 3b),owing to the half-metallic nature of the LSMO electrodes. More insights into the role ofthe barrier on the tunneling process were gained from transport experiments performed onLa0.7Sr0.3MnO3/SrTiO3/Co tunnel junctions [71,72,73,74]. These results are displayed in Figure 8.In the case of LSMO/Al2O3/Co junctions (Figure 8b), the TMR is normal (the resistance is larger inthe antiparallel state than in the parallel one) which indicates a positive spin polarization for Co atthe interface with Al2O3, as always found with Al2O3 barriers and transition metal electrodes [75].On the contrary, the TMR is reversed (see Figure 8a) in the case of an SrTiO3 barrier. This cor-responds to a negative spin polarization for Co at the interface with SrTiO3. These results thusclearly evidence the role played by the barrier [71].
Furthermore, by inserting an ultrathin Al2O3 layer at the interface between SrTiO3 and Coin LSMO/SrTiO3/Co tunnel junctions, De Teresa et al. [72] have shown that a normal TMR is
Figure 8. TMR curves recorded at 40 K and 10 mV for (a) Co/SrTiO3/LSMO, (b) Co/(Ce,La)O2/LSMO,(c) Co/Al2O3/LSMO and (d) Co/Al2O3/SrTiO3/LSMO junctions (from J.M. De Teresa et al., Science, 286,p. 507, 1999 [72]. Reprinted with permission from The American Association for the Advancement ofScience).
restored (Figure 8d). This last result indicates that bonding at the interface is a key parameter in thedetermination of the spin polarization which is in agreement with the theoretical work of Tsymbaland Pettifor [76]. The very different bias dependences of the TMR found in the cases of SrTiO3 orAl2O3 have been interpreted in terms of the d-character (or s-character, respectively) of the tunnel-ing electrons through the SrTiO3 (respectively Al2O3) barrier. In the case of LSMO/SrTiO3/Co,the TMR presents a maximum (in absolute value) at negative bias (i.e. when electrons are injectedinto the Co electrode). The authors related it to the DOS of d character of the Co electrodes.First-principles density functional studies of the Co/Al2O3 and Co/SrTiO3 interface by Oleinikand coworkers [77,78,79] suggested the same interpretation, i.e. the inversion of the Co spinpolarization for SrTiO3 (presented in Figure 9) or thick Al2O3 tunnel barriers. Furthermore, theypredicted a moment of 0.25μB on the Ti atom at the interface due to an antiferromagnetic exchangecoupling between Co and Ti mediated by oxygen atoms. Results in the case of SrTiO3 barriers arepresented in Figure 9 [78]. These calculations indicate a clear non-zero DOS inside the barrier.These metal-induced gap states with negative spin polarization are believed to be responsible forthe tunneling and determine the sign of the spin polarization, in this case negative. However, asalso shown by Oleinik et al. [77] in the case of Al2O3 barrier, the whole mechanism, i.e. bondingand propagation, has to be taken into account to determine the spin polarization (then the interfacebonding promotes a negative polarization that becomes positive for barrier thicknesses greaterthan 1 nm).
We point out that Bibes et al. and Garcia et al. also found a negative spin polarization for Coat the interface with epitaxial TiO2 [80] and LaAlO3 [81] barriers, respectively. The TMR(V) ofCo/LaAlO3/LSMO junctions is strikingly similar to that of Co/SrTiO3/LSMO junctions [81]. Thisstrongly suggests that wave-function symmetry selection by the epitaxial barrier is essential indetermining the tunnel current in these junctions. Preliminary calculations of the complex bandstructure of LaAlO3 [82] seem to indicate a negative spin polarization for Co/LaAlO3, which isin agreement with experiments.
More recently, the high bias regime of the bias dependence of the TMR of LSMO/SrTiO3/LSMO tunnel junctions has been related to the complex band structure of SrTiO3 [83].Bowen et al. argue that due to the symmetry mismatch between the Bloch wave-function in LSMOand the lower conduction band, the Fowler Nordheim regime is shifted to higher bias and occursonly above the hole barrier height with correct symmetry. These results illustrate the potential ofcomplex insulating oxides to craft the bias dependence of the TMR according to some specificneeds.
2.3. Ferro- and ferrimagnetic dielectric oxides
Ultrathin films of ferromagnetic metals have been studied for decades, but little is known concern-ing ultrathin films of ferro- and ferrimagnetic insulators. One reason is the relative scarcity of suchmaterials compared to magnetic metals.As we will see, ferromagnetic insulators are rare, and mosthave low ferromagnetic Curie temperatures (T M
C ). This is because in insulators, there are no carriersto mediate an exchange interaction between magnetic sites: then, the dominant exchange interac-tion is usually super-exchange that, following Goodenough–Kanamori–Anderson rules [84,85,86],cannot be ferromagnetic and strong. However, in insulating compounds with more than one type ofmagnetic sites, antiferromagnetic super-exchange interactions can produce a ferrimagnetic order-ing. The T M
C can then be high if the super-exchange antiferromagnetic interactions are strong (180◦type).
In spintronics, the main interest of ultrathin films of ferro- or ferrimagnetic insulators is astunnel barriers that can filter electrons selectively according to their spins. In the following, we
first present the phenomenon of spin filtering [87] and then review experimental results on spinfilters based on several types of ferro- and ferrimagnetic dielectric barriers.
2.3.1. The physics of spin filtering
As compared to the classical spin-dependent tunneling through a diamagnetic insulating barrier,the phenomenon of spin filtering through a ferromagnetic or ferrimagnetic insulating barrier hasbeen little studied. Because of the exchange splitting, the bottom of the conduction band in thebarrier material lies at different energies for spin-up and spin-down electrons, which yields differenttunnel barrier heights. In an intuitive vision based on the free electron model, due to the exponentialdependence of the tunnel transmission with the barrier height (see Section 2.1), electrons froma non-magnetic electrode will be transmitted differently depending on their spin. If the bottomof the conduction band is at a lower energy for spin-up than for spin-down (see Figure 10), thena large positive spin polarization is expected for the current emerging from the barrier. The spin
polarization of this current, or spin filtering efficiency of the barrier, is expressed as
PspinF = J↑ − J↓
J↑ − J↓, (10)
where J↑ (respectively J↓) is the spin-up (respectively spin-down) current that can be expressedby the Simmons model at small bias as [13]
J↑ =√
φ0 − �φ
2exp
(−A
√φ0 − �φ
2d
), (11)
J↓ =√
φ0 + �φ
2exp
(−A
√φ0 + �φ
2d
). (12)
In these expressions, φ is the averaged barrier height, �φ the spin-splitting of the bottom ofthe conduction bands and d the thickness of the barrier. It follows that the spin filtering efficiencyP
spinF will increase when the spin splitting �φ and the thickness of the barrier are increased. The
exponential dependence makes this filtering mechanism very efficient and large spin polarizationof the current is expected. In order to measure the spin-filtering efficiency, a reference layer actingas a spin detector has to be added. If a ferromagnetic counter-electrode is used, this defines aspin-filter tunnel junction. Depending on the orientation of the magnetizations of the barrier andthe counter-electrode, the current will be small or large. Figure 10 represents the case of a bottomof the conduction band in the barrier at lower energy for the majority spin-up (spin-down) and ahalf-metallic counter-electrode with only majority spin states at the Fermi level. In that example,spin-up electrons of the non-magnetic electrode will be highly transmitted by the barrier and willhave a lot of available states to be injected into when the magnetizations are parallel. This will resultin a large current in the parallel configuration. On the contrary, for an antiparallel arrangementof the magnetizations, the highly transmitted spin-up carriers have no empty available states inthe counter-electrode at the Fermi level. The current in that case will then only be due to poorlytransmitted spin-down electrons and as a result be small. In an extension of the Jullière model, theTMR of a spin filter can be expressed as
TMR = 2Pspin1 P
spinF
1 − Pspin1 P
spinF
. (13)
The dependence of the TMR on the thickness of the barrier and with the bias applied to thejunction has been calculated by Saffarzadeh [88]. In general, the TMR is expected to increase withbias voltage, which is a typical signature of spin-filtering.
As in the case of classical MTJs, for an epitaxial or semi-epitaxial spin filter, the problemis more complex and the role of wave-function symmetry has to be taken into account [89].Nevertheless, it is always possible to use the expression of the TMR but one has to consider P
spinF
as an effective spin-filtering efficiency of the barrier.
2.3.2. Europium chalcogenides
Until 2004, all the work on spin filtering focused on low T MC Eu chalcogenide materials. EuS and
EuO are ferromagnetic semiconductors with Curie temperatures of 16 and 69 K, respectively [90].There are also reports with EuSe that is an antiferromagnetic semiconductor in which a transitionto a ferromagnetic state occurs in a magnetic field of a few teslas [91].
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Antiparallel: lowI, large RParallel: large I, lowR
ϕΔ
Non Magn.Metal
Ferro.Insulator
ϕ
Ferro.Half Metal
0
exch
Figure 10. Sketch of the tunneling process through a spin-filtering tunnel barrier. The black vertical arrowsindicate the direction of magnetization in the magnetic barrier and ferromagnetic counter-electrode (thatwe choose half-metallic for simplicity). The red and blue vertical arrows indicate the spin direction and thehorizontal one the tunnel current.
Early indications of spin filtering were reported in field emission experiments by Müller et al.[92] and in transport experiments by Esaki et al. [93], both using EuS. About 20 years later,Moodera and colleagues [94,95] performed spin-polarization measurements at 400 mK usingthe Meservey–Tedrow technique in tunnel junctions with EuS barriers, a normal metal electrode(typicallyAg orAu) and a superconductingAl counter-electrode (see Figure 11a). This technique tomeasure the spin polarization of the tunnel current (P spin
F ) was developed by Meservey and Tedrowin the 1970s and is illustrated in Figure 11(a–c). It consists in measuring the bias dependence ofthe tunnel conductance in tunnel junctions in which one electrode is superconducting, in a largemagnetic field [75]. The field spin splits the DOS of the superconductor by Zeeman effect, which inturn selectively collects tunneling electrons according to their spin orientation. Fitting the obtainedG(V ) curves with Maki equations [96] yields the value of the tunnel current spin polarization.If the other electrode is ferromagnetic and the barrier non-magnetic, the analysis yields the spinpolarization of the ferromagnet.Alternatively, if the other electrode is non-magnetic and the barrierferromagnetic, it yields P
spinF .
Using this technique, very large spin-polarization values were found with Eu chalcogenide bar-riers, e.g. P spin
F = 85% for EuS (see Figure 11d). By applying a large magnetic field onAg/EuSe/Aljunctions, driving the EuSe ferromagnetic, an even larger value of 97% was found [97]. Thefabrication of high-quality EuO tunnel barriers is more complicated than that of EuS and EuSe,because Eu2O3 is more stable than EuO. Nevertheless, a P
spinF of 29% was reported in Al/EuO/Y
junctions [98] (see Figure 11e).It is only recently that magnetic tunnel junctions with ferromagnetic barriers (sometimes called
‘quasi-magnetic tunnel junctions’ or ‘spin-filter junctions’) have been defined and measured. Theearliest published report was by LeClair et al. [99] who measured a TMR around 100% at 2 Kin Gd/EuS/Al junctions. These results are displayed in Figure 12(a) and (b). A few years later,Nagahama et al. [100] reported a detailed study ofAl/EuS/AlOx /Co junctions showing TMR ratiosof about 25% (see Figure 12c). A 1.2-nm AlOx layer was inserted between the EuS magneticbarrier and the Co magnetic electrode to decouple these two layers, which improved the magneticswitching compared to the case of LeClair et al. A detailed analysis of the bias dependence of theTMR (see Figure 11d) showed that after a decrease at low bias, the TMR increased again in thehigh bias range, as expected for spin-filter junctions from a simple tunneling model (see e.g. [88]or the model included in [100]).
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22 M. Bibes et al.
2.3.3. BiMnO3
The main limitation of spin-filter junctions based on Eu chalcogenides is the low T MC of these
compounds. This observation has triggered a search for other families of materials containingferromagnetic insulators. Perovskites were a natural choice but, although there are many anti-ferromagnetic insulators (some with high Néel temperatures such as orthoferrites [101]) andseveral ferromagnetic metals (such as the colossal magnetoresistance manganites [6] or double-perovskites [33]) in this family, there are very few ferromagnetic insulators. Exceptions includeSeCuO3 [102], YTiO3 [103] and BiMnO3. So far, only the latter compound has been grown in theform of thin-films.
BiMnO3 (BMO) is a monoclinic perovskite first synthesized in Japan and the Soviet Unionin the 1960s [104,105]. BMO was soon recognized as a ferromagnetic insulator with a T M
C ofabout 105 K [104,105,106]. This ferromagnetic behavior was unexpected because the very similarcompound LaMnO3 (the ionic radii of Bi3+ and La3+ ions are 1.24 and 1.22Å, respectively [107])is an A-type antiferromagnetic [108]. While the Jahn-Teller effect lifts the degeneracy of theeg states in both compounds, the presence of stereochemically active 6s2 lone pairs on the Biions [109] triggers a peculiar three-dimensional orbital ordering of the Mn dx2−z2 orbitals [110].This results in globally ferromagnetic super-exchange interactions between the Mn ions. Thisorbital ordering was recently revealed by neutron diffraction [110] and resonant X-ray scatteringexperiments [111].
Based on reports of a non-centrosymmetric space group (C2, see Ref. [112]), BMO has beenconjectured to be ferroelectric, and thus multiferroic. Very convincing evidence of a ferroelectriccharacter is lacking for the moment and this is why we discuss BMO in this section, not in thatdevoted to multiferroics (2.5). We point out that a related compound, La0.1Bi0.9MnO3 (LBMO)was reported to be ferroelectric, being thus one of the very few ferroelectric-ferromagnets. LBMOwill be presented in Section 2.5.3.
While the synthesis of bulk BMO requires high temperature and pressure, BMO can be grownin thin-films by epitaxial stabilization. A few groups have reported the growth and propertiesof BMO thin-films [114,113,115,116,117,118]. While BMO films can have T M
C close to that ofthe bulk [115,113,117], the saturation magnetization is systematically lower than the bulk vale
of 3.6μB/Mn [119]. The presence of Bi vacancies [120] and strain effects [115,118] have beenproposed as mechanisms to explain this behavior.
Few nanometers-thick BMO films have been grown and used as tunnel barriers with LSMO andAu electrodes by Gajek et al. [113]. A TMR of 50% was found at 3 K, decreasing with temperatureto vanish around 60 K (see Figure 13). This corresponds to a maximum spin-filtering efficiency bythe ferromagnetic barrier of 22%. As visible on the right inset of Figure 13(a), the TMR of thesespin filters decreases with bias voltage in the whole range probed, as opposed to that of EuS-basedspin filters of Nagahama et al. [100] (see Figure 12d). This suggests that inelastic processes suchas magnon- or defect-assisted tunneling are important in these junctions.
2.3.4. NiFe2O4
Spinel oxides [121] (general formula MM’2O4) are usually cubic (space group Fd3m) and consistof a close-packed f.c.c. array of oxygen ions with holes partially filled by the cations. Dependingon the coordination, there are two types of cationic sites: A sites (one per formula unit) that aretetrahedral and B sites (two per formula unit) that are octahedral. Electroneutrality considerationslead to three basic spinel types, depending on the cation valence combinations in MM’2O4, i.e.M2+M’23+O4 (2-3 spinels), M4+M’22+O4 (4-2 spinels) and M6+M’21+O4 (6-1) spinels. Mostspinel ferrites are 2-3 spinels.
For a given set of cations, whose valences satisfy the electroneutrality criterion, differentarrangements over the A and B sites of the spinel structure are possible. Assuming a spinelMM’2O4, when both M’ ions are located on the B sites and the M ions on the A sites, the spinelis called normal. In the opposite case where half of the M’ ions occupy the A sites and the B sitesare occupied by M and M’ ions in equal proportion, the spinel is called inverse. The stability ofone type of cationic arrangement over the other depends on the ionic radii of the different species.The energy of the inverse and normal configurations has been calculated for some spinels byCormack et al. [122]. In practice, many spinels actually have a mixed inverse–normal structureand the cationic distribution is sensitive to parameters such as temperature, processing conditions,particle size in ceramics [123] and thickness in films [124].
Spinel oxides are very ionic compounds, and magnetic interactions between the cations areindirect and generally of the super-exchange type. Three interaction paths have to be considered:A–A, A–B and B–B. In general all three interactions are antiferromagnetic and in spinel ferrites,the A–B interaction is usually much stronger than the A–A and B–B ones. This leads to a collinearferrimagnetic ordering: cations among each (A or B) sublattice are coupled ferrromagnetically,and the two sublattices are coupled antiferromagnetically. This generally results in a finite mag-netization as the moments of the two sublattices are not equal. Note that when the A–B interactionbecomes comparable with one or both of the intrasublattice interactions, structures with cantedspins (Yafet–Kittel type [125]) or spiral ordering) emerge [126].
Although NiFe2O4 (NFO) films can be made conductive by specific growth conditions [127,128], they are usually insulating as the bulk material. Research on NFO films was first motivatedby possible use in microwave applications. NFO films have been grown by sputtering [129,130,131,132,133,124] and pulsed laser deposition [134]. Epitaxial growth can be achieved on severalsubstrates including MgO, MgAl2O4 and SrTiO3 [134]. Most of the effort has been put on growingrather thick films, in the 100-nm range or more. The saturation magnetization was found to dependon the structural quality [131] and on strain [133]. Remarkably, films with saturation magnetizationlarger than the bulk value have been reported [131,124], which is thought to arise due to changesin the cationic distribution. Indeed, an hypothetic NFO with a normal spinel structure would havea magnetization of 8μB/f.u. (i.e. 1200 emu cm−3) instead of 2μB/f.u. for the bulk inverse spinel.Any change in the cationic distribution is thus expected to have an impact on the magnetization.
At first, it may seem surprising that cationic inversion occurs in NFO as the inverse spinelstructure is more stable than the normal one. Indeed, Robertson et al. [135] found experimentallyan energy difference of 0.8 eV and Cormack et al. [122] calculated 1.6 eV. However, substantiallevels (up to about 10%) of cationic inversion were found in NFO quenched crystals [135] and atthe surface of nanoparticles [136,137,138]. Enhanced magnetization values due to large levels ofcationic inversion have also been reported for other spinel ferrites such as CuFe2O4 and ZnFe2O4,either in nanoparticles [123,139] or in thin-films [140,141].
Ultrathin NFO layers have been used as spin-filtering tunnel barriers by Lüders et al. [142,128].An example of TMR curve obtained in LSMO/NFO/Au spin filters is shown in Figure 14. Amaximum TMR of about 50% at low temperature is obtained, corresponding to a spin-filteringefficiency of 23%. This value is certainly limited by the difficulties to achieve a good antiparallelalignment, arising from the poor micromagnetism of the NFO films. This is also a possible reasonfor the early disappearance of TMR upon increasing temperature in these junctions [142]. However,positive TMR values ranging from 20 to 50% can reproducibly be obtained. The positive sign ofthe spin-filtering efficiency stands in contrast with what is expected from the band structure ofNFO. This band structure has been calculated by several groups [143,144,145,146] and the energydifference between the Fermi level and the bottom of the conduction bands is always foundlarger for spin-up than for spin-down. As suggested by Lüders et al. [89], a way to reconcile thesecalculations with the experimental data may be to consider that symmetry-filtering effects occur inaddition to spin-filtering effects in epitaxial spin-filter barriers. Depending on the spin-dependentcomplex band structure of the magnetic insulator, both effects can either add or compete, so thatit is difficult to really predict which type of tunneling wave-functions will be more favorablytransmitted from the real band structure only. This will also influence the bias dependence of theTMR. As shown in Figure 14, the TMR decreases quite rapidly with voltage. While the sharpdrop at very low bias may reflect inelastic processes such as those observed with other magneticbarriers such as NiO barriers [147], the smoother decrease at larger voltage may be caused by thecompetition between spin- and symmetry-filtering in the barrier [89]. Unfortunately, complex bandstructure calculations for NFO and other spin-filtering barriers are not available for the moment.The increasing activity on spin filtering may stimulate theoretical work on these issues in the future.
2.3.5. CoFe2O4
Like NFO, cobalt ferrite (CoFe2O4; CFO) is also an inverse 2-3 spinel in bulk. However, the energydifference between the inverse and normal spinel configurations is lower than for NFO (0.81 eVfor CFO and 1.6 eV for NFO [122]), which often results in mixed spinel structures, e.g. in bulk
samples cooled rapidly [148]. As for NFO, changes in the cationic distribution can increase themagnetization beyond its value for inverse spinel (3.7μB [148]). A specificity of CFO compared toother spinel ferrites is its strong spin-orbit coupling arising from the unquenched orbital momentof Co2+ ions in octahedral sites. This results in a large magnetocrystalline anisotropy, a largemagnetostriction and in coercive fields of several kOe [149].
CFO films have been grown by pulsed laser deposition [133,150,151], sputtering [152] andmolecular beam epitaxy [153]. As for NFO, epitaxial growth can be achieved on a number ofsubstrates including MgO, MgAl2O4 and SrTiO3. As expected from the strong magnetostrictioncoefficient, the magnetic properties of CFO films were found to depend critically on strain, eithervia studies of films grown on a given substrate but showing different strain states (e.g. differentthickness [154,150] or different thermal treatments [155]) or via studies of films grown on sub-strates presenting different lattice mismatches [154,156]. Due to its large coercive field, CFO hasalso been used as a pinning layer for spin-valve structures [152] and for purposes of exchangebias [157,158].
More recently, CFO ultrathin films have been integrated as tunnel barriers in spin-filter-typejunctions. Chapline et al. [159] have grown CFO barriers onto Fe3O4 electrodes and used Au padscontacted by a conductive AFM tip as the top electrode. Goto et al. [161] use CoFe2 as bottomelectrodes and Ta as the top electrode. While this latter group have only found a small MR of
−0.1%, Chapline et al. have reported a TMR of about −25% at room temperature (see Figure 15)that should however be confirmed in patterned junctions. In 2007, Ramos et al. [160] reported thefirst evidence of room-temperature spin filtering in solid-state devices (Co/Al2O3/CFO/Pt spin-filter junctions) (see Figure 15b–d). Remarkably, the TMR was negative, which is in agreementwith the electronic structure of CFO, and increased at high bias (i.e. beyond the low-bias regimewhere magnon excitations often cause the TMR to decrease), as expected for spin filtering [100].The negative TMR was also confirmed by Meservey–Tedrow experiments on Pt/CFO/Al2O3/Aljunctions [162].
2.4. Diamagnetic ferroelectric oxides
2.4.1. The physics of tunneling through ferroelectric barriers
The recent progress in oxide film growth and in the understanding of ferroelectricity at thenanoscale have motivated the design and fabrication of heterostructures for data storage in whichinformation is encoded by the direction of the ferroelectric polarization and read non-destructively.This would represent a major advance over nowadays, ferroelectric random access memories(FeRAMS) [163] in which information readout is destructive, so that the initial orientation of thepolarization has to be restored after reading, which is time- and power-consuming. One such typeof heterostructures would be a tunnel junction integrating an ultrathin ferroelectric film as the tun-nel barrier. The basic idea of this type of structures dates back to the early 1970s [164] but thefirst attempts to realize them are much more recent [165,166]. Sketches and early experimentalresults on ferroelectric tunnel junction are shown in Figure 16.
Beyond its potential for applications, a ferroelectric tunnel junction (FTJ) is expected to showvery interesting physics resulting from the interplay between tunneling and ferroelectricity atthe nanoscale. Tsymbal and Kohlstedt [167] have recently proposed three possible mechanismsthrough which the tunnel current would be modulated by the reversal of polarization in the ferro-electric barrier (see Figure 17). First of all, charges accumulated at the ferroelectric/electrodeinterface are only partially compensated by the electrodes, depending on the Thomas–Fermiscreening lengths of the metals. This induces an asymmetric variation of the electrostatic potentialacross the tunnel barrier (‘1’ in Figure 17). When the ferroelectric is connected by two differ-ent electrodes, the screening and hence the electrostatic variation are different at the interfaces.This can be described as a shift of the average barrier height of φ ± �φ when the ferroelectricpolarization is flipped [168,169,170] with
�φ = dP (δ1 − δ2)
2ε0ε(δ1 + δ2), (14)
where P is the remanent ferroelectric polarization, δ1,2 are the Thomas–Fermi screening lengthsof the electrodes, ε0 is the vacuum permittivity and ε the dielectric constant of the ferroelectric.
In the second one, the so-called interface effect, the interfacial DOS is modified according tothe position of the ions in the last atomic layer in the ferroelectric, which in turn affects the tunnelcurrent [171].
The third mechanism is related to the converse piezoelectric effect through which the tunnelbarrier thickness would be changed upon switching the polarization direction. Since the tunnelcurrent depends exponentially on the barrier width, a substantial modulation of the current canindeed be expected [168,169,170,172] .
To realize a ferroelectric tunnel junction, a first challenge is to grow a ferroelectric layer thinenough that electrons would tunnel across it. This has been an experimental challenge for manyyears and we review the progress toward this goal in the following section.
Figure 17. Schematic diagram of a tunnel junction, which consists of two electrodes separated by a nanome-ter-thick ferroelectric barrier (Egap is the energy gap, EF is the Fermi level, V is the applied voltage, VCis the coercive voltage, t is the barrier thickness and �t is the thickness variation under an applied electricfield). From E.Y. Tsymbal and H. Kohlstedt, Science, 313, p. 181, 2006 [167]. Reprinted with permissionfrom The American Association for the Advancement of Science.
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2.4.2. Critical thickness for ferroelectricity
Although much progress has been made in the understanding of ferroelectric thin-films [173,174],the existence of a minimum thickness for ferroelectricity is still the subject of debate. Recentexperimental advances (notably the development of piezoresponse force microscopy [175,176],X-ray photoelectron diffraction techniques [177,178], synchrotron X-ray studies [179,180] or UVRaman spectroscopy [181,182]) and the development of powerful first-principle calculations [183]have shed light on these ferroelectric size effects. The influence of film thickness on the ferroelectricpolarization amplitude and ferroelectric domain pattern appears to be due to the interplay betweendifferent phenomena including intrinsic surface effects related to dipole–dipole interactions [184]and the presence of a depolarizing field. Both effects strongly depend on the boundary conditions atthe ferroelectric/electrode interface. Additional strain effects produced by external stress imposedby the underlying substrate or electrode/substrate system strongly affect the ferroelectric characteras well [3]. Extrinsic factors such as low sample quality also contribute as evidenced by the factthat the minimum thickness for ferroelectricity has decreased by orders of magnitude over theyears [185].
The screening of the depolarizing field appears as the key parameter that sets the criticalthickness. The effect of the depolarizing field increases as the film thickness decreases [183] andmay lead to the suppression of ferroelectricity and the concomitant reduction of the tetragonalityof the unit cell. Other ways to reduce this large electrostatic energy at low thickness are by theformation of domains with ferroelectric polarization pointing in opposite directions but also byelectrical conduction within the film. This depolarizing field arises from uncompensated chargesappearing at the surfaces of the ferroelectric thin-film. In an ideal FE capacitor, composed ofperfectly conducting plates sandwiching the ferroelectric film, the screening of charges located atthe electrode/FE interface exactly compensate the surface charges related to the FE polarization.However, in real ferroelectric capacitors, the screening charges extend over a finite region in themetallic electrodes resulting in the presence of finite interface dipoles and a subsequent non-zero depolarizing field. The spatial extension of this region, i.e. the effective screening length,
depends strongly on the material used as electrodes (e.g. 0.2–1.9 nm for LSMO [187,188], ∼0.5 nmfor SrRuO3 [183] and <0.1 nm for Au). Through its influence on the screening length of thedepolarizing field, the choice of the electrodes has important effects on the critical thickness and/oron the formation of domains. For example, using high-resolution X-ray to study single-domainPbTiO3 deposited on conductive Nb-doped SrTiO3 substrates, Lichtensteiger and coworkers [189]pointed out in 2005 the systematic decrease of the c-axis lattice parameter with decreasing filmthickness below 20 nm, reflecting the decrease of the FE polarization (see Figure 18a). Thisreduction in the polarization is attributed to the presence of a residual unscreened depolarizingfield. When grown on LSMO electrodes, the same PbTiO3 thin-films first show a decrease of c/a
with decreasing film thickness followed by a recovery of c/a at small thicknesses (Figure 18a).This recovery is accompanied by a change from a single-domain to a polydomain configuration ofthe polarization, as was directly shown by piezoresponse atomic force microscopy measurements(Figure 18b) [186]. Surprisingly, the LSMO electrodes do not seem to screen as well as Nb-dopedSrTiO3 electrodes despite their better bulk metallicity.
More recent X-ray scattering measurements and ab initio calculations performed by Wang et al.[192] evidenced how the chemical environment can control the polarization orientation in a PbTiO3
ferroelectric thin-film. Interestingly, theoretical predictions from first-principle calculations ofultrathinAu/BaTiO3/Au ferroelectric capacitors predict that the covalent bonding mechanism at theinterface between Ba–O-terminated films and the simple metal can lead to an overall enhancementof the driving force of the film toward a polar state rather than a suppression [193]. These resultsnot only evidence the limitation of the simple Thomas–Fermi screening approach to understandthe existence of a critical thickness, and that a microscopic analysis will be generally necessaryto describe interfacial effects in ferroelectric capacitors, but also emphasize the opportunity toimprove the ferroelectric properties of thin-films by selecting the appropriate electrodes.
Practically, characterizing the ferroelectric behavior at the nanometer scale is a difficult task.Indeed for films as thin as few nanometers, the tunneling current impedes the characterizationthrough standard polarization versus electric field loops (P(E) loops). Noticeable exceptions (seeFigure 19a and b) are P(E) loop measurements realized on fully strained 3.5-nm-thick BaTiO3
at 77 K [190] and 5 nm at room temperature [191] in BaTiO3 capacitors with SrRuO3 electrodesdeposited on SrTiO3. As shown by the current–voltage response of the capacitor (Figure 19a), alarge contribution of the leakage to the total current is observed in this tunneling regime. Piezore-sponse force microscopy (PFM) appears as the technique of choice for probing ferroelectricityin ultrathin films. Indeed, even in the presence of a sizeable leakage, the piezoresponse of thematerial can still be detected (provided that the film resistivity is not low enough to impede theapplication of electric fields larger than the coercive field, required to pole the ferroelectric intoartificial domains).
In the following, we describe the state of the art of ultrathin films of two important ferroelectricmaterials and discuss their use as tunnel barriers in ferroelectric tunnel junctions.
2.4.3. Pb(Zr,Ti)O3
Lead-zirconium-titanate (PZT) is arguably the most widely studied ferroelectric material. It isalso the most technologically relevant as the active element of FeRAMs, which is due, to agreat extent, to its rather large polarization at low Zr content. Many groups have studied theproperties of ultrathin films of the end-member PbTiO3 (PTO). For instance, Fong et al. [179]have used synchrotron X-ray diffraction to determine a critical thickness of 1.2 nm for PTO filmsgrown on STO. Those films have a ferroelectric Curie temperature T E
C of about 700 K [194](see Figure 20a). The same critical thickness was found by Despont et al. [177] using X-rayphotoelectron diffraction. As previously mentioned, PFM was used by Lichtensteiger et al. [189]
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to determine a critical thickness of 2.8 nm for PTO films grown on LSMO. More recently, Crassouset al. [195] also used PFM to report that PTO films of only 1.6 nm (four unit cells) were ferroelectricat 300 K (see Figure 20c). For Pb(Zr0.2Ti0.8)O3, Tybell et al. [175] found that ferroelectricity wasstable down to 2.4 nm.
The first attempts to use PZT ultrathin films as tunnel barriers were by Rodriguez-Contreraset al. [166] who observed a strong electroresistance effect in SrRuO3/PZT(6 nm)/Pt junctions,without being able to be conclusive on the origin of the effect. The main result of this study isshown in Figure 16(d). Hysteretic I (V ) curves are obtained, as expected if the tunnel current weremodulated by the ferroelectric polarization. However, the authors concluded that hysteretic I (V )
curves alone could not prove that resistive switching is related to ferroelectric switching [197].They proposed some methods to carefully link ferroelectric switching to resistive switching [197].This thorough study emphasized the difficulty to demonstrate the role of ferroelectric switchingon resistive switching in ferroelectric tunnel junctions. Indeed, resistive switching is observedin many systems including oxide tunnel junctions [198] and may be to many other aspects thanferroelectricity such as filamentary conduction, oxygen vacancies, etc. [199].
Following this procedure, Maksymovych et al. [196] demonstrated large modulations, corre-lated to ferroelectric switching, of tunneling current flowing through a Schottky barrier formedat the interface between a conductive tip and a ferroelectric surface (see Figure 20b). Combiningsimultaneous PFM with conductive-tip atomic force microscopy (CTAFM) measurements on aPb(Zr0.2Ti0.8)O3 (30 nm)/LSMO bilayer, the authors were able to follow piezoelectric loops (giv-ing rise to ferroelectric switching) and I (V ) showing typical characteristic features of electronsflowing through a Schottky barrier. They observed large variation of the Fowler–Nordheim tunnel-ing current when switching locally the electrical polarization of the ferroelectric film [196]. In theultrathin film regime, where electrons may travel by direct tunneling across the barrier, Crassous
et al. reported large electroresistance effect for 1.6 and 3.6 nm PTO films, correlated with PFMcontrast. These data are displayed in Figure 20(c) and (d).
2.4.4. BaTiO3
Much experimental [200,191] and theoretical effort [183,201] has also been devoted to the prop-erties of ultrathin BaTiO3 films useable as tunnel barriers. Theoretically, the critical thickness forBTO films has been determined to range between 12 nm to less than 1 nm [202,183,201,203].Importantly, Wang et al. [204] predicted that it should depend on compressive strain, reachingonly two unit cells for strains of −3.5 to −4%. As screening is essential in determining the criticalthickness, the nature of the materials used as electrodes also plays a key role.
We already noted that experimental evidence for ferroelectricity had been provided throughP(E) loops at 77 K in 3.5-nm BTO films [190] and at room temperature in 5-nm films [190,191].Using PFM, Gruverman et al. [205] showed that BTO films grown on SrRuO3//SrTiO3 wereferroelectric down to a thickness of 2.4 nm. Garcia et al. [206] pushed that limit down to 1 nm inhighly strained BTO films grown on LSMO//NdGaO3 (see Figure 21a).
The earliest report of electroresistance in tunnel junctions with BaTiO3 barrier was by Kohlstedtet al. [185] in SRO/BTO(6 nm)/SRO samples, but again these authors could not related the hys-teretic switching observed in the I (V ) curves to ferroelectricity. In 2009, a clear correlation
Figure 20. (color online) (a) The c lattice parameter versus T for PTO films of different thickness, with solidlines showing the break in slope used to estimate T E
between the ferroelectric character and tunnel electroresistance phenomena was reported for 1–3-nm thick BTO films by combining PFM and CTAFM techniques at room temperature [206].Using PFM, Garcia et al. wrote ferroelectric domains pointing either up or down in highly strainedBTO films (Figure 21a). Using a high-bandwidth lab-made CTAFM [207], they were able tocollect resistance maps over regions with previously poled ferroelectric domains. As visible inFigure 21(b–d), the tunnel resistance contrast (or tunnel electroresistance) between up and downferroelectric domains reaches 200 and 75,000% for 1- and 3-nm thick BTO films, respectively.The exponential increase of the TER with BTO thickness (Figure 21d) is reminiscent of thebehavior predicted by electrostatic models (Figure 21e [169]), reflecting a dominant contributionof ferroelectricity-induced modulation of the barrier potential profile to the TER. These resultswere confirmed by further experiments from Gruverman et al. [205] on BTO (4.8 nm) depositedon SrRuO3 electrodes (Figure 21f–g), who also observed large TER using PFM and CTAFM. Inaddition, by modulating the poling voltage, they were able to show that TER was related to theferroelectric switching of the tunnel barrier [205].
Although the precise mechanisms underlying these giant TER effect have not been completelyclarified yet, it seems that the first mechanism proposed by Tsymbal and Kohlstedt (see Figure 17[167]) and related to the incomplete screening of polarization charges is dominant at large barrierthickness. In the context of spintronics, the second mechanism, according to which the tunnelcurrent may be modulated via the influence of ferroelectric polarization direction on the electrodeinterfacial DOS, is particularly appealing if the electrodes are made of ferromagnetic metals.Then, modifications of the interfacial spin polarization at the Fermi energy may occur. This opensa route to ferroelectrically controlled spintronic devices. We will devote a special section to theseinterfacial magnetoelectric effects in the second part of the review (Section 3.6).
2.5. Multiferroic oxides
2.5.1. Introduction to multiferroics
Multiferroics are a relatively rare class of multifunctional materials that simultaneously exhibitseveral ferroic orders among ferromagnetic, ferroelectric and ferroelastic (ferrotoroidic ordering[208] is also sometimes included) [209,210,211]. Given the scarcity of compounds that presenttwo or more strictly ferroic orders, antiferroic orders (e.g. antiferromagnetic) are often considered.Most of the currently investigated multiferroics are generally magnetic and ferroelectric, and veryfew showing a finite large magnetization (corresponding to ferro- or ferrimagnetic ordering).Practically, the vast majority of multiferroics are in fact ferroelectric antiferromagnets or weakferromagnets.
While the coexistence of several ferroic orders in the same material was thought since the1970s to be an interesting way to realize multiple-state memories [212], what looks more appealingtoday is the coupling that often exists between the ferroic orders. As sketched in Figure 22, thiscoupling may enable the manipulation of a given ferroic order parameter (ferroelectric polarization,magnetization, strain) by an external stimulus different from the usual one (electric field, magnetic
Figure 22. (color online) Phase control in ferroics and multiferroics. The electric field E, magnetic fieldH and stress s control the electric polarization P , magnetization M and strain e, respectively. In a ferroicmaterial, P , M or e are spontaneously formed to produce ferromagnetism, ferroelectricity or ferroelasticity,respectively. In a multiferroic, the coexistence of at least two ferroic forms of ordering leads to additionalinteractions. In a magnetoelectric multiferroic, a magnetic field may control P or an electric field may controlM . From N.A. Spaldin and M. Fiebig, Science, 309, p. 391, 2005 [210]. Reprinted with permission fromThe American Association for the Advancement of Science.
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field, stress, respectively). In the context of spintronics, a promising type of coupling is the so-calledmagnetoelectric coupling [213] that links the ferroelectric polarization and the magnetization andpotentially allows the manipulation of polarization by a magnetic field and, most importantly, ofmagnetization by an electric field.
Single-phase ferroelectric-magnetic multiferroics (simply referred to as ‘multiferroics’ hence-forth) are scarce and many are oxides [43,214]. The technological advances in oxide thin-filmgrowth in the 1990s has naturally led researchers to favor oxide materials to explore the physicsand device potential of multiferroics in thin-film form. Very thin-films of multiferroic materialshave started being investigated only a couple of years ago, and so far there have been very fewattempts to functionalize them as barriers in tunnel junctions. However, aside from the interest instudying the influence of thickness reduction of physical properties in compounds with multipleand/or coupled order parameters, such multiferroic or magnetoelectric barriers might bring excit-ing novel functionalities to electronics and spintronics. In the following, we will review the resultsobtained in ultrathin films of several important multiferroic compounds.
2.5.2. BiFeO3
Since 2003, BiFeO3 has attracted a lot of attention as it is one of the few room-temperature mul-tiferroics and because of its potential as a lead-free compound for ferroelectric devices. Researchon this system was boosted by the paper of Wang et al. [215] who reported a large ferroelectricpolarization (up to ∼60 μC cm2) and an enhanced magnetization (up to 1μB/Fe) in BFO thin-films.While this paper started many groups to work on BFO, it also opened a controversy concerning itsmagnetic properties. Several studies have now confirmed that even in thin-film form, BFO is notferromagnetic [216,217,218], but may develop a weak ferromagnetic behavior due to the absenceof the cycloidal modulation [219], with saturation magnetization values in the 0.01 − 0.1μB/Ferange [220,216,219].
On the other hand, the large ferroelectric polarization values reported by Wang et al. [215]have been reproduced [222,223,224,225,226,227,228] and incited Fujistu to consider BFO as thematerial of choice for next-generation FERAMs [229]. One of the reasons invoked to explainthe large polarization of BFO thin-films compared to single crystals was strain [215], but theobservation of a polarization of ∼60 μC cm2 in high-quality single crystals [230,231] confirm therelatively weak strain dependence of ferroelectricity in BFO [232].
The interest of BFO for spintronics resides mainly in the exploitation of its room-temperaturemagnetoelectric properties.A possibility is to switch the magnetization of a ferromagnetic elementexchange coupled to a BFO layer, via the application of an electric field [233]. Understanding therelation between the ferroelectric and antiferromagnetic domains is thus a crucial point to achievethis goal, as is achieving robust exchange coupling to a ferromagnet. The ferroelectric domainstructure of BFO films has been studied extensively by PFM [234] and can now be controlled usingseveral growth parameters [235]. Mapping the antiferromagnetic domain structure has proved moredifficult. Zhao et al. [236] have shown that X-ray photoemission electron microscopy (XPEEM)is sensitive to ferroelectricity in addition to antiferromagnetism, which complicates the analysis.However, XPEEM imaging has allowed to show that, in certain conditions, the antiferromagneticvector can be rotated by the application of an electric field, at room temperature [236].
Another prerequisite to exploit the magnetoelectric effect in BFO for spintronics is the obser-vation of exchange coupling to a ferromagnetic element. Dho et al. [225] and Béa et al. [237]have reported an exchange bias [238] of about 50 Oe at room temperature in BFO/NiFe andBFO/CoFeB structures, respectively. We note that this exchange bias effect can be used to shiftthe switching fields of the bottom layer of a spin valve, as demonstrated by Kim et al. [239] andBéa et al. [219,214]. Interestingly, the magnitude of the exchange field is inversely proportional
to the ferroelectric domain size [228] (or, equivalently, to the density of ferroelectric domainwalls [240]), providing a route to control it by an electric field.
Another possible use of BFO for spintronics is as a tunnel barrier in magnetic tunnel junctions.The properties of BFO ultrathin films grown on LSMO have been studied by Béa and coworkers[221,241]. Significantly, BFO films as thin as 2 nm retain their ferroelectric character [221,242](see Figure 23) and may thus be used as ferroelectric tunnel barriers [167]. When combined withLSMO and Co electrodes, BFO gives rise to a positive TMR of ∼30% at low temperature [241](see Figure 24). The TMR decreases rather fast with temperature (Figure 24b), possibly signalinga local deoxygenation of the LSMO before and/or during BFO growth [237].
This value increases to 140% when a 0.8-nm-thick SrTiO3 spacer is inserted at the BFO/LSMOinterface, in order to preserve the large spin polarization of LSMO [214]. These large and positiveTMR values are very striking. Indeed, spin-dependent tunneling experiments on junctions withLSMO and Co electrodes, but with SrTiO3 [71], LaAlO3 [81] or TiO2 [80] barriers all yield anegative TMR, with a maximum amplitude of about −50% (corresponding to a spin polarizationof −22%). With BFO, this TMR of 140% corresponds to a positive spin polarization of +43%for Co, which is equivalent to the largest values obtained with alumina barriers. It is only with theintroduction of epitaxial MgO barriers that larger TMR and spin polarization with Co electrodeshave been obtained. This observation, together with the positive sign of the spin polarization ofCo at the interface with BFO, suggests that epitaxial BFO barriers can select electronic wave-functions according to their symmetry. Consequently, it is possible that even larger TMR valuescould be achieved after further optimizing the junction quality.
Béa et al. [243] also investigated the influence of ferroelectricity on the TMR in theseLSMO/BFO/Co junctions. These preliminary results are displayed in Figure 25. A small butvisible influence of the poling voltage on the junction resistance is found, but appears to decrease
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with repeated poling. These results are reminiscent of tunnel electroresistance effects discussedin Section 2.4.1 and of multiferroic junctions discussed in Section 2.5.3.
The influence of ferroelectricity on tunnel resistance was more carefully investigated by Maksy-movytch et al. (Supplementary Online Material of [196]) and Crassous et al. [244]. As visiblein Figure 26(a), resistance switching connected with piezoelectric switching was observed at anegative bias in BFO(5 nm)/LSMO samples; Figure 26(b) shows combined PFM and CTAFMmappings evidencing a tunnel electroresistance effect of about 3000% at room temperature insimilar samples [244]. The reason for this relatively small TER (compared to, for example, thegiant TER found with BaTiO3 [206] and PbTiO3 [195] barriers) has not been clarified yet.
2.5.3. La0.1Bi0.9MnO3
In Section 2.3.3, we discussed the properties of BiMnO3 films and their use as spin-filteringtunnel barriers. Here we present results on La-substitued BiMnO3 films. La substitution is known
Figure 25. (color online) Influence of electric poling on TMR curves collected at 4 K and 10 mV onLSMO/BFO(5 nm)/Co junctions. The arrows indicate the polarization direction, upward meaning towardCo and downward toward LSMO. [243].
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38 M. Bibes et al.
Figure 26. (color online) (a) Simultaneous measurements of local piezoresponse and conductance of a 5-nmBFO/LSMO film. The discontinuities in the strain loop corresponding to ferroelectric switching events atapproximately −1.4 and +0.8V are still visible despite the low signal (From P. Maksymovych et al., Science,324, p. 1421, 2009 [196]. Reprinted with permission from The American Association for the Advancementof Science). (b) PFM phase and amplitude mapping of a BFO(5 nm)/LSMO sample after writing up anddown domains together with the simultaneously recorded topography image. Resistance contrast is visibleacross the poled domains in the conductive-tip AFM map [244].
in the bulk to stabilize the perovskite phase compared to pure BiMnO3 [245]. Troyanchuk etal. [245] have studied the La1−xBixMnO3 series and shown that at low La content, the compoundsexhibit a large magnetization as BiMnO3 and a T M
thin-films have been grown by Gajek et al. [246,247,120]. As in the bulk, the presence of La wasfound to facilitate the growth of single-phase perovskite films manifested by a broadening of thedeposition pressure–temperature window to obtain good quality films [248]. LBMO films are alsoferromagnetic [246,120] with Curie points of about 95 K [120]. Remarkably, PFM experimentson LSMO/LBMO bilayers grown on SrTiO3(001) demonstrated the ferroelectric character of thiscompound [120] (through stable domain imaging and d33(V ) cycles; see Figure 27). Even more,the ferroelectric character was found to persist down to a thickness of only 2 nm [120], as shownby the PFM images of Figure 27(c–e).
As for BMO, one of the interests of LBMO films for spintronics is as tunnel barriers inspin-filter-type junctions. Spin filters based on LBMO tunnel barriers with LSMO and Au elec-trodes have been fabricated and reported to show a TMR of up to 90% [247]. These TMR valuescorrespond to spin-filtering efficiencies by the ferromagnetic barrier of about 35%. Just as theferromagnetic character of the LBMO barrier influencing tunnel transport through spin filtering,the ferroelectric character is expected to produce an electroresistance effect (see the discussionin Section 2.4.1). To probe it, Gajek et al. measured I (V ) cycles between −2 and +2V andobserved a finite hysteresis corresponding to a TER effect of about 20%. No vertical shift ofthe G(V ) curves was observed [120], indicating a negligible contribution of piezoelectricity tothe TER (third mechanism in Figure 17 [168]). The electroresistance (defined by the normalizeddifference between the I (V ) curves collected upon increasing or decreasing voltage) could befitted within the model of Zhuravlev et al. [169], assuming that the P(E) loop of the ferroelectricbarrier is hard to saturate (as can be inferred from the d33 versus E loop shown in Figure 27) anda polarization value of 2 μC cm−2 [120]. This supports the interpretation of the TER effect basedon ferroelectricity.
Finally, the simultaneous occurrence of TMR and TER effects in the same junctions yields fourdifferent resistance states at low bias voltage (see Figure 28). Two of these states are related to the
-4 -2 0 2 4
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Figure 29. Phase diagram of RMnO3 compounds in zero magnetic and electric field. AF: antiferromagnetic;Sin-AF: antiferromagnetic with sinusoidal modulation; Spi-AF: antiferromagnetic with a spiral modulation;PM: paramagnetic. TN is the Néel temperature, Tsin the transition temperature from sinusoidal to spiralorder, TSR the spin-reorientation temperature, TRE the ordering temperature of the rare-earth ions and T E
C theferroelectric Curie temperature. The green hatched area correspond to the ferroelectric phase. The transitiontemperatures were extracted from references [252,257].
relative orientation of the magnetizations of the barrier and the LSMO counter-electrode, whereasthe other two are related to the orientation of the ferroelectric polarization which modulates thebarrier height. In other words, the resistance state of the junctions is encoded by the two orderparameters, M and P , in the tunnel barrier [120].
While those results were only obtained at low temperature, they should also be observable at300 K and above if a room-temperature ferroelectric and ferromagnetic multiferroic is eventuallydiscovered. Several device concepts derived from the multiple-state junction of Figure 28 haveindeed been proposed, such as 8-state memories [249] or multiple switches for spin injection [250]and await to be tested experimentally.
2.5.4. RMnO3
Rare-earth manganites with simple perovskite structure (RMnO3) can be divided into two groupsdepending on their most stable crystal structure in bulk form. From R = La to Dy, the compoundscrystallize in an orthorhombically distorted perovskite structure (space group Pbnm), while forR = Ho to Lu, an hexagonal structure (space group P 63cm) is energetically more favorable. Itis, however, possible to stabilize perovskite compounds in the metastable hexagonal phase, andvice versa, using high-pressure synthesis or strain in thin-films (see later). Both orthorhombic andhexagonal manganites have very rich phase diagrams and some exhibit multiferroic character insome temperature range. We do not go into the details of the physics of bulk RMnO3 perovskites(described in detail in [211,251]) but just recall in Figure 29 a tentative phase diagram (in zeromagnetic field) illustrating the range of functionalities shown by these compounds.
The competition between magnetic interactions in small rare-earth orthorhombic manganitesresults in strong couplings between the electric and magnetic orders. Interesting examples ofsuch couplings include the possibility to turn on or turn off ferroelectricity by a magnetic field
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in GdMnO3 [258], magnetic-field-induced changes of the ferroelectric polarization direction inDyMnO3 and TbMnO3 (‘polarization flop’) [259,253] (accompanied by a huge variation of thedielectric constant in the direction of the polarization after the flop [253]), electric-field-inducedchanges of the spiral ordering chirality in TbMnO3 [260] or electric-field-induced magnetictransitions in hexagonal HoMnO3 [261].
The research on RMnO3 thin-films is recent. As previously mentioned, an advantage of thin-film growth for the RMnO3 series is that it allows in some cases the stabilization of metastablecrystallographic structures via strain effects [262]. For example, HoMnO3, TmMnO3 and LuMnO3
can be grown with an orthorhombic structure on LaAlO3 [263]. Alternatively, it is possible to growEuMnO3, GdMnO3 [264], DyMnO3 [265] and TbMnO3 [266] in hexagonal form.
The most widely studied compound RMnO3 in thin-film form is YMnO3 that has been grownon a wide range of substrates including MgO, ZnO, SrTiO3, GaN and Si [267,268,269]. Theobserved properties on these rather thick films are qualitatively similar to the bulk single crystalproperties, albeit the electric polarization and dielectric constant appear to be somewhat reduced inthin-film samples. When film thickness reaches a few tens of nanometers, the physical propertiesare modified, such as the Néel temperature that decreases from ∼70 K [270] to 52 K for 50-nmfilms [271]. The weak ferromagnetic moment also increases, as well as the magnetocapacitance[272].
Some interesting results have already been achieved for other RMnO3 thin-films. From thetemperature dependence of their magnetization, epitaxial TbMnO3 films grown on SrTiO3(001)seem to exhibit similar phase transitions as bulk TbMnO3 [273]. High-quality hexagonal HoMnO3
films have also been reported, with indications of antiferromagnetism and ferroelectric polarorder reminiscent of those of the bulk [274]. In epitaxially stabilized hexagonal DyMnO3 andTbMnO3, enhanced ferroelectric properties, compared to their orthorhombic counterparts, havebeen observed [266,265]. The structural properties of TbMnO3 films down to 2 nm have beenstudied by Daumont et al. [275,276]. In these films, the magnetization tends to increase asthickness decreases, either due to strain effects or to the enhanced density of domain walls[277].
In spite of their appealing multiferroic and magnetoelectric character, RMnO3 perovskiteshave not yet been used as tunnel barriers. The strong magnetoelectric coupling existing in thesecompounds and the possibility of manipulating magnetic orders by an electric field look veryinteresting to explore new multifunctional device concepts at low temperature.
3. Novel functionalities at oxide interfaces
3.1. Introduction to oxide interface physics
Section 2 has described how the rich variety of functionalities of bulk transition metal oxides canbe exploited in the tunneling regime to modulate the spin-dependent tunneling phenomena. Thissection explores the novel functionalities that may appear at oxide interfaces, further enlargingtheir profusion of functionalities but also offering new opportunities to tailor their properties.
The rich physics of transition metal oxides resulting in this wide variety of properties is relatedto the delicate balance between charge, spin and orbital degrees of freedom [10,280]. This largediversity is observed in materials, mainly of the perovskite family (see the diagram shown inFigure 1), having similar structure and lattice constant, allowing for the growth of heterostruc-tures with very high structural quality. Using modern synthesis methods, it is now possible toengineer interfaces between complex transition metal oxides with an atomic-scale precision asshown, for example, in Figure 30. Interfaces break the symmetry, induce stresses, consequently
altering the distances and bonds between the ions and giving rise to changes in bandwidths, interac-tions and in energy levels degeneracy, therefore possibly modifying the electronic phase of thesestrongly correlated electron materials. Together with unconventional electronic reconstructionsthat appears for polar surfaces – a mechanism not present in conventional semiconductor-basedheterostructures – this may promote the appearance of new phases at surface or interfaces. Indeed,whereas in conventional semiconductors, surface charges are generally compensated throughatomic reconstructions, and electronic reconstruction related to charge transfer is often possiblein oxide-based heterostructures due to the potential mixed-valent character of the ionic speciesinvolved. This charge transfer induces carrier densities that are different at the interface than in thebulk, resulting in physical properties at the interface which may completely differ from those ofthe constituent materials alone [281]. The recent development of new theoretical approaches nowallows for reliable predictions on these interfaces between strongly correlated oxides. Tailoringand controlling (taking advantage of the sensitivity of these new phases to external stimuli) thephysical properties at these interfaces between different oxide materials thus provides a new play-ground for researchers and offers a new nanoelectronics fabrication platform for future electronics,spintronics and optronics [282].
In very recent years, a large number of groups have explored, theoretically or experimen-tally, this emerging field of complex oxide interfaces. Among all the appealing phenomenaobserved in these heterostructures are the metallic [278,283] or even superconducting behav-ior [284] at the interfaces between two insulators promoted by electronic reconstruction due tocharge transfer. Charge transfer is also responsible for the novel magnetic phases that appear atthe CaMnO3/CaRuO3 [285] or LaMnO3/SrMnO3 [286] interfaces. Also fascinating is the pos-sibility to induce magnetism in a superconductor and to rearrange the magnetic domains inthe ferromagnet at the superconducting transition temperature in superconductor/ferromagnet(YBa2Cu3O7−x /La2/3Ca1/3MnO3) heterostructures [287] due to orbital rearrangement and stronghybridization [288]. In the following, we present an overview of recent advances in the field ofoxide interfaces, starting with the paradigmatic system LaAlO3/SrTiO3.
3.2.1.1 General properties LaAlO3 (LAO) and SrTiO3 are two wide bandgap insulators withEg = 5.5 eV for LAO and 3.1 eV for STO (see Section 2.2.2). Both share the same perovskitestructure, but at room temperature bulk STO is cubic, while bulk LAO is slightly rhombohedrallydistorted. Their pseudo-cubic lattice constants are 3.905Å for STO and 3.79Å for LAO, so thatan LAO film growing onto a (001)-oriented STO substrate experiences a tensile strain of 3%. Akey difference between STO and LAO is that in STO each sub-plane of the perovskite unit cell,namely SrO and TiO2, is electrically neutral, while in LAO both sub-planes are charged (LaO+and AlO2
−).In 2004, Ohtomo and Hwang [283] reported that samples consisting of an LAO thin-film epi-
taxially grown onto a single-crystalline (001)-oriented STO substrate showed a metallic behavior,with an electronic mobility reaching about 10000 cm2/Vs at low temperature. Importantly, thismetallic character was only observed when the STO substrate was chemically treated beforegrowth to show TiO2-type single-terminated terraces-and-step surface morphology [289,290]. Incontrast, with SrO-terminated substrates (defined by growing a single unit cell of strontium oxideon a TiO2-terminated STO crystal, before the LAO layer), an insulating behavior was consistentlyobserved [291].
Schematically, these two types of structure can be visualized by supposing a stacking ofperovskite blocks (see Figure 31). At the interface, the last neutral sub-plane from STO will beadjacent to a charged sub-plane from LAO, charged either negatively or positively dependingon the STO substrate termination, resulting in a polar discontinuity. As argued by Nakagawaet al. [292], as the number of LAO layers increases, this polar discontinuity leads to a divergenceof the electrostatic potential (‘polar catastrophe’). A simple way to suppress the polar catastropheconsists in transferring half an electron per two-dimensional unit cell for a TiO2-type interface,or half a hole for an SrO-type one, across the interface (corresponding to a sheet charge densityof 3.5 × 1014 carriers/cm2). This process leaves the overall structure neutral, with the Ti ionat the interface becoming Ti3.5+ or Ti4.5+, respectively, and the potential no longer diverges.Importantly, a 3.5+ valence for Ti is stable (e.g. in La0.5Sr0.5TiO3 [293,294]) but a 4.5+ valence isalmost inaccessible. Thus, in this simple picture, an n-type interface can be formed in TiO2-type
samples, while a p-type one is highly unlikely. In other words, for the SrO-type interface, a differentmechanism must come into play to suppress the polar catastrophe.
Experimentally, the n-type interface has been by far the most studied. These films are usuallygrown by pulsed laser deposition, at a temperature of 700–800◦C and at different oxygen partialpressures (10−7–10−3 mbar). The growth proceeds in a layer-by-layer mode (as inferred fromRHEED monitoring) and the film thickness is usually limited to a few nanometers, which yieldsfully strained films (see Figure 32). In early samples, the sheet carrier density often exceededthe theoretical value of 3.5 × 1014 cm−2 [283–297] strongly suggesting the existence of anothersource of carriers in the system. There are at least two possible additional origins of carriers in thesystem. One is oxygen vacancies and indeed it is important to recall that oxygen vacancies are n-type dopants in STO that becomes metallic with low-temperature mobilities of up to 10,000 cm2/Vsat carrier densities as low as ∼1017 cm−3 [298–300]. We note that, these early LAO/STO sampleswere grown at high temperature and low oxygen partial pressure. A third scenario considers Laions diffusing from the LAO into the STO, which will be discussed in detail later.
Systematic studies of the influence of growth conditions on the transport properties haveallowed the identification of several regimes. As reported by Herranz et al. [297] and shownin Figure 33, films grown at very low oxygen pressure (i.e. 10−6 mbar and below) and notreoxygenated by post-annealing have three typical features: (i) very low sheet resistance RS
(around 10 m� at low temperature), (ii) large ratio R300 KS /R4 K
S (around 1000) and (iii) very highlow-temperature mobility (close to 10000 cm2/Vs). In these samples, oxygen vacancies clearlycontribute to transport [301,296]. Films grown at higher pressure and/or reoxygenated after growthhave (i) much larger RS (by six or more orders of magnitude), (ii) weaker R300 K
S /R4 KS (typically
on the order of 10) and (iii) mobilities usually lower than 1000 cm2/Vs). As visible in Figure 33(a)and (b), the temperature dependence of the sheet resistance may show a minimum (we will comeback to this point in Section 3.4.3). Remarkably, in these samples, a metallic behavior is onlyachieved above a critical LAO thickness of four unit cells (see Figure 33c), thinner films beingfully insulating.
We point out that detecting small amounts (below 1%) of oxygen vacancies is extremelydifficult. A technique of choice to measure vacancy defects at such low concentration in positronannihilation spectroscopy (PAS) [302] and PAS measurements on LAO/STO interfaces have shownthat the density of such vacancy defects depends on the growth conditions, as expected, and can beas small as in as-received substrates in metallic LAO/STO samples annealed at high temperatureand oxygen pressure after growth [303].
From the very low RS of samples grown at very low pressure, it can be inferred that the extensionof the electron gas is much broader than a few nanometers. Direct evidence for this was providedby high-field magnetotransport measurements on low-pressure-grown LAO/STO samples [297].Shubnikov–de Haas [306] oscillations in the magnetoresistance allowed the determination of thecarrier density. Combined with the sheet carrier density deduced from Hall experiments, thisyielded an electron gas thickness of several hundred microns. The extension of the electron gaswas measured directly by Basletic et al. by conductive-tip AFM in cross-section geometry (seeFigure 33d and e). While in non-reoxygenated samples, the electron gas extends hundreds ofmicrons away from the interface, whereas in reoxygenated ones, the electron gas is confined towithin a few nanometers from the interface. More recent measurements have confirmed that thegas extension is about the same at low temperature [307], in contrast with predictions by Siemonset al. [296].
Although much has been learnt on its physical properties, the precise origin of the electron gas atLAO/STO interfaces has not been completely clarified. Besides severe doping by oxygen vacanciesin non-reoxygenated samples – a scenario now excluded – two main lines of interpretation currentlycoexist. One is related to the polar catastrophe scenario and the other to extrinsic doping effetsby cations.
3.2.1.2 Origin of the electron gas: polar catastrophe On the first scenario, interesting insightshave been brought by first-principle calculations [308]. The role of lattice relaxation has beencarefully taken into account (only polar shifts [309,310] or polar shifts and rotations [311]) and astrong polarization in the layers close to the interface has been found. Figure 34(a) shows theseshifts for a 4-unit-cell-thick LAO film on STO. Strong ionic displacements are present in the LAO.The resulting dipole is oriented antiparallel with respect to the bare interface dipole, and latticerelaxation strongly contributes to reducing the electric field generated by the polar LAO film. Asshown in Figure 34(b), the energy of each sub-plane shifts higher in energy when going awayfrom the interface. In the calculations, when the LAO thickness reaches five unit cells, electronicreconstruction appears due to the overlap in energy of the Ti 3d states from the interface TiO2 layerand the O 2p states in the surface layer. This results in a finite occupation of the Ti 3d band andholes in the surface O 2p band. In these generalized gradient approximation (GGA) calculations,the insulator-to-metal transition found experimentally at four unit cells occurs at five unit cells.However, using different calculation techniques and different in-plane lattice parameters, thetransition may be found to occur from three to six unit cells [312,313,314,315]. Experimentally,lattice distortions at the interface have been evidenced by high-resolution electron microscopy[316] and X-ray diffraction [317]. Several groups also demonstrated electronic reconstructionsusing X-ray spectroscopy techniques [318,319] and second harmonic generation [320].
Despite the progress in both first-principle calculations and such local probe measurements,some experimental facts have been hard to reconcile with the polar catastrophe picture. One isthe discrepancy between the expected carrier density (ns = 3.5 1014 cm−2) and the measuredvalues (a few 1013 cm−2). It has to be noted that these experimental ns values are deduced fromHall measurements, in a free electron model considering one type of carriers. However, there isnow evidence that there are more than just one type of carriers, with different sheet density andmobility. Indirect evidence was provided by Copie et al. [307] who showed that some electrons thateffectively screen the interfacial electric field do not contribute to transport. Saluzzo et al. [321]
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Figure 35. (color online) (a) Sheet resistance (top) measured at 300 K and applied back-gate voltage (bottom),both plotted as a function of time for a 3 unit-cell-thick sample. (b) Voltage–current characteristics of aheterostructure with three unit cells of LaAlO3, measured at 4.2 K with various voltages applied to its backgate. From S. Thiel et al. Science, 313, p. 1942, 2006 [305]. Reprinted with permission from The AmericanAssociation for the Advancement of Science.
also showed that the Ti 3d orbital degeneracy is lifted at the interface so that electrons occupyorbital states with different energies, and the dxy orbital lying the lowest. Comparing electricaland optical transport data, Seo et al. [322] also concluded on the existence of multiple types ofcarriers. This multiple band picture is consistent with calculations taking orbital degeneracy intoaccount [323].
The influence of correlations on the electronic properties of the interface has been addressedthrough calculations. As expected, increasing correlations promote charge and orbital ordering onthe Ti ions at the interface [324,309,308], which may have consequence for magnetic properties(see also [325] and Section 3.4.3). Experimentally, Breitschaft et al. [326] have found that a modelincluding correlations could fit scanning tunneling microscopy data much better, suggesting thatwhat is commonly referred to as an electron gas is actually an electron liquid. Noteworthy is alsothe observation by Caviglia et al. [282] of a large Rashba spin-orbit interaction arising from theinterfacial breaking of inversion symmetry.
3.2.1.3 Origin of the electron gas: extrinsic doping After the early clarification of the role ofgrowth pressure and reoxygenation procedures on the extension of the electron gas [297,304], thecommunity seemed to progressively favor the polar catastrophe scenario. However, the apparentincompatibilities mentioned above (e.g. low experimental sheet carrier density, lack of irrefutableevidence for hole transport at the LAO surface) and more recent careful compositional studieshave thrown doubt on the validity, or at least the exclusive role, of the simple charge transfermechanism. Since La3+ is also an n-type dopant in STO [294], it is not unreasonable to expectthat minute contents of La ions diffusing from the LAO into the STO could also produce a high-mobility metallic state. Note that a very high mobility was very recently reported in intentionallyLa-doped STO films [327]. It has thus been proposed that minute amounts of La diffusing intoSTO from the deposited LAO film could be the source of carriers and thus responsible for theobserved transport properties.
Practically, it is hard to exclude the presence of La in STO for concentrations on the orderof 1019 cm−3. Electron energy loss spectroscopy has been used to infer the absence of suchdopants [292], but the resolution of this technique is at best 1%. On the other hand, using X-raysurface diffraction, Wilmott et al. [328] concluded that La/Sr intermixing may occur on the scaleof two unit cells. More recently, an extensive study by Chambers et al. [329], combining Ruther-ford backscattering, secondary ion mass spectroscopy and electron energy loss spectroscopy, hasrevealed a strong tendency toward intermixing, with substantial amounts of La diffusing into the
STO. In addition, the authors could not find any indication of electric field in the system from theanalysis of core-level and valence band photoelectron spectra [329]. This latter finding stands incontrast with the calculations reproduced in Figure 34 or the observation of a strong Rahsba fieldby Caviglia et al. [282]. This apparent contradiction exemplifies the current debate on the mecha-nisms behind the formation of a metallic electron gas in the LAO/STO system and obviously callsfor further investigation from a broad variety of experimental and theoretical approaches.
3.2.1.4 Field-effect device perspectives One of the many exciting features of the LAO/STOsystem lies in the ability to tune its transport properties by an electric field. This has been demon-strated for 3 to 4 unit-cell thick films, i.e. just on the limit of the insulator-to-metal transition [305].Figure 35 presents transport measurements as a function of back-gate voltage in an LAO(3-unit-cell)/STO sample. Very large changes are observed at room temperature. Even more exciting isthat this voltage-induced resistance change can be exploited at the nanoscale, as reported by Cenet al. [330,331]. As sketched in Figure 36(a), these authors use a conductive-tip AFM to apply alocal voltage to an LAO/STO film on the verge of the insulator-to-metal transition, which changesthe local resistance. Narrow lines or dots with smallest dimension as small as 2 nm can then bedefined. Smart arrangements of lines and dots can define nanoscale oxide electronics logic devices,as exemplified by Figure 36(b) and (c).
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3.2.2. Other SrTiO3-related systems
In parallel to the intense research on LaAlO3/SrTiO3 interfaces, other approaches have beendeveloped to create a two-dimensional electron gas based on SrTiO3. It has been known forseveral years that the strong sensitivity of transport properties to carrier density in STO makes itpossible to use it as an oxide channel in field effect transistors [332] (for review on electrostatingdoping in oxides, the reader may consult [333,334]). More recently, this approach has been takenfurther to induce a transition from an insulating state to a metallic state using optimized gate–channel interfaces (with CaHfO3 [335] or parylene [336] gate insulators). In 2009, Nakamura etal. [337] and Ueno et al. [338] reported gate-voltage-induced transitions for an insulating state to ahigh-mobility metallic state (with low-temperature mobility exceeding 10,000 cm2/Vs), believedto be two-dimensional.
A natural approach to generate an STO-based two-dimensional metallic state would be to growmetallic films of n-type STO thin enough for quantization effects to show up. However, to growfilms with mobilities in the range of 1000–10,000 cm2/Vs, the carrier density must be rather low,around 1018 cm−3 (if Nb or La ions are used as dopants, their concentration must thus be on theorder of 0.01%). The problem is then that the density of defects that would trap or compensate thesecarriers must be lower than 1018 cm−3, which in oxide films is extremely difficult to achieve [339].Until recently, the highest mobility achieved in an n-type 40-nm thick Nb-doped STO film was300 cm2/Vs, for a carrier density of 3 × 1019 cm−2 [340]. However, in 2009, Kozuka et al. [341]reported mobilities exceeding 1000 cm2/Vs in 5.5-nm thick Nb-doped STO films, in which a cleartwo-dimensional behavior was demonstrated through the angular dependence of Shubnikov–deHaas oscillations (see Figure 37).
3.3. Superconductivity at interfaces
3.3.1. Interplay between superconductivity and ferromagnetism at cuprate/manganiteinterfaces
Superconducting/ferromagnetic (S/F) hybrid structures have been thoroughly investigated duringthe last decades. Superconductivity and ferromagnetism are antagonistic long-range order phe-nomena, whose competing interaction is promoted by the reduced dimensionality, confinement
Figure 37. (color online) Two-dimensional quantum oscillations in the normal state. (a) Longitudinal resis-tivity in the perpendicular (ρ⊥
xx ) and parallel (ρ‖xx ) geometry, from magnetic fields of 0–14 T at 100 mK.
Shubnikov–de Haas oscillations are visible (arrowheads) in ρ⊥xx(H). The sudden increase in ρxx at low fields
and the intimate contact at the S/F interfaces. A vast amount of work has been largely focused onstructures combining low-T S
C superconductors and metallic ferromagnets [342] (T SC is the super-
onducting critical temperature). Some of the topical research lines include ‘classical’ proximityeffects [343], ‘inverse’ proximity effects [344,345], vortex pinning [346], stray-magnetic-fieldmanipulation of superconductivity [347,348] and spin injection into superconductors [349,350].During the last years, all-oxide S/F heterostructures combining cuprate superconductors and man-ganites have attracted increasing attention. These systems are fundamentally interesting as theygather ingredients such as unconventional d-wave superconductivity, the nearly 100% spin polar-ization of half-metallic ferromagnets and other effects characteristic of oxide heterostructures, suchas charge transfer across the interfaces.As it turns out, all-oxide S/F heterostructures have produceda large number of new, unusual behaviors from unexpected long-range proximity effects [351],to giant magnetoresistance [352], transient photoconductivity [353] or superconductivity-inducedrearrangements of the magnetic state [287,354]. We describe below some of these novel effects.
3.3.1.1 Basic properties and proximity effects Several groups have succeeded in the fabrica-tion of high structural quality heterostructures combining superconducting cuprates of the familyREBa2Cu3O7−δ (RE = rare earth) with manganites (such as La1−xCaxMnO3 or La1−xSrxMnO3),using molecular beam epitaxy (MBE) [357], sputtering [358,359,360] or pulsed laser deposi-tion techniques (PLD) [361,362]. Atomically flat interfaces with very little disorder are obtained(see, e.g. Figure 38a), which allows to rule out structural effects in the interpretation of thevariety of unusual behaviors exhibited by these heterostructures. The early studies focused on thebasic magnetic and superconducting properties [363,357,358,361,359,362,364,356,355,365]. Thedependence of the superconducting critical temperature T S
C on the thickness of the individual con-stituents in YBCO/LCMO heterostructures [359,362,364,356,355] (Figures 38c and d) revealed astrong effect of magnetism on superconductivity: T S
C was depressed forYBCO layers as thick as 10unit cells [356], and completely supressed for thickness below 3 unit cells (Figure 38c) [356,355].Superconductivity depression was found to be much stronger than in superlattices with a non-magnetic spacer material [356,366], which suggested that the magnetic character of LCMO playsa revelant role in it. On the other hand, evidence for superconducting coupling between YBCOlayers across LCMO over unexpected long distances (∼10 nm) was found in the Tc dependence onLCMO thickness for YBCO/LCMO superlattices and trilayers [351]. As shown in Figure 38(d),the T S
C is higher for [YBCO/LCMO]n superlattices (with n the number of repetitions) than forLCMO/YBCO/LCMO trilayers and superpositions of trilayers [LCMO/YBCO/LCMO]n havingequal thickness of their individual constituents dF (LCMO) and dS (YBCO) [351]. The possibilityof long-range superconducting coupling across LCMO was also supported by the superconducting-like hysteresis loops observed in the magnetization of YBCO/LCMO superlattices with LCMOthickness as thick as dF equal to 15 unit cells [351]. Together with superconductivity depression,these results were regarded as evidence for the penetration of the superconducting condensate fromYBCO into LCMO (proximity effect). However, the conventional proximity effect is unexpectedin this system since, because of the nearly 100% spin polarization of LCMO, F behaves essentiallyas an insulator for the minority spin band, and the ordinary spin-singlet pair amplitude should besuppressed in the F side shortly away from the interface with the S [367]. It has been theoreti-cally proposed that, under certain conditions (the presence of magnetic inhomogeneities [368] orof strong spin-flip scattering at the interfaces [369]), a spin-triplet component of the supercon-ducting condensate is generated in an F in contact with an S. In this case, superconductivity canpenetrate into the F over much longer distances, comparable to the case of non-magnetic met-als. Whether spin-triplet pairing is generated or not at YBCO/LCMO interfaces is currently thesubject of debate. Although different magneto-transport experiments [370,371] have been inter-preted as evidence for spin-triplet pairing at YBCO/LCMO interfaces, a clearcut experimental
evidence (such as the observation of long-range Josephson coupling acrossYBCO/LCMO/YBCOjunctions) has not been found so far. As shown below, other interface mechanisms concomitantof proximity effects are relevant to explain the above-described phenomenology: charge transfereffects and the diffusion of spin-polarized quasiparticles.
3.3.1.2 Charge transfer effects Charge transfer effects across the interfaces were early recalledto explain the strong dependence of the LCMO magnetization saturation MS and Curie temperatureT M
C on the YBCO thickness in YBCO/LCMO bilayers [355]. As shown in Figure 38(b), themacroscopic magnetic properties of LCMO are monotonically depressed as the thickness ofYBCOincreases. This was considered as an indication of charge transfer from the ferromagnet into thesuperconductor [355] (as also suggested by infrared absorption experiments [374]), which would
induce a modulation of the LCMO magnetic properties in the direction perpendicular to theinterfaces. The in-depth magnetic profile of LCMO/YBCO heterostructures was studied laterusing polarized neutron reflectometry (PNR) [372,373]. The analysis of the PNR spectra lead totwo possible scenarios [372], which are depicted in Figure 39(a) as ‘model 1’ and ‘model 2’. Inthe first case scenario (model 1), a sizeable magnetic moment is induced in the YBCO layer thatcouples antiferromagnetically to the one in LCMO. Model 2 considers the existence of a magnetic‘dead layer’ within the LCMO layer. X-ray magnetic circular dicroism (XMCD) experimentssupported the first scenario [287]. In particular, it was argued that the interface CuO2 plane is holedepleted due to the lack of CuO chains in the YBCO unit cell adjacent to the interface, leadingto a localized magnetic moment 1μB per Cu atom [287]. Localized Cu moments would coupleantiferromagnetically with Mn moments at the interface, inducing spin canting of the former and
a net magnetization in the CuO2 plane, antiparallel to that in the MnO2 one (see Figure 39b). Itwas later suggested that covalent bonding between Mn and Cu ions across the interface [288],and the resulting electronic reconstruction in the CuO2 planes, might be at the origin of the Cunet moment and the antiferromagnetic coupling to Mn atoms. On the other hand, a clear evidencefor a longer range charge transfer from LCMO into YBCO, leading to reduced magnetization inthe LCMO close to the interface, was found in experiments combining PNR and electron energyloss espectroscopy (EELS) [373]. In particular (see Figure 39c and d), the in-depth magnetizationprofile showed a strong depression close to the interfaces, which correlates with the increase onthe number of 3D electrons per Mn atom within a few unit cells from the interface (at the expenseof a decrease of the electron occupation near the LCMO layer center). As theoretically confirmedby first-principle density-functional-theory calculations [375], such a continuous in-depth varyingdoping within LCMO explains by itself the formation of a magnetic dead layer at the interface withYBCO. In addition to explaining the depressed magnetization in YBCO/LCMO heterostuctures,long-range charge transfer from LCMO intoYBCO [376] could be a crucial mechanism to explainthe anomalous depression of superconductivity in YBCO layers as thick as three unit cells whenin contact with LCMO [377].
3.3.1.3 Spin injection and diffusion effects The injection and diffusion of spin-polarized car-riers was early considered as a key mechanism to explain the depression of superconductivityin half-metallic ferromagnet/cuprate superconductor heterostructures. Pioneering experimentsin which the critical current of a cuprate thin-film was modulated by the injection of currentfrom a manganite electrode were interpreted in this sense [357,361]. The effects of spin injec-tion were later recalled to explain the T S
C depression of YBCO/LCMO bilayers as a functionof YBCO thickness [355], and under this assumption the length scale for spin diffusion inYBCO was estimated as ∼10 nm. The diffusion and accumulation of spin-polarized quasipar-ticles is also believed to play a major role in the giant magnetoresistance observed across thenormal-to-superconducting transition of YBCO/LCMO trilayers and superlattices [352,378,379].
This effect is shown in Figure 40(a), which displays isothermal R(H) curves (current-in-planeconfiguration) measured in an LCMO/YBCO/LCMO trilayer at various temperatures. The resis-tance peak observed around H = 0 implies a magnetoresistance of up to 1000% for the lowesttemperatures [352]. Figure 40(b) displays a low-field zoom of one of the R(H) curves, withthe magnetic hysteresis loop M(H) superposed to it. This shows that the magneto-resistanceis hysteretic and reproduces the magnetization reversal details displayed by the M(H) loop.The maxima in the magnetoresistance develop as the magnetization in the LCMO layers arealigned antiparallel [352]. This ‘inverse spin switch’ [380], as well as the ‘conventional spinswitch’ [381,382] (in this case the magnetoresistance is higher when the F layer magnetizationis aligned parallel), has also been observed in F/S hybrid structures combining conventionallow-T S
C superconductors and metallic ferromagnets. In some of the latter systems, the strayfields from the F domain structure play a dominant role in the magnetoresistance [382,383].Stray fields have also been found to induce resistance jumps associated to magnetic switch-ing in YBCO/LCMO heterostructures with rough interfaces [384]. However, this mechanismwas experimentally ruled out in the case of LCMO/YBCO heterostructures having smoothinterfaces [379]. For these, the switching behavior is explained by the injection of spin-polarized quasiparticles and their reflection at the the interfaces, which is strongly enhancedwhen the magnetization in the LCMO layers sandwiching the YBCO one is aligned antiparal-lel [352,378,379]. The resulting spin accumulation in the YBCO layer would depress T S
C viapair-breaking.
3.3.1.4 Magnetic coupling Another important issue regarding all-oxide S/F heterostructuresis the occurrence of different forms of magnetic coupling. Magnetostatic coupling between thestray fields from the domain structure in the LCMO layers and flux quanta in the YBCO onesseems to be responsible for flux pinning and the enhancement of critical currents [385,386,387].Conversely, magnetostatic interactions can also modify the domain structure in the LCMOlayers, as shown by off-specular neutron reflectivity experiments [287]. A novel remarkableeffect, recently uncovered by PNR experiments, is the giant superconductivity-induced mod-ulation of the magnetization [354] in Y0.6Pr0.4Ba2Cu3O7 /LCMO superlattices, in which themagnetic moment profile in the direction perpendicular to the interfaces is modulated as thesystem undergoes the superconducting transition. This effect has been explained in terms ofthe phase separation between ferromagnetic and non-ferromagnetic nanodomains in the LCMOlayers [354]. Finally, the existence of exchange coupling between LCMO layers across YBCOones [388] remains controversial. While the observation of exchange bias in LSMO/YBCOsuperlattices was interpreted as evidence for it [365], soft X-ray XMCD experiments showedno evidence of magnetic exchange coupling of LCMO layers across an YBCO spacer layer[389].
3.3.2. Superconductivity at the interfaces between non-superconducting oxides
The highly mobile 2DEG induced at the LaAlO3/SrTiO3 interface has generated a vast amount ofexperimental and theoretical work (see Section 3.2.1). One of the unexpected properties of this sys-tem is that the electron gas condenses into a superconducting phase at temperatures around a fewhundreds milli-Kelvin [284,390,391,392,393,394]. Superconducting behavior has been observedin samples grown at high O2 pressure (over 10−5 mbar), in which the conduction is confined tothe interface [295] and doping can be related to the polar nature of the LaAlO3 (polar catastro-phe scenario) [282]. While it is well known that SrTiO3 becomes superconducting on chemicaldoping with Nb (SrTi1−xNbxO3) or La (La,Sr)TiO3) or via the introduction of oxygen vacancies(SrTiO3−x) [395,396,397,341], the possibility of the bulk of the SrTiO3 being superconducting
as a consequence of substrate doping during LaAlO3 growth was discarded [284] due to cer-tain characteristic of the superconducting behavior of LaAlO3/SrTiO3 heterostructures. On theone hand, the slope of the I (V ) characteristics and the temperature dependence of the resistiv-ity across the superconducting to normal transition suggested a Berezinskii–Kosterlitz–Thoules(BKT) behavior [284,392], which is proper of purely two-dimensional systems. On the other hand,the study of the superconducting critical fields H ∗ in transport experiments provided with furtherevidence for the two-dimensional character of system, and allowed an estimate of the supercon-ducting layer thickness [391]. In particular (Figure 41a) the in-plane critical field H ∗
|| is muchhigher than the out-of-plane one H ∗
⊥, and displays the temperature dependence H ∗‖ ∝ [1 − T/Tc]
expected for a two-dimensional film. The scaling of the critical fields (H ∗‖ )2/H ∗
⊥ = πφ0/2d2 ≈ 25(Figure 41b) implies a superconducting layer thickness d ∼ 11 nm [391], much shorter than thein-plane coherence length ξ ∼ 100 nm [284], which suugests that superconductivity is confinedwithin a thin layer in the direction perpendicular to the interface. Whether this corresponds toa thin doped SrTiO3 sheet or is due to an ‘intrinsic’ interface effect was not clearly established.However, chemical doping of the SrTiO3 surface was considered unlikely due to the fact that thein-plane coherence length in superconducting LaAlO3/SrTiO3 heterostructures was much largerthan in Nb-doped SrTiO3 with similar T S
C , and also because both superconducting and insulatingbehavior were observed on the same sample depending on the precise LaAlO3 thickness [284].
Electric-field doping experiments showed that the electronic ground state of the LaAlO3/SrTiO3
interface could be modified by tuning its sheet charge carrier density [390,392]. Field-effectmodulation of two-dimensional superconductivity had been demonstrated before in Nb-doped
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SrTiO3 using a ferroelectric oxide as gate material [398], and more recently in pristine insulatingSrTiO3 single crystals by gating across an organic electrolyte [338]. In the case of LaAlO3/SrTiO3
heterostructures, the electric field was applied as in standard field-effect devices, between a metallic(gold) gate evaporated on the back of the SrTiO3 substrate and the conducting channel formedat the LaAlO3/SrTiO3 interface [390,392]. The experimental phase diagram as a function of theapplied gate voltage is displayed in Figure 41(c). The superconducting ‘dome’ resembles that ofcuprate superconductors, with an optimum doping (maximum T S
C ≈ 300 mK), overdoped (largepositive voltages) and underdoped (toward negative voltages) regimes. For negative voltages ofincreasing magnitude, the T S
C depression is accompanied by an increasing sheet resistance. Asthe critical voltage at which superconductivity vanishes is reached, an upturn is observed in thenormal-state sheet resistance versus gate voltage (see Figure 41c). For this range of negative appliedvoltages, a crossover into an insulating behavior is observed in the resistance versus temperaturemeasurements (not shown) [390,392]. This behavior was explained in terms of a continuousquantum phase transition separating a superconducting from an insulating ground state, in whichthe control parameter is the variation of the carrier density induced by the gate voltage [390,392].The temperature dependence of the resistance and the large negative magnetoresistance in theinsulating regime were explained in terms of weak localization [390]. Further analysis of the gate-voltage-dependent sheet resistance data and the BKT critical behavior in the same LaAlO3/SrTiO3
heterostructures led to the conclusion that not only does electrostatic tuning change the carrierdensity, but also the interface electronic inhomogeneity landscape [392]. Furthermore, recentexperiments [399] showed that the electron mobility at the LaAlO3/SrTiO3 interface changes withthe gate voltage and suggested that gate-voltage-induced variations of the effective disorder mayplay a role in the modulation of the superconducting-insulator transition [399].
3.3.3. Other systems
Another example of superconductivity at the interface between non-superconducting materials isprovided by La1.55Sr0.45CuO4/La2CuO4 metallic/insulating (M/I) bilayer heterostructures [400,401,402,403]. Depending on the layering sequence (M–I or I–M), a T S
C as high as ∼30 or ∼15 Kwas observed (see Figure 42). In I–M bilayers (I is the bottom layer), the samples are insulatingat low temperatures for M layers up to 1.5 unit cells thick. Traces of superconductivity appearabove 2.5 unit cells, and further increase of the M thickness raises T S
C to a plateau of ∼15 K. InM–I bilayers, superconductivity is observed when the bottom M layer is covered by an I layeronly 0.5 unit cell thick, and the T S
C reaches its saturating value ∼30 K for 1.5 unit cells of I.It was also found [400] that M–S bilayers combining La1.55Sr0.45CuO4 and the oxygen-dopedsuperconducting (S) La2CuO4+δ showed a T S
C ∼ 50 K, in excess of the T SC ∼ 40 K observed for
the La2CuO4+δ single-phase films. The origin of this T SC enhancement has not been clarified.
For I–M and M–I bilayers, several scenarios were considered, including oxygen non-stoichiometry and cation interdiffusion at the interface [400]. With respect to the latter, resonantsoft X-ray scattering experiments [401] showed no correlation between the Sr2+ and hole distri-butions across the I–M interface. This suggested that cation interdiffusion alone could not explaininterface superconductivity and that an ‘intrinsic’charge accumulation effect could be at its origin.In particular, hole redistribution across the interface was considered, which could be caused by thedifferent chemical potential of La1.55Sr0.45CuO4 and La2CuO4 [401]. It was indeed found that thefilling of the La2CuO4 layer nearby the interface was close to optimum doping, suggesting thatsuperconductivity would reside within the I layers [401]. Further evidence for this was found indelta-doping experiments [402] where selected I or M layers were doped with Zn (see Figure 42c).Cu substitution with Zn caused almost no effect on the superconducting properties of the I–Mstructures except when the second La2CuO4 layer from the interface (N = 2) was doped (see
Figure 42d). Moreover, this was considered as evidence for most of the superfluid density beingconfined within the N = 2 La2CuO4 layers. This agrees with interface superconductivity beingcaused by a combination of both Sr interdiffusion and hole redistribution effects [402].
3.4. Magnetic effects at interfaces
One of the remarkable intrinsic effects in complex oxide heterostructures is the appearance offerromagnetism at the interface between non-ferromagnetic materials. An early example of this isprovided by the LaFeO3/LaCrO3 (LFO/LCO) system [404,405]. Both LFO and LCO are antifer-romagnets in bulk single phase. Ferromagnetism was pursued in heterostructures combining bothmaterials since, following the Anderson–Goodenough–Kanamori rules [86,84,85], ferromagneticcoupling was expected between Cr3+ and Fe3+ ions due to superexchange interaction throughoxygen. This was achieved using superlattices that alternated single-unit-cell layers of LFO andLCO [404], so that Cr3+ and Fe3+ ions were artificially arranged forming 180 d3-O-d5 metaldimers (dn indicates the electron state). Further examples of modified magnetic properties dueto interface effects include the ferromagnetic behavior of CaMnO3/CaRuO3 antiferromagneticinsulating/paramagnetic heterostructures [285], or conversely the emergence of antiferromag-netism at the interface between La0.67Sr0.33MnO3 and SrRuO3 ferromagnetic materials [406,407],both of which have been related to charge transfer effects. Interface exchange interactions are
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responsible for the Mn magnetic moment observed in SrRuO3/SrMnO3 intinerant ferromag-net/antiferromagnet superlattices [408]. A key ingredient for the observation of these effects isthe possibility of fabricating the so-called ‘digital’ superlattices, in which an accurately controllednumber of single-unit-cell layers of the heterostructure constituents are alternated, with atomicallyabrupt interfaces. This is especially true in the case of interface ferromagnetism induced by chargeredistribution effects, which we will review below.
3.4.1. Predicted states at correlated oxide interfaces
Charge ordering effects are ubiquitous in perovskites (see, e.g. Section 3.3.1). Modulation of theelectron density in the form of slabs can be realized in digital superlattices in which the formalvalence of the transition metal ion is alternated.This is the case, for instance, of SrTi4+O3/LaTi3+O3
(STO/LTO) superlattices. STO is a band insulator with an empty d band, while LTO has one delectron per site and is a Mott insulator owing to strong Coulomb repulsion [294]. EELS ofatomically flat STO/LTO superlattices showed that, in the vicinity of an LTO monolayer, thespatial distribution of Ti3+ in the direction perpendicular to the interface spreads over a lengthscale considerably wider than the LTO thickness [278]. This implies a ‘leakage’ of electrons fromLTO into the STO. Thus, in the region associated with the LTO layer, the Ti exhibits mixed valencebetween +3 and +4 (as in bulk solid solutions of La1−xSrxTiO3), and superlattices show a metallicbehavior [278]. The question that arises is what is the effect of the above-described charge transferon the magnetic properties of the interface.
This issue was theoretically addressed within a model that considers multiorbital interactions(intraorbital Coulomb U , interorbital Coulomb U ′ and interorbital exchange/pair hopping J inter-actions) and a density-functional-theory (DFT)-derived tight-binding band structure [409]. Thecalculated charge density across the LTO/STO interfaces reproduced the experimental results byOhtomo and Hwang [278]. Figure 43(a) shows the calculated d filling (or electron density n)as a function of the transversal coordinate z (the LaO central plane is at z = 0). The densityntot(z) = 1 is characteristic of Ti3+ in bulk LTO (d1 filling), while the value ntot(z) = 0 is char-acteristic of Ti4+ in bulk STO (no d electrons). A leakage of electronic charge density from LTOinto STO is visible, with an approximately three-unit-cell ‘transition region’ in which electronsshow metallic behavior. It was found that the strength of the on-site Coulomb interaction (U)does not have a significant impact on the electron transfer, which is essentially controlled by theelectrostatic potential arising from La cations. However, the magnitude of U has a strong effecton the magnetic and orbital order of the interface [409]. This is shown in Figure 43(b), wherethe ground-state phase diagram is displayed as a function of U and the inverse of the numbern of LTO monolayers. For small U values, the ground state is a paramagnetic metal with noorbital ordering (PMM region). As U increases, an orbitally disordered magnetic state is sta-bilized (M-OD). This phase is ferromagnetic for n = 1: the spin and orbitally resolved spatialcharge distribution (Figure 43c) shows full spin polarization and equal occupancy for the threedxy , dxz and dyz orbitals. In some intermediate U regime and for with n > 1, each (001) Ti layeris uniformly polarized, but the magnetization direction alternates from layer to layer, producinga ferrimagnetic state when an odd number of occupied Ti layers are present (n = 2, 4, 6, . . .),or antiferromagnetic for an even number of Ti layers (n = 3, 5, 7, . . .). In the large U regime,a fully polarized ferromagnetic state with (00π ) orbital order appears (FM-OO). In this, fullspin polarization persists, but orbital occupancy is unequal (see Figure 43d): dyz and dxz arerespectively dominant at each side of the LTO layer, and dxy dominates further away from theinterface. Finally, for sufficiently thick LTO layers, bulk behavior is expected. Further theoret-ical investigation on this system included dynamical-mean-field calculations, which confirmedthat the extent of the metallic region nearby STO/LTO interfaces ∼3 unit cells [410]. Studies
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Figure 43. (color online) (a) Dependence of total and metallic-subband charge densities ntot(z), nmetallic(z)
on transverse spatial coordinate z for a heterostructure with six LTO layers and U = 10 t . The upper curve(triangles on dashed line) shows the electron density as a function of position. The lower curve (circles onsolid line) shows the density of electrons in subbands exhibiting metallic behavior. The association of metallicbehavior with the near-interface region is evident. (b) Ground-state phase diagram computed in Hartree–Fockapproximation as a function of the on-site Coulomb interaction normalized U/t (t is the hopping amplitudebetween Ti sites) and the inverse of the La layer number n. (c,d) Spin and orbitally resolved charge densitiesas function of transverse (001) coordinate z for heterostructure with one LTO layer. The La plane is at z = 0.Filled (open) symbols indicate majority (minority) spin densities for xz, yz and xy orbitals (see key in figure).(c) Intermediate U (M-OD) regime; full spin polarization but all three orbitals equally occupied. (d) Large U
on the role of lattice relaxation, earlier overlooked, revealed that polar distortion of the TiO6
octahedra nearby La regions substantially affects screening, leading to a wider spatial charge dis-tribution away from the LTO dopant layers [411]. As indeed theoretically shown by Kancharlaand Dagotto [412], the extent of the metallic at the interface strongly depends on the dielectricconstant of the material.
Manganite [(RMn3+O3)n/(AMn4+O3)m]l superlattices (with R = La, Pr, . . . a trivalent rareearth, A = Sr, Ca, . . . a divalent alkaline cation, (n, m) the number of layers of each materialand l the number of repetitions of the superlattice modulation length) constitute an interest-ing case of Mott insulator (one eg electron)-band insulator (no eg electron) heterostructures, inwhich the spatial modulation of the transition metal valence induces charge transfer effects, andcarriers are subject to the double-exchange interaction [413]. We will review in Section 3.4.2some of the most relevant experimental results on this type of superlattices, mainly on the(LaMn3+O3)n/(SrMn4+O3)m (LMOn/SMOm) system. As we will discuss later on, the magnetic
and transport properties of these are related to those of the random alloy La1−xSrxMnO3, whosephase diagram [10,414] is depicted in Figure 44.
Much work has been done from a theoretical point of view (see [415,416,417,418,419,420]).Early calculations for (n, m) = (2, 1) superlattices (schematically represented in Figure 45a)predicted a rich variety of interface magnetic states depending on how confined is charge inthe direction perpendicular to the interfaces [415]. The electronic density profile is controlled bythe size of the screening length LTF ≈ a/α (with α being the parameter measuring the strengthof the Coulomb interaction as compared to the electron hopping and a the lattice parameter).Figure 45(b) displays the calculated [415] phase diagram of (2, 1) superlattices, at the temperature-screening length plane. If the screening length is long, the charge is weakly confined. In this case,the superlattices are expected to show the same properties as the randomly doped bulk materialR2/3A1/3MnO3. In the limit of long screening lengths (furthermost right side of the phase diagram),a paramagnetic (PM) to ferromagnetic (FM) transition at the Curie temperature is observed. Fordecreasing screening lengths, the spatial modulation of the electronic and magnetic propertiesbecomes stronger, with the electronic density being higher in the central Mn monolayer (filledcircles in Figure 45a). Various transitions between phases not present in the bulk material areexpected depending on the size of the screening length. For sufficiently short screening lengths,the electron density in the central Mn nonolayer reaches values at which FM is not favored. Thisinduces at low temperature a state in which there is an in-plane phase separation (PS) betweenantiferromagnetic (AF) and FM states in the central monolayer, and the still sufficiently doped outerlayers (sandwiched between R and A cations, open circles in Figure 45a) remain FM. This regimecorresponds to the range 1.4 < 1/α < 2.8 in Figure 45(b). A further decrease in the screeninglength (0.6 < 1/α < 1.4) induces AF order in the cental layer, while the the outer ones remainFM, leading to FM–AF–FM modulation in the direction perpendicular to the interfaces. Finally,
when a yet stronger charge confinement is produced by shorter screening lengths (α < 0.6), anovel ‘layer ferromagnet’ state (LFM) appears in which both the central and outer layers are FM,but their magnetization are antialigned [415].
Further theoretical work has been devoted to investigate the properties of longer-periodsuperlattices, such as (LaMn3+O3)n/(SrMn4+O3)m (LMOn/SMOm) [416] or (LMO2n/SMOn)[417,419,420] superlattices. The general consensus is that, as a first approximation, the expectedmagnetic state of a particular layer in the superlattice can be predicted once the charge distri-bution is given and approximately corresponds to that of the bulk phase with similar doping[416,417,419,420]. The charge distribution is weakly dependent on temperature and mainlydepends on electrostatic interactions [416]. Figure 45(c) shows the calculated charge densitydistribution and corresponding magnetic states for a series of (LMO2n/SMOn) superlattices withn = 1–4 [417]. A nearly homogeneous electronic and magnetic (FM) state is observed only for
n = 1, while for larger n a strong modulation of the electronic and magnetic properties is observed.In particular, the electronic density is strongly reduced to its bulk value inside the SMO layer asits thickness increases, so that the bulk AF state is quickly recovered away from the interface forn ≥2 [417,419]. In summary, long-period superlattices are expected to show interface FM andinner bulk AF phases further away from them [419]. Finally, while the overall properties of thesesuperlattices are closely related to the phase diagram of the bulk compound, novel phases arepredicted which are not observed for the bulk phase, such as a spin-canted CE phase [420]. Theseexotic states would appear in the transition zone between interface and bulk-like regions awayfrom the interface [420].
3.4.2. Novel magnetic phases at manganite interfaces
A snapshot of the characteristic experimental magnetic and transport properties of LMOn/SMOm
superlattices can be seen in Figure 46. The behavior of short-period superlattices (in whichthe modulation length contains one or two layers of its individual constituents, i.e. (1,1) or(2,1) superlattices) is similar to that of the corresponding random alloy, e.g. La0.5Sr0.5MnO3 orLa0.67Sr0.33MnO3 [421,286,422,423,424]. However, as the superlattice period is increased (keep-ing (n + m)/n) fixed, and therefore the same average stoichiometry), the magnetic and transportproperties exhibit a progressive deviation from those of the random alloy. On the one hand, long-period superlattices exhibit insulating behavior at low temperatures [421,286,422,423,424] (seeFigure 46a). In this regime, transport is consistent with Mott’s variable range hopping [423,424]between disorder-induced localized states at the interfaces [423,417]. On the other hand, asthe period of the superlattices increases, magnetism is progressively depressed, since the T M
C
(see the evolution of the insulator-to-metal transition temperature in Figure 46a) and the mag-netic moment per Mn atom (Figure 46b) decreases monotonously with increasing number oflayers [421,286,425,422,423]. These results early suggested that the metallic behavior and ferro-magnetism are confined at the interfaces [421,286,425]. Moreover, they supported the theoreticalpredictions discussed above (Figure 45), from which a homogeneous ferromagnetic state isexpected for short-period superlattices, whereas for long-period ones the strong charge densitymodulation confines ferromagnetism to the interface regions in the LMO side [417,419] (thusyielding a reduced average magnetic moment per Mn atom in the superlattice). A direct exper-imental evidence for electronic reconstruction and charge density modulation was provided bysoft X-ray scattering (RSXS) experiments [426]. The corresponding spatial modulation of themagnetic properties was observed in PNR experiments [423] (Figures 46c and d). The in-depthmagnetic profiles show large oscillations of the local magnetic moment per Mn atom, the ampli-tude of which increases with the superlattice period. The magnetic moment is much higher in theregion corresponding to LMO (highlighted in grey) than in the one corresponding to SMO (ingreen). For the (10,5) superlattice (Figures 46d), a maximum M = 3.8μB/Mn is observed withinthe LMO layers versus a minimum M = 0.1μB/Mn in the SMO ones. This was explained con-sidering that SMO layers remain AF, as theoretically predicted [417,419]. This assumption wasjustified based on the enhanced coercive field Hc (Figure 46b) (implying magnetic pinning) andsign reversal of the magnetoresistance for long-period superlattices [423], which pointed to thepresence of FM/AFM boundaries within the superlattice. Additional evidence for this came fromthe observation of two spin populations (fast and viscous spins) in time-resolved magneto-opticalKerr effect measurements [427], which was indicative of magnetic disorder and also supportedthe presence of AFM/FM interfaces within the superlattice. PNR experiments also evidenced astrong asymmetry in the magnetic profile, which is visible in Figure 46(d). LMO/SMO interfacesshow an enhanced magnetization as compared to SMO/LMO ones. This asymmetry arises from
a difference in the structural roughness of both types of interfaces [428] and is therefore a purelyextrinsic effect.
Some other issues explored in LMO/SMO superlattices include the effect of strain. In concomi-tance with electronic reconstruction, this parameter has a strong effect on the interface magneticproperties and orbital occupation, as experimentally [425] and theoretically shown [429]. Forinstance, recent experiments that combine X-ray linear and magnetic circular dichroism haveinvestigated LMO orbital occupation as a function of the superlattice period [430], and found dz2
preferential orbital occupation on long-period superlattices [(10,5) or (16,8)], in contrast to dx2−y2
one for (2,1) superlattices.In summary, LMO/SMO superlattices show novel transport properties, magnetic and orbital
occupation states, which do not correspond neither to the bulk properties of the individual con-stituents nor to a simple ‘mixing’ of them. Those arise essentially as a consequence of chargeredistribution across the interfaces induce a modulation of the physical properties. This promotesnew states that are not found in the corresponding randomly doped bulk alloys, which may pro-vide with novel functionalities. Examples of this are the possibility of formation of a fully spinpolarized two-dimensional electron gas at LMO/SMO interfaces, as theoretically proposed [419]and recently suggested by time-resolved magneto-optical Kerr effect experiments [431]. Finally,although not directly related to charge density modulation, cation-site ordering is responsible fordramatically enhanced ordering temperatures in AF LMO1/SMO2 superlattices as compared tothe corresponding bulk material [432,433].
3.4.3. Hints of magnetism at LaAlO3/SrTiO3 interfaces
As we discussed in Section 3.2.1, first-principle calculations showed that charge transfer effectsacross LaTiO3/SrTiO3 interfaces may be accompanied by a ferromagnetic alignment of the electronspins induced within the Ti 3d conduction band [409]. Similar predictions have been made forthe LaAlO3/SrTiO3 interface [324,311]. Ferromagnetism has not been found so far in the formerinterfaces, but a few magneto-transport experiments on the latter have been interpreted as evidencefor ferromagnetic order [304,393].
The first report claiming ferromagnetic ordering at LaAlO3/SrTiO3 interfaces used samplesgrown at very high O2 partial pressure (over 10−3 mbar), in which the 2DEG formed at theinterface seems to be related to the polar nature of the LaAlO3 (see Section 3.2.1). The temperaturedependence of the sheet resistance of this type of samples shows an upturn at a characteristiccrossover temperature ∼70 K (see Figure 47a), below which the temperature dependence was
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found to be logarithmic. On the other hand, a large negative magneto-resistance is observed atlow temperatures (see Figure 47a), of up to 30% over a field range of 30 T at T = 0.3 K. The factthat the magnetoresistance was found to be independent of the orientation of the magnetic fieldwith respect to the interface led the authors to rule out weak localization effects as the origin ofthese behaviors and was considered an indication that the behavior shown in Figure 47(a) and (b)could be ascribed to spin scattering of conduction electron off localized magnetic moments. In thisscenario, the logarithmic increase in the resistance at low temperatures was explained in terms ofthe Kondo effect [434], with T ∼ 70 K, the Kondo temperature. Furthermore, by assuming thatthe magnetoresistance was related to the presence of a net magnetization M , the M(H) curveswere calculated out of the magnetoresistance ones, and the low-field magnetic susceptibilityχ = dM/dH obtained from those (see Figure 47c). χ(T ) was found to follow a Curie–Weiss law(inset to Figure 47c). This, together with the observation of hysteretic magnetoresistance at lowtemperatures (see Figure 47d), led the authors to conclude that localized magnetic moments presentat the LTO/STO interface are ferromagnetically ordered. This was explained by considering thatelectrons transferred from the LaO layer into the TiO2 one form either localized 3d magneticmoments on the Ti site, or conduction electrons that are scattered by the former (see sketch inFigure 47a).
More recent experiments where the magnetoresistance displays a strong anisotropy have alsobeen interpreted as evidence for magnetic order at the LaAlO3/SrTiO3 interface [393]. In thiscase, samples show remarkably different properties. On the one hand, the resistance monotonouslydecreases with temperature down to T ∼ 15 K, below which it saturates until a superconductingtransition is observed at Tc ∼ 150 mK, which is in contrary to the above-described experiments,and the magnetoresistance was found to be strongly dependent in the direction of the appliedfield with respect to the interface: below 35 K, a positive magnetoresistance was observed withthe field applied perpendicular to the film plane, and a large (up to 70%) negative one when thefield was applied parallel to it. Moreover, a strong in-plane anisotropic behavior was found, asthe magnetoresistance was strongly dependent on the relative direction between the applied fieldand the injected current. The positive perpendicular magnetorresistance was ascribed to orbitaleffects, the negative one was found symptomatic of magnetic scattering and suggested the presenceof magnetic order, and the in-plane anisotropic one was interpreted in terms of the anisotropicmagnetoresistance proper of ferromagnetic materials [393].
All in all, a clear picture of the origin of these unusual magneto-transport effects has notemerged, and the nature of the possible magnetic order at the interface has not been identified.
3.5. Polar and ferroelectric interfaces
The ability to grow oxide thin-films layer by layer and combine them in high-quality superlatticeshas been applied to ferroelectrics with tailored properties [435] or showing radically new physicssuch as improper ferroelectricity [436]. A particularly original approach is that of tricolor superlat-tices. Whereas bicolor superlattices (A/B)n preserve centrosymmetry, the asymmetric stacking oftricolor superlattices (A/B/C)n, artificially breaks the space-inversion symmetry, and is expectedto produce an effective polarization (see Figure 48) in the stacking direction as predicted bySai and coworkers [437]. Experimentally, this electrical polarization has been evidenced throughthe enhanced dielectric constant and its asymmetric field dependence [438] or through enhancedpolarization [279] observed in (BaTiO3, SrTiO3, CaTiO3)-based superlattices.
This approach is also one of the interesting routes toward a tailor-made multiferroic [439] ifone of the layer or one interface is ferromagnetic. The concomitant non-zero toroidal moment [9](defined as T = 1/2�ri × Si ∝ P × M , with P and M being the polarization and magnetization,respectively) gives rise to optical magnetoelectric effects as shown in ferromagnetic superlattices
combining the ferromagnet La0.6Sr0.4MnO3 and the band insulators LAO and STO [440,441]but also in superlattices combining non-ferromagnetic oxides such as LaMnO3, SrMnO3 andLaAlO3 [442] or such as CaRuO3, CaMnO3 and CaTiO3 [443]. In the latter cases, the ferromagneticstates are induced by charge transfer either at the interface between the two antiferromagnetic Mottinsulators LaMnO3 and SrMnO3 [425] or at the one between the paramagnetic metal CaRuO3 andthe antiferromagnetic Mott insulator CaMnO3 [285]. This kind of tricolor superlattices could,in principle, be of great potential to design new multiferroics with optimized properties, but themodulation of the induced polarization by an electric field and its consequence on the magneticorder have still to be demonstrated.
3.6. Magnetoelectric effects at interfaces
Recently, several theoretical studies have predicted that large variations of magnetic properties mayoccur at interfaces between ferroelectrics and ferromagnets such as Co2MnSi [444], Fe3O4 [445],SrRuO3 [446], manganites [447] and Fe [448,449,450]. Modifications of the magnetic anisotropyand of the magnetization were initially put forward, [451] and investigated experimentally [452,453,454,455,456]. Actually, switching the electric polarization of the ferroelectric is predicted toinduce modifications of the spin polarization as well [448]. When applied to tunnel junctions, suchferroelectrically controllable changes in the spin-dependent density of states can be expected tomodulate the TMR or the spin-injection efficiency [457].
To probe this kind of effects, Garcia et al. [458] fabricated such artificial multiferroic tunneljunction based on Fe/BTO(1 nm)/LSMO. At 4 K, they observed large negative TMR, reflectinga negative spin polarization for the Fe/BTO interface. By applying short voltage pulses of ±1V,they observed reversible changes of the tunnel resistance with a TER of about 30%. This indicatesa modulation of the tunnel current by the reversal of the ferroelectric polarization of BTO. Moreinterestingly, the TMR was found to strongly depend on the direction of the ferroelectric polariza-tion. As can be seen for a typical junction in Figure 50, the TMR collected at a fixed bias voltageof −50 mV varies from a high value (−17%) to a low value (−3%) when the electrical polar-ization points toward Fe or LSMO, respectively. Considering that the half-metallic LSMO/BTOspin-polarization is poorly sensitive to the ferroelectric polarization direction [447], this suggestsa modification of the Fe/BTO interfacial spin polarization by the ferroelectric polarization. Thiselectrical control of the TMR with the ferroelectric polarization is repeatable (Figure 50). Toobtain a more quantitative description of the effect, the authors defined a term called ‘tunnel
Figure 50. TMR versus magnetic field curves for a Fe/BaTiO3(1 nm)/La2/3Sr1/3MnO3 tunnel junction(VDC = −50 mV, T = 4 K) after poling the ferroelectric BaTiO3 tunnel barrier down (VP+), up (VP−), down(VP+), up (VP−). A clear modulation of the TMR with the ferroelectric polarization orientation is achieved.From V. Garcia et al., Science, 327, p. 1106, 2010 [458]. Reprinted with permission from The AmericanAssociation for the Advancement of Science.
where TMRhigh and TMRlow define the high and low absolute values of the TMR, respectively.Large TEMR values of 150–450% were deduced from transport measurements done on severalFe/BTO(1 nm)/LSMO tunnel junctions. Hence, ferroelectric tunnel barriers coupled to ferromag-netic electrodes may provide a local, large and non-volatile control of spin polarization [458].This new type of interfacial magnetoelectric coupling suggests a low-power approach to controlspintronic sources.
4. Conclusions and perspectives
The impressive range of functionalities shown by transition metal oxides provides a gigantic play-ground for scientists. Materials with similar structural but radically different physical propertiescan be combined into epitaxial heterostructures in which their functionalities can be used individ-ually or in a coupled manner. In this article, we have presented two approaches that make most ofthe progress in thin-film technology – now allowing the layer-by-layer growth of ultrathin layers– and aim at engineering these functionalities at the nanoscale in tunnel barriers and interfaces todesign novel electronics and spintronics devices.
The first section was devoted to the physics of tunnel junctions based on ultrathin oxide layers,classified according to their ferroic properties. After recalling the physics of tunneling and spin-dependent tunneling, we explained how the crystalline structure of the tunnel barrier could beused to select electronic wave-functions according to their symmetry and achieve giant tunnelmagnetoresistance. We then presented the concept of spin filtering and reviewed experimentalresults in this relatively young field. If large spin-filtering efficiencies and large TMR ratioshave been obtained at low temperature, notably using europium chalcogenide and BiMnO3-basedbarriers, it is only with spinel ferrite barriers that a finite TMR was obtained at 300 K. The modestTMR values (only 3% [160]) certainly leaves room for optimizing the detailed structural andmicromagnetic properties of the CoFe2O4 barrier. Key issues when dealing with ultrathin spinelfilms, namely cationic disorder and antiphase boundaries, will have to be addressed to attain largerTMR values.
We also introduced the new field of ferroelectric tunnel junctions that emerged from theimproved understanding of the critical thickness issue in ferroelectricity, the progress in charac-terization techniques such as piezoresponse force microscopy and the advances in first-principlecalculations. Evidence for ferroelectricity in films as thin as a few unit cells has been providedfor BaTiO3, PbTiO3 and BiFeO3 through PFM or advanced diffraction measurements. Such filmshave been used as tunnel barriers, and a strong influence of ferroelectric polarization direction onthe tunnel resistance (defining giant tunnel electroresistance effects of almost 100,000% at 300 K)was independently provided by three groups in 2009 [206,196,205,195]. These results pose excit-ing questions on the interplay between ferroelectricity and quantum mechanical tunneling andpave the way toward novel physical effects and devices.
We briefly surveyed the topic of multiferroics, emphasizing the work on ultrathin films. So far,there have been very few reports, and almost all on BiFeO3. Tunnel junctions integrating ultrathinBiFeO3 films as barrier have shown large tunnel magnetoresistance (when combined with LSMOand Co electrodes), suggesting some interesting symmetry or spin-filtering effects, and large tunnelelectroresistance. These results need confirmation but are important steps toward the magnetoelec-tric control of tunneling properties in multiferroic tunnel junctions. Multiferroic La0.1Bi0.9MnO3
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thin-films are both ferromagnetic and ferroelectric with T MC � 90 K and T E
C >300 K and, whenused as barriers with LSMO and Au electrode, give rise to both tunnel magnetoresistance and tun-nel electroresistance, defining a four-resistance-state system [120]. A key challenge in this fieldis now to extend these features to higher temperatures. An approach to reach this goal may be tocombine room-temperature ferroelectrics with room-temperature ferromagnets into artificial mul-tiferroic tunnel junctions. We presented the first attempt in this direction by Garcia et al. [458] whoused LSMO/BaTiO3/Fe junctions that not only show four resistance states, but also a dependenceof the TMR amplitude with the direction of the polarization in the ferroelectric barrier. This sug-gests a ferroelectric control of the spin polarization at the BaTiO3/Fe interface that should alsobe achievable at room temperature, thereby providing a novel ingredient for future low-power,electric-field-controlled spintronics devices.
In the second section, we focused on oxide interfaces in which the ground state maybe completely different from that of the constituent materials. The paradigmatic case is thetwo-dimensional metallic electron gas that forms at the interface between band insulatorsLaAlO3/SrTiO3. As we saw in Section 3.2.1, the transport properties (mobility, carrier density,spatial extension) of the gas depend critically on the growth and reoxygenation procedures. Inoptimized conditions, the presence of carriers from undesired sources such as oxygen vacanciesand La3+ ions may be avoided and the gas is confined within a few nanometers at the interface,with sheet carrier densities in the 1013 cm−2 range and mobilities of a few 100 cm2/Vs. A widelyaccepted scenario to explain the formation of the electron gas considers the charge transfer of0.5 electron per unit cell at the interface, from the LAO to the STO, in order to avoid the polarcatastrophe due to the stacking of a polar material onto a non-polar one. A full description of theinterface ionic and electronic structure is, however, not available yet. An exciting feature of theLAO/STO system is the strong sensitivity of its transport properties to electric-field effects that,when applied at the nanoscale through AFM-sketched contacts, enable the design of a variety ofultrasmall devices, thereby considerably advancing the practical potential of oxide electronics.
Moreover, a superconducting state was found at LaAlO3/SrTiO3 interfaces (T SC ∼ 100–
200 mK), which seems to be purely two-dimensional as suggested by the Kosterlitz–Thoulesscharacter of the superconductor-to-normal transition. As we saw in Section 3.3.2, this groundstate can also be modulated by electrostatic tuning, which changes both the charge carrier den-sity and the effective disorder at the interfaces, and controls the two-dimensional quantum phasetransition between superconducting and insulating states. The nature of the pairing (symmetry,whether conventional or not) in this artificial superconductor remains basically unexplored to dateand should be receiving attention in the near future. In any case, this system provides with a toymodel where interesting experiments could be possible, such as electric-field-induced confinementof 2D superconductivity.
We discussed in Section 3.4.1, the emergence of ferromagnetism at the interface of non-ferromagnetic oxides.As we explained, the basic mechanism responsible for these effects is chargeredistribution across the interfaces. In this sense, LaMnO3/SrMnO3 superlattices, where chargetransfer is concomitant with superexchange interactions, are paradigmatic from an experimentalpoint of view. As we described in Section 3.4.2, a modulation of the physical properties alongthe direction perpendicular to the interfaces has been observed in this system: ferromagnetismappears near the interfaces, whereas the antiferromagnetic bulk state of the individual constituentis recovered further away from them depending on the superlattice period. The local ferromagneticproperties can be generally perdicted, once the local doping is known, by direct comparison withthe phase diagram of the corresponding bulk LaxSr1−xMnO3 random alloy. However, novel states(nor found in random alloys) are theoretically expected to appear at the boundary between interfaceand bulk-like behavior regions.
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Finally, we reviewed in Section 3.3.1 the interplay and competing effects atREBa2Cu3O7/LCMO or REBa2Cu3O7/LSMO superconducting/ferromagnetic interfaces. Onceagain, charge transfer, in conjunction with superconducting proximity, spin injection and magneticcoupling effects, is found to give rise to a plethora of unexpected behaviors. Not only does the inti-mate contact with LCMO induce a depression of superconductivity in REBa2Cu3O7 compoundsbut, conversely and more surprisingly, the magnetic state (domain structure, magnetic saturationand Curie temperature) of LCMO is dramatically affected by the contact with REBa2Cu3O7. It isstill not clear how proximity effects are possible in this system, given the high spin polarization ofthe LCMO, and the possibility of spin triplet superconductivity at the interfaces is being explored.It is also not clear what is the microscopic mechanism giving rise to the superconductivity-inducedmodulation of the magnetic state. Surely, further investigation is necessary. In any case, this sys-tem also provides with interesting functionalities, such as the ‘spin switch effects’ yielding gianthysteretic magnetoresistance in LCMO/YBCO/LMCO trilayers.
Before closing, we point out that, because interface properties are essential in tunnel junctions,the tunneling geometry is very well suited to investigate novel interface-driven phases in oxide-based heterostructures. Examples of such effects that could be readily studied in this way includethe enhanced magnetic moment in BiFeO3 at the interface with LSMO [459] (as discussed inSection 3.4.2, LSMO/BFO/Co tunnel junctions have already been characterized, but certainlydeserve more attention as spin-filtering may be present) or modified magnetic order at manganiteinterfaces (presented in Section 3.4.2). On this latter phenomenon, interesting magnetotransportproperties have been reported by Sefrioui et al. [460] that suggest that after playing a key role inexchange bias for spin valves, uncompensated moments at engineered antiferromagnetic interfacesrepresent a novel route for generating highly spin-polarized currents with antiferromagnets.
In summary, we have seen that oxide heterostructures often exhibit distinct, novel physi-cal properties and unexpected behaviors, radically different from those shown by each one ofthe heterostructure constituents separately. The possibility of fabricating heterostructures hav-ing interfaces with superior structural properties, where disorder is limited and plays a minorrole, favors that their physical properties are dominated by competing interactions, interplay andpurely intrinsic interface effects. Several microscopic mechanisms are found to be relevant. Besidesstrain, superconducting proximity effects and magnetostatic and exchange coupling, charge trans-fer effects play a central role. The predominant role of charge transfer is due to the fact thatmany oxide materials are low-carrier-density strongly correlated electron systems for which slightchanges of the carrier concentration (‘doping’) lead to dramatic changes of their physical proper-ties, yielding very different phases (e.g. superconducting or insulating, ferro- or antiferromagnetic)for the very same material. Finally, a key ingredient, which makes oxide heterostructures espe-cially interesting, is that external stimuli (such as magnetic and electric fields, or light illumination)having moderate effects on the individual constituents may induce dramatic changes on the het-erostructures properties, as they break a delicate balance resulting from the competing interactionsat the interface. This possibility, together with the large variety of homostructural oxide materialswith different physical properties available (high-TC superconductors, insulators, ferromagnets,ferroelectrics and multiferroics), allows endless combinations, and may pave the road to future ofall-oxide electronic devices with engineered functionalities.
Acknowledgements
We thank V. Garcia, G. Herranz and N. Reyren for helpful insights. Financial support by ANRprojects ‘Oxitronics’, ‘Méloic’, ‘Crysto’, ‘Superhybrids-II’ and ‘Alicante’, RTRA Triangle dela Physique project ‘Supraspin’, PRES Universud ‘Nano-Oxide’ and C-Nano Ile de France‘Magellan’ is acknowledged.
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