Review on Spin _electronics

7/28/2019 Review on Spin _electronics

1/35

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 35 (2002) R121R155 PII: S0022-3727(02)88955-0

TOPICAL REVIEW

Spin electronicsa reviewJ F Gregg, I Petej, E Jouguelet and C Dennis

The Spin Electronics Group, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK

Received 28 February 2002Published 4 September 2002Online at stacks.iop.org/JPhysD/35/R121

AbstractAn overview is given of the state of the art in spin electronics. The technical

basis is reviewed and simple ideas of giant magnetoresistance discussed.The connection between spin electronics and mesomagnetism is explored.Three-terminal spin-electronic devices are introduced of various typesincluding hot carrier and hybrid spin/semiconductor devices. Spin-tunneldevices are examined and single spin electronics is also treated. The paperconcludes with an outlook on future prospects in this field.

Hence you long leggd spinners, hence. William Shakespeare

1. Introduction

For most of the twentieth century it was known thatthe electrons which mediate electrical current in electroniccircuitry possess angular momentum: yet no practical use hasbeen made of this. With the dawn of the new millenniumhas emerged a novel technology which exploits electron spinand uses it to differentiate electrical carriers into two differenttypes according to whether their spin projection onto a givenquantization axis is 12 .

Spin-electronic devices function by transferring magneticinformation from one part of the device to another by usingnanoscale magnetic elements (mesomagnets) to encode itonto (and subsequently read it off) the itinerant electron spinchannels. This coding may be changed by remagnetizingthe mesomagnets thus enabling the creation of electroniccomponents whose characteristics may be engineered torespond to applied magnetic fields.

The aim of this paper is to introduce the field of spinelectronics by giving a description of the relevant physicalsystems and length scales on which the spin effects becomeimportant. Early devices are described, some more recentdevelopments are illustrated and the authors conclude byoutlining their own thoughts on the future potential of thisrapidly expanding field.

2. Technical basis of spin electronics: the twospin-channel model

The technical basis of this new spin-electronic technologyhas been within grasp since the mid-1930s when Mott sought

an explanation for the anomalous resistivity trends exhibitedby ferromagnetic (FM) materials which were progressivelydoped with impurities. Unlike the behaviour of non-magneticmetals which obey Matthiesens rule to good approximation,the resistance of metallic ferromagnets is a complex functionof contamination. The solution of this riddle lies in thetwo-channel model which treats spin-up and spin-downelectrons as different families between whom there is rarelyanyinterchangeof personnel (i.e.spin-flip scattering)at leaston the brief timescales defined by all the other processes inthe system. Spin-flip scattering does, of course, occur in thesematerialsbutitissocomparativelyrarethatitmaybeneglectedwhen considering the dissipative processes that give rise toelectrical resistivity.

This relative independence of the two families of chargecarriers in the two-channel model is half the story behind

spin electronics. The other essential ingredient is that thedensities of states, and consequently the mobilities of the twochannels are typically very different in a FM metal. Theorigins of this mobility difference between spin channels is,unsurprisingly, closely related to the exchange interactionwhich causes ferromagnetism itself. The exchange splitting ofthe itinerant electron conduction bands presents different partsof the band structure to the Fermi energy and these differentband structure segments generally have different densities ofstates. This implies that if a ferromagnet passes an electricalcurrent, then the current is mediated primarily by the highmobility carriers. In turn, this implies that when an electricalcurrent passes in an Ohmic contact from a FM metal to

a paramagnetic (PM) metal, this current is spin polarized,due to the mobility differential (and hence indirectly to thedifferent densities of states). Likewise if the current passes

0022-3727/02/180121+35$30.00 2002 IOP Publishing Ltd Printed in the UK R121
http://stacks.iop.org/jd/35/R121http://stacks.iop.org/jd/35/R121


2/35

Topical Review

Figure 1. Spin splitting of the density of states () in a ferromagnetdue to the exchange field.

from a ferromagnet to a paramagnet by tunnelling throughan insulator, this current is also polarized due directly to the

density of states asymmetry. FM elements may thus be used asspin-polarizedcurrent sources in spin-electroniccircuits. Mostspin-electronic phenomena are based on either one or both oftheseasymmetries(whosecommonoriginisthebandstructuresplitting) prevailing in the relevant physical system [1].

2.1. Spin asymmetry: density of states asymmetry versus

mobility asymmetry

In fact, the two asymmetries often compete with one anotherin spin electronics. The Fermi surface in most FM materialscontains components which have both s- and d-character.The s-like effective masses are small compared to the d-like

masses and so any current that flows is primarily mediated bys-electrons. However, the d-electrons are significantly split bythe exchange interaction and as a result present very differentdensities of states into which the s-electrons may be scattered.Thus, from figure 1, the down s-channel (whose spin type hasa large d density of states at the Fermi energy) suffers themost scattering and hence has lower mobility than the others-channel: this latter consequently carries most of the current.

Thus in a system with s- and d-like character at the Fermisurface, the tendency is for the current to be carried by theminority carriers (where minority is taken to mean thosewith the lower density of states at the Fermi energy, and thisconvention will be used throughout this paper) whereas in a

half-metallic ferromagnet (see next section), the current mayonly be carried by majority carriers. This conflict between thetwo types of asymmetry is one reason why spin-tunnel devices(section 6) have an advantage over their competitors sincethey exploit only the density of states asymmetry; hence, themobility asymmetry has no chance to compete and reduce theoverall device performance. This has direct relevance to thequestion of spin injection into semiconductors.

2.2. The half-metallic ferromagnet

In the extreme limit of spin asymmetry lies the half-metallicferromagnet [2] in which the band structure splitting is such

that only one spin channel has available states at the Fermisurface andhence all current must be carried by these so-calledmajority spins. Practical examples include chromium dioxide

Figure 2. Schematics of the difference in the densities of statesbetween a ferromagnet and a half metallic ferromagnet.

Figure 3. Illustration of the spin accumulation at theferromagnet/paramagnet interface.

(CrO2), lanthanum strontium manganite (La0.7Sr0.3MnO3)and some Heusler alloys. In reality, obtaining half-metallicspin-electronic behaviour is fraught with problems mainly todo with the interfaces. Conversely, some materials whosebulk electrical conduction deploys both spin channels may,due to hybridization, form half-metallic interfaces with othermaterials.

2.3. Spin injection across an interface: spin accumulation

Now that we have considered the basic principles behindthe origin of spin asymmetry, we can briefly consider animportant phenomenon which lies at the heart of early spin-electronic devices. Providing one carrier spin type is dominantin the electrical transport of a ferromagnet, when a currentis passed from this ferromagnet to a PM metal such assilver or aluminium, it brings with it a net injection of spinangular momentum and hence also of magnetization [3]. Themagnetization which builds up in the new material is knownas a spin accumulation (figure 3). Its size is determined by theequilibrium between the net spin-injection rate at the interfaceand the spin-flipping rate in the body of the paramagnet. It

follows that the spin accumulation decays exponentially awayfrom the interface on a length scale called the spin diffusionlength.

R122


3/35

Topical Review

2.4. How long is the spin diffusion length? the simple

estimate

Because of its importance in the field of spin-electronicdevices, it is instructive to do a rough back of the envelopecalculation to see how large is this spin diffusion length, lsd,and on what parameters it depends. We can consider a newlyinjected up-spin arriving across the interface into the non-magnetic material. It undergoes a number N of momentum-changing collisions before being flipped (on average aftertime ). Theaveragedistancebetweenmomentumscatteringcollisions is , the mean free path. We can now make tworelations. By analogy with the progress of a drunken sailorleaving a bar and executing a random walk up and down thestreet, we can say (remembering to include a factor of 3 since,unlike the sailor, our spin can move in three dimensions) thatthe average distance which the spin penetrates into the non-magnetic material (perpendicular to the interface) is

N/3.

This distance is lsd, the spin diffusion length which we wish

to estimate. Moreover, the total distance walked by the spin isN which, in turn, equals its velocity (the Fermi velocity, vF)times the spin-flip time . Eliminating the number N ofcollisions gives

lsd =

vF3

. (1)

A rigorous analysis of the spin-accumulation length in termsof the respective electrochemical potential of the spin channelsfollows the model of Valet and Fert [4] and this is discussedbelow. The fact that the conclusions drawn are very similarshowsthatthecrudedrunkensailormodelgivesaremarkablyaccurate insight into the physics of this problem. Various

practical methods of measuring the spin diffusion length havebeen described [5].

2.5. How large is a typical spin accumulation?

Using the above relationship, the resulting magnitude of spinaccumulation can be given in terms of the spin density n atdistance x from the interface, and is

n = n0ex/ lsd . (2)Integrating,

0n dx = n0lsd

is the total number of spins in the accumulation and the spindecay rate

n0lsd

= n0vF

lsd

must be equal to the injected spin current P J / q where P is thepolarization of the ferromagnet, J is total electrical current, qis electronic charge, is mean free path, vF is Fermi velocityand n0, the density at the interface, is given by

n0 = 3P J lsdqvF

. (3)

Substituting typical numbers of J

=1000Acm2,

=1,

vF = 106 m s1, = 5nm, lsd = 100 nm gives a value of spindensity of 1022 m3 as opposed to a total electron density ofabout 1028 m3.

2.6. The dominance of the Fermi surface in spin electronics

That such minute asymmetries in total spin density cangive rise to large electrical transport effects as giantmagnetoresistance (GMR) is yet one more example of thedominance of the electrons at the metal Fermi surface whichis where these spins are concentrated. The spin densityasymmetry represents only about one part in 106 of the totalelectron density; hence, measurement of the spin densityor its associated magnetization is difficult due to problemsin distinguishing convincingly the magnetic fields generatedby the effect itself (around 10nT for the example above)and those caused by the current which is generating theaccumulation. However, if we estimate the non-equilibriumelectron density responsible for carrying the total current, wefind nnoneq = J/qvF. This means that the ratio between thespin-accumulation and the current-carrying electron density is

nspin

nnoneq =lsd

.

This implies that the spin depth to which the Fermi surfaceis polarized exceeds the Fermi surface displacement due to theapplied electric field by about 2 orders of magnitude.

2.7. The role of impurities in spin electronics [6]

From the expression

lsd =

vF3

,

it becomes evident that introducing impurities into the PMmaterial diminishes the spin diffusion length (l

sd) rapidly,

because they shorten not only the mean free paths of thecharge carriers, but also the spin-flip time via the mechanismof spin-orbit scattering. The latter may be thought of asa relativistic effect: under Lorentz transform, electric fieldsassume a magnetic component. To electrons at the Fermisurface which have weakly relativistic velocities, the electricfields generated by impurity atoms appear weakly magnetic.If the symmetry of the impurity site is sufficiently low, thisfield may Zeeman-couple to spin operator terms in s+ ands which induce spin-flip transitions. Hence materials withpoint defects and low symmetry structural disorder are likelyto exhibit reduced spin diffusion lengths [7,8].

2.8. Scattering processes and their effects

Various processes exist to curtail the diffusion coefficient D,which directly relates to the mobility and the mean free path ,spin-flip time and e, the energy decay length scale forhot carriers. Table 1 illustrates the contributions of the variousmechanisms. Note, in particular, that e includes some but notall momentum diffusion processes, an important considerationin comparing thermal and electrical GMR.

2.9. The ValetFert theory of electrochemical potential

splitting

Valet and Fert established that if the electron spin-flip length ismuchlargerthanthemeanfreepath,thenthespinaccumulationmay be macroscopically treated in terms of the respective

R123


4/35

Topical Review

electrochemical potentials for the two spin channels. In thistreatment J istheelectricalcurrentand Jm is the magnetizationcurrent. The overall current of particles Jn is the sumof diffusion current JD and electric field-driven current JEwhere Jn, JD and JE represents number currents, and may

be expressed as

Jn = JD + JE = Ee

D nz

, (4)

where is the conductivity, E the electric field, q the electroncharge, D the diffusion constant and n the number of carriers.In turn, by introducing the density of states at the Fermi level,(F), these may be, respectively, expressed as gradients ofthe chemical potential and the electrostatic potential energyqV, hence also as the gradient of the electrochemical potentialwhich is defined as = + qV:Jn = D(F)(qV) D(F)() = D(F)()

(5)

Now we consider, at a point in the material, the magnetizationassociated with the spin accumulation which is constant indynamic equilibrium, so that

0 = dMdt

= Jm 2M

, (6)

where Jm is the magnetization current given by Jm =B(JnJn), and is the spin-flip time which is doublethe magnetization decay time.

Jm =2M

(7)

( Jn Jn)B = 2B(n n)

, (8)

where n and n arenumberdensitiesofupanddownspinsandmagnetization is the Bohr magneton, B, times the differencein up and down spin concentrations.

Using the relation in (5) above between number currentand density of states, leads to the following relation:

B(D(F)) ( ) = 2B(F)[ ]

BD2() = 2B

(). (9)

Table 1. Contributions of the various mechanisms.

Spin Momentum EnergyScattering process flip change change Influences

Phononsmall angle 0 0 1 eImpurities, defects, 0 1 0 D

dislocationsPhononlarge angle 0 1 1 D, eRegular spin orbit, 1 0 0

JitterbugFM resonance 1 0 1 , eParamagnetic impurity 1 1 0

, D

spin orbit, interfaceMagnon 1 1 1 , D , e

This equation has decaying exponential one-dimensionalsolutions of the form

= [Be(z/lsf) + Ce(z/lsf)] (10)where B and C are constants which serve to satisfy the

boundary conditions at the interfaces of the material, namelythe continuity of currents and electrochemical potentials(the latter only if there is no interface scattering). lsd =(D/2)1/2 is the spin diffusion length as found by thesimple random walk treatment. Errant factors of 2 in varioustreatments arise from uncertainty as to whether is the spin-flip time or the magnetization decay time: the former is doublethe latter.

This treatment is for a PM material where the mobility(proportional to the diffusion constant D) is the same for upand down spin. For a spin-asymmetric material such as aferromagnet, D and D are different and the spin diffusionlength in this case is given by l2sf = {1/D + 1/D}/.

3. Two-terminal spin electronicsGMR

Having outlined the origins of the spin-accumulation length atthe interface between a ferromagnet and a normal metal, wecan now consider the operation of arguably the most simplespin-electronic device: a thin layer of PM material sandwichedbetween two FM electrodes, such as the one shown in figure 4.

The device acts as a two-terminal passive spin-electroniccomponent, which, in some realizations, is known as a spinvalve and it passes muster in the world of commerce as a keycomponent in GMR hard-disk read-heads.

Empirically, the function of the device is simple. If we

measure the electrical resistance between the two terminalsin an externally applied magnetic field (supplied for exampleby the magnetic information bit on the hard disk whoseorientation it is required to read), we can use the field toswitch the relative magnetic orientations of the FM layersfrom parallel to antiparallel. It is observed that the parallelmagnetic moment configuration correspondsto a lowelectricalresistance and the antiparallel state to a high resistance.Changes in electrical resistance of order 100% are possiblein quality devices [9], hence the term GMR (figure 5) since bycomparison with, for example, anisotropic magnetoresistance(AMR) in ferromagnets, theobservedeffectsare about 2 ordersof magnitude bigger.

Figure 4. Schematics of a simple GMR device.

R124


5/35

Topical Review

Figure 5. Experimental illustration of GMR (after Baibich et al [10]).

3.1. The analogy with polarized light

There are a variety of different waysof varying rigourto explain the operation of this spin-valve structure. Tokeep things simple, let us invoke only density of states spinasymmetry and analyse it by analogy with the phenomenonof polarized light. In the limit in which the ferromagnetsare half-metallic, the left-hand magnetic element supplies acurrent consisting of spin-up electrons only, which produce aspin accumulationin thecentral layer. If thephysical thicknessof the central layer is comparable with or smaller than the spindiffusion length, this spin accumulation reaches across to theright-hand magnetic layer which, on account of its being half-metallicand thus offering a density of states to only one spintypeacts as a spin filter, just as a piece of Polaroid spectaclelens acts as a polarized light filter. The spin accumulationpresentsdifferentdensities ofupanddownelectrons to this spinfilter, which thus lets through different currents depending onwhether itsmagnetic orientation is parallel or antiparallelto theorientation of the polarizer (i.e. the first magnetic layer). Theonly difference with the case of crossed optical polarizers isthat in optics the extinction angle is 90. In the spin-electronic

case it is 180. As expected from this model, theGMRdependson the cosine of the angle between the magnetic layers [11].

3.2. Simple resistor model of GMR

Alternatively, if we invoke mobility spin asymmetry, a simpleparallel resistor model may be used to describe the GMRof the multilayer stack shown in figure 6: the two parallelpaths, each consisting of five series resistors, represent therespectivespin channels andthe resistorsin each path representthe resistances which they experience in each of the layers.If we arbitrarily assign resistance values of 1 and 10 tothe majority and minority layer resistances, it is seen that

the magnetization parallel and antiparallel configurations haveoverall resistance of 4.5 and 13 , respectively. This modelgives a primitive insight into themechanicsof GMR. However,

like the polarized light model, it crudely fails to reflectthe symmetry or antisymmetry of what occurs at adjacentinterfaces. Nor does it give due emphasis to the criticalrole played by the interfaces themselves. A more pleasingapproach which respects these symmetries and so affordsdeeperinsightintotheroleofthespindiffusionlengthisofferedby the extension of the ValetFert model to a magnetic trilayersystem.

3.3. The ValetFert interpretation of trilayer GMR

Extension of the ValetFert model to trilayers involves writingthe one-dimensional solution of equation (10) as a the sum offorward and backward decaying exponentials for each layerand matching the electrochemical potentials and spin currentsatinterfacesforeachchannel. Theresultsareplottedinfigure7for both parallel and antiparallel alignment of the magneticlayers. The central lines are the asymptotes to which theelectrochemical potentials would collapse if their divergencewas allowed to decay to zero at large distance. Projected backto the interfaces, these central asymptotes are discontinuous

and to the outside observer making transport measurementsthe discontinuities represent apparent interface resistances.From the diagrams it may be seen that these pseudo-

interface-resistances and the effective resistance of thesandwich layer vary with magnetic configuration and hencetranslate into magnetically dependent changes in the resistanceof the overall device, i.e. GMR. The key to this variation is inthe overlap in the PM layer of the non-zero electrochemicalpotential divergences which interfere with each other togenerate the magnetic effect [12].

3.4. Current in plane and current perpendicular to

plane GMR

It is important to note that there are two configurations inwhich our simple two-terminal device can workthey are,

R125


6/35

Topical Review

Figure 6. Two resistor model of GMR.

Figure 7. Results of the ValetFert model on a trilayer system forthe case of (a) parallel and (b) antiparallel arrangement. Note thatAP > P.

respectively, described as current in plane (CIP) and currentperpendicular to plane (CPP).

Above, we have discussed only the latter in which thecritical length scale for the magnetic phenomena is the spindiffusion length. Chronologically however, CIP GMR was

Figure 8. CIP and CPP geometry.

first discovered, its geometry being easier to realize than theCPP geometry whose implementation requires sophisticatednanolithography techniques [13], and indeed it is to this typethat figure 5 refers. The physics involved in CIP operationis rather different to the CPP geometry and the critical lengthscale here is the mean free path. CIP GMR is characterized bythe same drop in electrical resistance of the thin film samplewhen a magnetic field is applied. However the explanationis fundamentally differentsymmetry considerations showclearly that no spin accumulation is set up in this case since

current flow is parallel to the layers. Instead the explanationinvokes the differential mobilities of the spin-up and spin-down electrons and relies on the non-magnetic interlayer

R126


7/35

Topical Review

Figure 9. Polar plot of the mean free path versus momentumdirection of an up spin in the centre of the PM layer where the eitherside of the magnetic layers is oppositely magnetized. The layers aredrawn to the same scale as the mean free path. The circular dottedline shows the bulk mean free path in the non-magnetic (N) layerand allows comparison with the direction-dependent effective mean

free path which occurs due to the effects of the neighbouring layers.

Figure 10. Two-resistor model of GMR in CIP configuration forFM and antiferromagnetic layer alignment, respectively.

being sufficiently thin that a high proportion of the current-carryingelectronsexperiencesuccessivemomentumscatteringevents in different magnetic layers. This in turn meansthat if the layers are antiparallel, neither spin type has highmobility since each experiences heavy scattering in one orother layer. However if the layers are parallel, one spin typeis heavily scattered in both layers and the other spin type isrelatively unscattered and hence its high mobility electricallyshort-circuits the device.

As an illustration of this magnetically sensitive mobility,figure 9 shows a polar plot of the mean free path versusmomentum direction of an up spin in the centre of the PMlayer where on either side are the magnetic layers oppositelymagnetized. The dotted circle represents the mean freepath which the same spin would experience in the bulkparamagnet [14].

The resistor model of figure 10 models the CIP geometry:the two parallel paths are representative of the two-spinchannels in each non-magnetic layer, and each path comprisestwo resistances which represent the scattering they experiencein theadjacent magnetic layers, assuming that their trajectoriessample both these magnetic layers.

3.5. Comparative length scales of CIP and CPP GMR

It is evident from this discussion that two quite different lengthscales are relevant to CIP and CPP GMR. For CPP GMR,the interlayer must be less than the spin diffusion lengthasclearly shown by the ValetFert treatmentwhereas for CIP

GMR toappearthe interlayermustbe lessthana meanfreepathwhichisarathershorterdistance. Asaresult,typicalCIPGMRmultilayers usenon-magneticspacers of order 2030 or less.

Figure 11. GMR curves for (A/Cu2.3nm/Co0.4nm/Cu2.3nm) times

20 multilayers with (a) A = NiCr5%, tA = 1 nm, (b) A = NiCr5%,tA = 7nm, (c) A = NiCr2.5%, tA = 10 nm and (d) A = FeCr,tA = 7 nm (after Vouille [16]).

3.6. Inverse GMR

In the above discussion of GMR, it is assumed that the metalsinthetwoFMlayersaresimilar,oratleastthatthesignsoftheirpolarizations are the same. In other words, the majority spinfor each ferromagnet is parallel to the magnetization (positivepolarization) or antiparallel to the magnetization (negativepolarization). If a combination of two ferromagnets withopposite polarizations is used to make a GMR trilayer, theGMR is inverted, i.e. the resistance of the device increases on

application of external magnetic field. This is because whenthe ferromagnets have parallel magnetizations, theydisagree asto which spin direction is the majority type [15,16] (figure 11).

3.7. Methods for obtaining differential switching of

magnetizationRKKY coupling versus exchange pinning:

spin valves and AAFs

There are two techniques used to engineer GMR systems suchthat the two FM layers in the trilayer switch differentially inan externally applied field. The first one involves makingthe metallic interlayer of such a thickness (of order 10)that the RudermanKittelKasuyaYosida (RKKY) coupling

across it between the magnetic layers is antiferromagneticand so the layers anti-align in zero applied field but alignparallel to one another in applied field [17]. This techniqueimposes constraints on the device design which may militateagainst obtaining the best GMR signal. The other techniqueis to fabricate one layer magnetically harder, for example, byexchange pinning it to an antiferromagnet on the side oppositeto that which abuts the GMR device. In this case only theunpinned soft layer moves in small magnetic fields. Theresulting device is termed a spin valve (figure 12) [18].

There is a third technique, using materials knownas artificial antiferromagnets (AAF), which use a clevercombination of the two above ideas. Here, no RKKY coupling

is used in the GMR spacer layer. However, one of the FMelectrodes is rendered magnetically hard by fabricating it fromtwo distinct FM layers A and B of almost identical thickness

R127


8/35

Topical Review

Figure 12. Schematic of a spin valve [19].

which are coupled such that in zero applied field they areantiparallelandhencetheirnetmomentissmall. Theswitchingfield of this artificial antiferromagnet block (A + B) is thusenhanced by a so-called Q-factor which is the ratio of the totalmagnetic moment when A and B are aligned in a high field tothe net moment when A and B are anti-aligned [20].

3.8. GMR in nanowires

An interesting realization of CPP GMR has been achievedby using electroplating technology to construct metallicnanowires in nanopores of a membrane [21]. With asuitable electrolyte containing a selection of ions, differentmaterials can be deposited with an interspacing of a fewnanometres along thewire simply by switchingthevalueof theelectroplatingpotential, thereby creatinga magneticmultilayerstructure. This technique has the added convenience that thegeometry of the wires is conducive to easy measurement,unlike thin evaporated films on which lithography must be

carried out on in order to obtain specimens whose resistanceis high enough for practical purposes.

4. Three-terminal spin electronics: the Johnsontransistor

Electronically, the natural progression is from a two-terminalGMR device to a three-terminal one, and this step was firstachieved by Johnson [2224] simply by placing a third contactattached to the intermediate PM base layer to create theJohnson transistor (shown in figure 13).

Now in the language of bipolar transistors, we canspeak of a base, an emitter and a collector, the last two

being the FM layers. Just like its bipolar counterpart, theJohnson transistor may be used in various configurations;the one we discuss here is chosen because it gives insightinto yet another way to analyse spin filtering and spinaccumulation. We leave the collector floating and monitor thepotential at which it floats using a high-impedance voltmeter.Meanwhile a current is pumped round the emitter-base circuitand this causes a spin accumulation in the base layer asbefore. The floating potential of the collector now dependson whether its magnetic moment is parallel or antiparallel tothe magnetization of the polarizing emitter electrode whichcauses the spin accumulation. Evidently, this potential may bealteredbyusinganexternalmagneticfieldtoswitchtherelative

orientation of the emitter and collector magnetic moments.To analyse this behaviour, consider again the limiting caseof a half-metallic ferromagnet as the collector electrode. It

Figure 13. Johnson transistor.

floats in equilibrium with the base electrodein other wordsin the steady state, no net current flows. But because it ishalf-metallic, it can only trade electrons with the base whosespin is (say) parallel to its magnetization and the no current

conditionthen means that its electrochemicalpotential is equalto the electrochemical potential in the base layer for the sameelectron spin type. In other words, thecollector is sampling theelectrochemical potential of the appropriatespin type (spin up)in the base. Reversing the collector magnetization means itnow samples the spin-down electrochemical potential in thebase. Since there is a spin accumulationin the base, these spin-up and spin-down electrochemical potentials are different [4]and the collector potential is thus dependent on the orientationof its magnetic moment. Thus we have a three-terminal spin-electronic mechanism for which the conditions at terminal 3maybesetbysuitableadjustmentoftheconditionsatterminals1 and 2, as for a traditional electronic three-terminal device.

However, in addition, these conditions can also be reversed byapplying an external magnetic field. The above encapsulatesthe essence of spin-electronic device behaviour.

4.1. Spin-electronic function as a spin-information

writeread process

Evidently in the above discussion, it is essential that the spinaccumulation penetrates right across the thickness of the baselayer in order that the collector may sample it. Likewise, inthe two-terminal device, it was important that the base layerthickness was small on the length scale of the spin diffusionlength. This provides us with an interesting new way to view

spin-electronic devices. We can regard their behaviour as awritereadprocessinwhichanencoderwritesspininformationonto the itinerant electrons in one part of the device and thisinformation is then conveyed to a physically different part ofthe device where it is read off by a decoder. The encoderand decoder elements are nanoscale ferromagnets and the spininformation decays in transit on the length scale of the spindiffusion length. The message then is that for successfulspin-electronic device operation, the device must be physicallyengineered on this length scale or smaller.

5. Mesomagnetism: the importance of characteristiclength scales in nanomagnetism

This is just one particular manifestation of the generalphenomenon of mesomagnetism which concerns itself with

R128


9/35

Topical Review

the appearance of novel physical phenomena when magneticsystems are reduced to the nanoscale. The underlying tenet ofmesomagnetism is that magnetic processes are characterizedby a variety of length scales and that when the physicaldimensions of a magnetic systemareengineered to dimensions

comparable with or smaller than these characteristic lengths,new andunusual magnetic phenomena appearsuch as GMR,superparamagnetism and perpendicular recording media.These characteristic length scales have various origins.Many of themdomain size, domain wall width, exchangelength and thin film perpendicular anisotropy thresholdare governed by a balance of energy terms. Others arethe result of diffusion processes for energy, momentum andmagnetization.

5.1. Giant thermal magnetoresistance

The spin-electronic readwrite phenomenon has a thermalanalogygiant thermal resistance. The Wiedemann Franzlaw (WFL) tells us that there is a close relationship betweenelectrical transport and heat transport in most materials aswitnessed by the Peltier and thermoelectric effects. Thermaland electrical conductivities are limited in most regimes bythe same scattering processes and the WFL tells us that inthese circumstances their quotient is a constant times absolutetemperature. Moreover, this close relationship extends tomagnetotransport in mesomagnetic systems. Figure 14 showsmeasurement of the giant thermal magnetoresistance in a giantmagnetoresistive mechanical alloy.

The analysis is identical to the electrical case. Spin

information is encoded onto a thermal current in one partof the device and read off again in a different part of thedevice: the result is a thermal resistance which varies withapplied magnetic field by many per cent [25]. The form of thespin information coding is qualitatively different to that of theelectrical case and it decays on a different (shorter) thermalspin diffusion length since it is susceptible to destructionby additional scattering processes. Thermal GMR is thususually less in magnitude than electrical GMR for the samesample.

Figure 14. (a) Schematics of an experiment designed to measure thermal magnetoresistance and (b) the thermal GMR effect seen in amechanical alloy. For comparison, the electrical GMR is also shown inverted (dots) and superimposed on the thermal trace.

5.2. The exchange length in spin electronics: FM domain

wall resistance

Another example of the intrigue of mesomagnetism can beseen by considering the geometrical similarity between a spin-valve structure and a FM domain wall (whose thickness isone possible definition of exchange length), as illustrated infigure 15. In both cases, regions of differential magnetizationare separated by an intermediate layer. In the formercase, this layer is in the form of a thin film of non-magnetic metal whereas in the latter it is a region of twistedmagnetization.

The spin-valve functions provided that spin conservationoccurs across the intermediate zone. By analogy, it is possibleto develop a model of domain wall resistance [2628] in whichthe value of the resistance is determined by the degree of spindepolarization of the charge carriers in the twisted magneticstructure formed at the heart of the domain wall. The model

invokes magnetic resonance in the FM exchange field in ordertodeterminethedegreeofelectronspinmistrackingonpassingthrough the domain wall. Two competing frequencies are inplay; the spins precession frequency P, on the one hand,and, on the other, the effective frequency w with which thespin sees the magnetization reverse as it traverses the wall.This latter frequency is clearly a function of wall thickness,d, and Fermi velocity vF, i.e. w = vF/d. From simplemagnetic resonance considerations, it may be seen that spinswhose precession frequency P w follow the changingmagnetization adiabatically. However, if P is comparablewith or lower than w, the spin has difficulty in following andmistracts the magnetization. This mistracking of, say, an up

spinleadstoitsmakinganaverageangle = KhvF/Eexdwiththelocalmagnetization directionin thedomain wall, where h isthe Planck constant, vF the Fermi velocity, Eex is the exchangelength, d domain wall thickness and K depends on the shapeof the Fermi surface. This is equivalent to its wave functionbeing contaminated by a fraction sin( /2) of the down-spinwave function (figure 16).

The up spin is then susceptible to additional scattering byan amount equivalent to sin2( /2) multiplied by the down-spin scattering rate. This model leads to a formula for the

R129


10/35

Topical Review

Figure 15. Geometric similarities between (a) a FM domain walland (b) a GMR trilayer (courtesy of W D Allen).

Figure 16. Spin orientation versus trajectory for the electricalcarriers in transit through a domain wall in Co. The blue vectorrepresents the cobalt magnetization and the red vector represents thespin orientation (courtesy of W D Allen).

spin-dependent contribution to the domain wall resistivity:

W

0=

+

2

sin2

2

(11)

where and are the majority and minority spin mean freepaths, 0 and W are, respectively, the bulkFM resistivity andthe resistivity increase for domain wall material [29].

This spin-dependent contribution differs from variousother proposed mechanisms for domain wall resistance in thatit predicts not a fixed value of resistance for the wall but rathera ratio increase based on the bulk value for the material. Inprinciple, therefore, the validity of the model can be assessedby measuring domain walls in increasingly impure samplesof the same ferromagnet and observing if the ratio W/0stays fixed. This model has been re-analysed [30] by replacingthis simple rotating frame approach with a more sophisticatedquantum mechanical analysis: to within a simple numericalfactor, identical results are obtained. The model has beentestedonapracticalsystemofcobaltstripedomains(figure17),and after correction for the Berger effect [31] satisfactory

agreement obtained with the model predictions.It is worth noting in this connection that very largemagnetotransport effects (of order 600%) have been observed

Figure 17. Domain patterns for a 1000 thick cobalt film asimaged by magnetic force microscopy. (a) The initial domainconfiguration in zero applied field. (b) The beautiful parallel stripedomain pattern which may be prepared by applying a large magneticfield in the plane of the film, then demagnetizing the film by cyclingthe in-plane field.

in FM nanocontacts between oppositely magnetized domains

of half-metallic ferromagnet (magnetite) [32] (see section 12on quantum transport in FM nanocontacts).

5.3. Granular GMR materials

When different proportions (say 20%, 80%) of twoimmisciblemetals are cosputtered and then annealed, the initialinteratomic mixture phase separates into granules of onemetal in a matrix of the other. If the granules are FM andthe matrix PM, the granules may behave as superparamagneticor may block depending on temperature: the resulting materialmay exhibit GMR. Such materials may also be formedby mechanical alloying. The effect was first observedby Gerritson [33] before the theory existed to explain thephenomenon. The GMR arises because in zero field the anglebetween adjacent magnetic granules is totally random whereasin high magnetic field the moments are virtually all aligned.Simple trigonometry shows that

GMR cos(ij) = cos( )j2M2 (12)

where ij is the angle between moments i and j and j is theangle between moment j and the applied magnetic field. TheGMR, which is again proportional to the cosine of these inter-grain angles, varies as the square of the sample magnetization.In the absence of significant interaction between the grains thisis experimentallyverified [34,35]. Dueto thegeometry of such

granular systems, the GMR which they exhibit is a mixture ofCIP and CPP and both characteristic length scales for thesetwo phenomena are in play. Pairs of particles within a meanfree path of each another contribute CIP GMR. Meanwhile,in the direction of the current, each magnetic particle whosesize is comparable with or larger than the FM spin diffusionlength has a decaying spin accumulation shadow in theadjacent paramagnet. The shadows from successive pairs ofsuch particles are capable of longer range interaction to giveCPP-like GMR.

5.4. Jitterbug depolarization

Granular GMRsystems comprise a spreadof magnetic particlesizes whose span depends on the mode of preparation. Thelarger particles whose diameters are of the order of electron

R130


11/35

Topical Review

mean free path contribute to the GMR. The smaller particlesare insufficiently big to cause appreciable scattering but theynevertheless play a role in determining the magnetotransportby causing passing spins to precess in their exchange field.This spin precession causes the spin to turn through an angle

which is a function of the incident spin orientation, the particlemagnetizationorientationandtheparticlethickness. Theresultis a progressive depolarization or mixing of the spin channelswhichmilitatesagainsttheGMR.Thisspinmixingmechanismis called the Jitterbug effect after the swing-dance of that namewhich the electrons successive random precessions resemble[36,37].

6. Spin tunnelling

6.1. Quantum tunnelling

If two conducting layers between which a potential is appliedare separated by a thin insulating film, electrical currentpasses between the metal electrodes by quantum mechanicaltunnelling of the current carriers through the insulating tunnelbarrier. The tunnelling rate for carriers of a particularenergy is proportional to the product of the carrier densitiesof states at that energy each side of the barrier. Also,the thinner the barrier and the lower the barrier height, thelarger the current. This phenomenon was extensively studiedin the context of superconducting thin films where it enablesaccuratedeterminationofthesuperconductingenergygap[38].

6.2. Spin-tunnel junctions

Spin-tunnel junctions are two-terminal spin-electronic devices

whose magnetotransport characteristics closely mirror thoseof CPP GMR trilayers, except that their parameters are morereadily adaptable to practical applications. They consist ofpairs of FM electrodes separated by electrical insulators andthey exhibit large changes in tunnel resistance dependingon the relative alignment of the FM electrode magnetizations.The thickness of the tunnel barrier must be in the lownanometre regime to obtain reasonable current densities.Theeffect maybe understood, at least simplistically, accordingto a model of Julliere [39] which was in turn inspired by theideas of Meservey andTedrow [40], in which thetunnelcurrentis proportional to the product of the densities of spin stateseither side of the tunnel barrier. In the simple case of half-

metallic ferromagnet electrodes whose magnetic moments areanti-aligned, it is clear that the product of the initial and finaldensities of states is zero for either spin type and no currentflows. However if the moments are aligned, the half-band ofmajority spins may tunnel and the device has low resistance.It may be seen that this device is highly analogous to the CPPGMR trilayer except that it relies exclusively on asymmetry indensity of states and does not invoke mobility spin asymmetry.This makes analysis cleaner and also means that in general theMR effects are larger. Also, because tunnelling and not Ohmicconduction is involved, the resistance of a tunnel junction ishigher than that of an all-metallic GMR system of comparablegeometry and this makes spin-tunnel junctions rather more

easily adaptable to practical applications.Tunnelling between FM electrodes, and the effect ofthe relative magnetic orientation of the electrodes upon it,

was an effect first investigated by Julliere [39] and Maekawa[41]. These early observations (figure 18) showed thatthe tunnelling conductance (for these dissimilar electrodes)increases when the relative orientation of the electrodeschanged from parallel to antiparallel, andthe effect wascoined

tunnelling magnetoresistance (TMR).Julliere was the first to give a classical description forthe cause of this effecthis argument was that the spinsplitting of the Fermi level in the magnetic metals causedan unequal distribution of up- and down-spin electron states.This, combined with the classical model of tunnelling [42]where the overall tunnelling conductance is proportional to theproduct of the densities of states of the twoelectrodes, with theassumption that spin is conserved in the process of tunnelling,resulted in a simple formula which stated that

R

R= R

P RAPRP + RAP

= 2P1P2P1 + P2

, (13)

where Pi is the polarization of the electrode defined as

Pi = i i

i +

i

(14)

and i being the density of states at the Fermi level. Here, RP

and RAP refer to the resistance of the tunnelling junction whenthe moments of the adjacent electrodes are aligned paralleland antiparallel to each other. This well-known Julliere modelwas successful in giving a physical insight into the possibleorigin of the effect. However, extensive research carried outover the last twenty years has posed new questions, some ofwhich remain unexplained even today. For instance, in a clas-sic experiment by Moodera and Kinder [43], it was found thatthe observed TMR is largely dependent not only on the type ofinsulatorusedasatunneljunction,butalsoonthebarrierheightand width. Many workers found that the TMR displays a largevariation with temperature and with applied bias, irrespectiveof the junction quality. In addition, barrier impurities and the

Figure 18. Experimental signature of spin tunnelling [43];resistance of CoFe/Al2O3/Co tunnelling junction plotted as a

function ofH in the film plane, at 295 K. Also shown is thevariation of CoFe and Co resistances. The arrows indicate thedirection of magnetization in the two films.

R131


12/35

Topical Review

introduction into barriers of controlled thicknesses of a spacermetal all affected the measured values: none of these effects isexplained by thesimpleclassical model. Thesearchfora com-prehensive theoretical model for TMR that is answerable to allavailable experimental data is as yet an unresolved challenge.

6.3. Theoretical description of spin tunnelling

Thebasic defect in theclassical theoryof spin tunnelling is thatit treats the twoFM electrodes as independent systems [39]. InJullieres model, the electron wave functions within the barrierare treated as evanescent and are assumed not to perturb theelectron wave function in the other electrode. It also considersonly the simple case of a square barrier, i.e. one which isunbiased, or at least where the effect of the bias voltage onthe barrier shape may be ignored. As a result, this earlymodel does not predict any barrier width or height dependenceof the TMR, in clear contradiction to the measured results.

The necessity of modifying Jullieres model was first realizedby Slonczewski [44], who argued that because most practicalbarriers are relatively permeable, the wave function overlapwithin the barrier means that wave function matching mustbe considered across the entire device. Using two parabolicbands (spin up and down) shifted relative to one another bythe exchange splitting, Slonczewski solved the Schrodingerequation for the wave functions of the polarized electronstunnelling across a rectangular barrier and determined theresulting conductancefrom the current operator. The principalresultof hiscalculationwas that theeffectivepolarizationof thetunnelling electron (which when substituted into equation (13)gives the TMR) now depends on the height of the barrier Vb

through an imaginary wavevector in the barrier defined byh =

[2m(Vb EF)] (15)

by an amount

P =

k kk + k

2 kk2 + kk

. (16)

This equation has a simple physical interpretation: since themagnitude of the Fermi wavevector for a particular spin chan-nel is proportional to the density of states at the Fermi energywe can see that the first factor (k k)/(k + k) is identicalto the polarizationobtained in Jullieres classical theoryof tun-

nelling, but is now multiplied by a new factor(2kk)/(2+kk). Since ranges from 0 (low barrier) to infinity (highbarrier), we can see that in the limit of high barrier height theeffective polarization reduces to Jullieres result; however, forlow barrier height it departs significantly and can even changesign. Hence, the matching of the wave functions across thetunnel barrier offers a plausible explanation for the observeddependence of TMR on the thickness and height of the tun-nelling barrier, and hence on the choice of insulator itself.

6.4. FowlerNordheim tunnelling regime

An additional sophistication, which may be added to the

Julliere and Slonczewski models alike, is the replacement ofthesimplesquarebarrierwithatriangulartoppedbarrierwhoseshapemore accurately reflects theappliedbias acrossthe tunnel

junction. This has the effect that the tunnelling electron wavefunction in the barrier is now an Airy function rather thana simple evanescent wave. The circumstances in which thismodification is necessary (i.e. when the bias potential termis not small compared with the barrier height) is termed the

FowlerNordheim tunnelling regime. The FowlerNordheimregime manifests itself experimentally as non-linearity in thecurrent/voltage curve for the tunnel junction.

6.5. Linear response theory

Although Slonczewskis model provides a much more realistictreatment of the F/I/F interface than the classical theory oftunnelling, its drawback is that it cannot be readily extendedto more complex systems with more than one electron band.Any rigorous model of TMR, however, has to include, or atleast justify the exclusion of, the multi-orbital structure of FMelectrodes. It is for this reason that a great majority of the work

undertaken in explaining TMR over the last decade was basedon the linear-response theory of electron tunnelling.The main assumption of this theory (often referred to as

the Kubo/Landauer formalism) is that the overall conductanceineitherspinchannelforany(insulatingorconducting)samplesandwiched between two electrodes can be written in terms ofits total transmission coefficient [45]. The basis of the linearresponse theory states that the expression for the conductanceineitherspinchannelcanbewrittenintermsoftheone-electronGreens functions in the left and right planes of the tunnellingjunction, in a direction parallel to the current flow [46]

G

=

4e2

h

k

Tr(T Im gR(EF, k)

T+ Im g

L (EF, k)).

(17)The theory includes more essential components necessary toexplain the observed effects than anyearlier model. TheGreenfunctions for each of the k-states Im gR,L(EF, k), (which areclosely related to the densities of states) are multiplied by amatrix T whose elements indicate the strength of the tightbinding hopping between atomic orbitals in the left and rightplanes. Furthermore, the matrix contains an element which isresponsible for the evaluation of the dependence of TMR onthe height and width of the tunnelling barrier, as will be shownbelow. Summation over the two-dimensional Brillouin zoneand taking into account the different characteristics of the s-,

p- and d-orbitals yields an overall conductance.As an illustration, we cansimplify theformalismandeval-uate the above equation for the simple case of coherent (k andspin conserved) tunnelling through a high barrier, assumingthat the electrons originate from only one band. In this caseit is found that the current in each channel is then propor-tional to the product of the surface densities of states of thetwo electrodes (as in the classical theory of tunnelling), butthe product is scaled by the denominator which describes themutual interaction of the two electrodes due to overlap of thewave functions. Such a model has been used to perform nu-merical calculations [46] on a structure chosen to resemblea junction with Co electrodes and the result (increasing TMR

withincreasingbarrierheight Vins, saturating when Vins isoftheorder of the bandwidth of the electrodes) is in excellent agree-ment with recent experimental results of Sousa et al [47,48].

R132


13/35

Topical Review

The observed weak variation of TMR with the barrier thick-ness[49]canbeexplainedbythemodelifweassumethatmostTMR experiments are performed in the high-barrier regime.

By adding a fully realistic band structure for the FMelectrodes to the above model (i.e. by distinguishing between

s-, p- and d-orbitals), it is possible to test whether theKubo/Landauer formula predicts the correct sign for thepolarization of the tunnelling electrons. Two such calculationshave been performedone dealing with tunnelling betweenCo electrodes through a vacuum gap [46] one through asimple step barrier [50]. The results from the first study areparticularly encouragingthe calculated polarization of thetunnelling electrons as the function of the tunnelling vacuumgap show that, when the tunnelling gap is small, of theorder of the lattice constant, the conductance is dominatedby d-electrons, and the polarization has the wrong sign, i.e.P < 0 as in the classical Julliere theory of tunnelling. There isa rapid crossover, however, as the width of the gap increases,

and the polarization changes to positive values. Moreover,the calculated saturation value of 3540% is in excellentagreementwiththe observed values [51]. The crossoveroccursdue to the fact that the overlap of the d-orbitals decreases withthe increasing gap much faster than that of s-orbitals, and itis, therefore, s-electrons which determine the conductance inmost tunnelling experiments. One may, therefore, deduce thatthe observed sign of the polarization in junctions betweenferromagnets and Al2O3 suggests that the sd-hybridizationbetween the two must be weak.

Going a step further in the Kubo/Landauer formalism, it ispossibletoconsidertheeffectontheobservedTMRofdisorderin the barrier. In most tunnelling experiments, the fabricated

barriers are amorphous and therefore the assumption ofconservation of momentum parallel to the tunnelling junction(k) is not satisfied. Advanced studies of the effect of disorderon spin tunnelling using a single orbital tight binding modeland the Kubo formalism showthat, in addition to the mixing ofthe k channels, disorder also induces resonant tunnelling vialocalized electronic states [5254]. These states are formed inthe barrier in the presence of impurities or defects. Resonanttunnelling results in quasi-one-dimensional high-conductancechannels which dominate the overall conductance when thedegree of disorder is high and the barrier is thick [55]. Itfollows that the overall tunnelling current, and hence theTMR, is not only determined by the intrinsic properties of

the densities of states of the ferromagnet, but also, to a largeextent, by the properties of the insulator. As a further testof this theory, it is useful to compare its predictions with theexperiments performed by several workers [56, 57] in whicha thin layer of non-magnetic metal is inserted between one ofthe FM electrodes and the insulating barrier. According to theclassical theory, as there is no spin asymmetry in one of themetal insulator interfaces, no TMR should be observed, whichcontradicts the experimental findings. In fact, calculationsusingtheKuboformalismbyMathonandUmerski[58]predictthat the TMR should oscillate with increasing thickness of theCu interlayer in a Co junction with a vacuum gap. For a verythin interlayer this leads to a negative TMR. This effect can be

explained by considering the Fermi surfaces of Cu andCo. Forthe majority spin electrons in Co, the matching of the surfaceswith Cu is good, whereas for the minority spins they are not.

It follows that the majority spin electrons can easily cross theCo/Cu interface while the poor match for the minority spinelectrons results in the formation of down-spin quantum wellstates in the Cu overlayer [5961], whose loss of transportgives rise to a spin asymmetry of the tunnelling current, and

hence to a non-zero TMR.We can see, therefore, that the linear response theory isrelatively successful in offering explanations for the many sub-tleties in theobserved TMR effects. Many questions, however,still remain unanswered. One of the more challenging prob-lems is the true origin of the fall in TMR with the increase intemperature and applied DC bias. For the former, there arecurrently two possible explanations: one involves the mecha-nism of spin-flip scattering arising from magnetic impuritiesin the barrier [62], which, being an inelastic process increaseswith temperature; the other suggests that the increase in tem-perature leads to a reduction of the overall magnetization inthe ferromagnet due to excitations of magnons [63, 64]. At

this stage it is not clear to what extent each of these holdstrue. In a similar way, bias dependence can be accounted forby Slonczewskis model [65, 44] although the initial decreaseof TMR is much slower than observed [66]. An alternativeexplanation invokes electronmagnon scattering which (sincemagnonsarespin1quasi-particles)flipstheelectronspinintheprocess [52]. Since the phase space for electronmagnon scat-tering increases with increasing bias, the total TMR decreases.Again, at present it is unclear to what extent these mechanismsare responsible for the observed behaviour.

6.6. Refinements in the understanding of spin tunnelling

The simple Julliere tunnelling theory gives good insight intothe physical basis of spin tunnelling but is incapable ofexplaining the finer experimental detail. For example, mostspin-tunnel junctions display a bias-dependent magnetoresis-tance whose explanation needs a more sophisticated treatment[67]. Moreover, simple spin-tunnelling theory suggests thata particular spin-asymmetric material should always exhibitthe same characteristic polarization for tunnelling processesand that this polarization value is closely related to and pre-dictable from its bulk band structure. However, experimentreveals that, on the contrary, the polarization which magneticelectrodes manifest for tunnelling purposes is found to be afunction of the magnetic metal/insulator combination, not justof the magnetic metal itself. The polarization of a particularspin-electronic material may actually change sign dependingon which insulator accompanies it [68]. The explanation isthought to be that the tunnelling electrons come from the firstfew atomic layers of the metal which are hybridized with theinsulator and hence do not have the bulk band structure. Sincespin-electronic effects arealmost all interfacerelated, it is gen-erally these interface band structures which are more relevantto practical device performance.

6.7. Spin-tunnel junction resistance and heat dissipation

Spin-tunnel junctions are characterized by a real conductanceper unitarea. The associatedjunction resistancescalesroughly

exponentially (according to the very simplest theory) withthickness and barrier height. However, the net dissipationassociated with this tunnel resistance when a tunnel current

R133


14/35

Topical Review

flows is not dissipated in the junction itself but rather in theconducting material on its downstream side. Hot carriersare injected into this region from the junction insulator andthermalize rapidly due to their being high above the Fermisurface where there is a high density of empty states into which

they may scatter.

6.8. Coherent spin tunnellingresonant structures

Clearly if two separate tunnel junctions are cascaded, theirresistances add according to Ohms law. However, if thejunctions are sufficiently close so that the wave functionof the electrons entering the first junction is coherentwith those exiting the second junctionin other words thetransport is ballistic in the layer separating the junctionsthe analysis is more complex. This implies that, sincethe electrons have at least partially preserved their phasememory, they have not been properly thermalized in the

intermediate layer andtheconcept of single junction resistanceis not valid. The entire multiple tunnel structure mustthen be analysed as an entity in similar fashion to thatin which optical thin film interference filters are treated.Such resonant tunnel structures are potentially useful formaking spin-tunneldevices with a high back-to-front electricaltransmission ratio. The relevance of such considerations toquantum coherent spin electronics is discussed in section 13.7below.

6.9. Applications of spin tunnelling

By analogy to the spin valve, the spin-tunnelling junction acts

as an electronic switch whose operation again mirrors that ofa pair of crossed optical polarizers which may be switchedon and off by application of external magnetic fields. If theelectrodes are not ideal half-metallic ferromagnets, then theon/off conductance ratio is finite and reflects the majorityand minority density of states for the ferromagnet concerned.Spin-tunnel junctions as described have the added advantagethat their operation depends only on the net properties atthe interfaces and do not invoke carrier mobility; hence,unlike GMR, there is no competition between these twoeffects. Moreover, unlike all-metallic systems, theyhave lowerconductances per unit area of device and hence larger signalvoltages(ofordermillivoltsormore)arerealizableforpracticalvalues of operating current. The device characteristics suchas the size of the on resistance, current densities, operatingvoltages and total current may be tuned by playing with thedevice cross-section, the barrier height and the barrier width.In particular, spin tunnelling offers much greater flexibility inchoosing the point in the electronic band structure where thespin injection is implemented. As we shall see below, this isjust one reason why they are very promising candidates for thespin-injector stages of futurespin-electronic devices. They arealso thebasis of thenext generation of tunnelmagnetic randomaccess memories (MRAM).

6.10. Practical considerations in the fabrication of

spin-tunnel devices

Spin-tunnelling elements appear as promising candidates forintegration into future spin-electronic devices. Many limiting

factors, however, can degrade the magnitude of the observedTMR, and a great deal of research is currently in place with anaim overcome these obstacles, and optimizing the spin-tunneljunction growth for future fabrication.

For high storage density magnetic heads, a low resistance

area product of the tunnelling junction is required, of the orderof 100 (m)2 . This serves to increase the TMR signal-to-noiseratio,aswellastodecreasethetimeconstantRC involvedin the reading and writing processes, where R is the resistanceof the junction and C its capacitance. The insulating tunnelbarrier employed in magnetic elements has to be of very highquality in terms of large-scale homogeneity of its parameters(thickness and height). Due to the exponential dependenceof tunnelling probablility on thickness, the roughness of theferromagnetinsulator interface is crucial for reliable spin-tunnel operation. Degradation of surface quality leads tohotspots (localized regions of low barrier thickness throughwhich electrons preferentially tunnel), or an even worse case

to pinholes (direct contact between the FM metals throughthe barrier). A recent study by Dimopulos et al [69] using atechnique of barrier impedance scanning microscopy (BISM),developedby Da-Costa etal [70], which is extremely sensitiveto fluctuations of the barrier parameters (


15/35

Topical Review

In addition, a recent study by Tiusan et al [72] foundthat the micromagnetic configuration within the FM layershas a strong impact on transport properties of magnetic tunneljunctions. In this study an artificial ferrimagnetic (AFi) trilayerstructure was used as a magnetically hard subsystem. The

fluctuations in magnetization in the AFi were found to affectthe resistance of the tunnel junctions and were fully reflectedin the shape and amplitude of the tunnel magnetoresistancesignal. Optimizing the micromagnetic structure, therefore, isanother aim of successful spin-tunnel device implementation.

7. Hybrid spin electronics

Although the early Johnson transistor is a useful and versatiledemonstrator device, it has practical limitations. The voltagechanges measured are small and it has no power gain withouttheadditionof twoextra electrodes anda transformer structure.The underlying design problem with the device is that it

is entirely Ohmic in operation simply because all of itsconstituentparts are metals. Moreover, the source impedancesof such devices aresmall, particularly those with perpendicularstructures. Optimizing noise figure when matching smallsource impedances to conventional electronics is difficult andrequires impedance transformation which is frequently bulkyand impractical.

Clearly another technologyprogressionis needed, namelythe introduction of hybrid spin electronics. This is thedevelopment of integrating spin-asymmetric materials withsemiconductors, thereby unleashing a wide range of noveldesign possibilities which exploit such semiconductor featuresas voltage blocking, depletionzones,diffusioncurrents andthe

tunnel effect in semiconductors.

7.1. The Monsma transistor

The first hybrid spin-electronic device was the Monsma[7375] transistor produced by theUniversity of Twente whichwas fabricated by sandwiching an all-metal spin-valve devicebetween two layers of silicon. Three electrical contacts aremade to the spin-valve base layer and to the respective siliconlayers. Thespinvalveismoresophisticatedthanthatillustratedin figure 4 and comprises multiple magnetic/non-magneticbilayers, but the operating principle is the same. Schottkybarriersformattheinterfacesbetweenthesiliconandthemetal

structure and these absorb the bias voltages applied betweenpairs of terminals. The collector Schottky barrier is reversebiased and the emitter Schottky is forward biased. This hasthe effect of injecting (unpolarized) hot electrons from thesemiconductor emitter into the metallic base high above itsFermi energy. The question now is whether the hot electronscan travel across the thickness of the base and retain enoughenergy to surmount the collector Schottky barrier. If not, theyremain in the base and get swept out of the base connection.

By varying the magnetic configuration of the basemagnetic multilayer, the operator can determine how muchenergy the hot electrons lose in their passage across the base.If the magnetic layers are antiferromagnetically aligned in the

multilayer, then both spin types experience heavy scattering inone or other magnetic layer orientation, so the density of bothspin types with energy greater than thecollector barrier EC as a

Figure 20. The Monsma transistor: the first attempt to integrate FMmetals with silicon (a); (b) shows the density as a function ofdistance into the base for majority hot spins with energy greater thanthe collector barrier. The thick line corresponds to anantiferromagnetically aligned multilayer and the thin line to FMalignment. There is a clear trade-off between the size of thecollected current and the sensitivity of collector current to appliedmagnetic field.

function ofdistance into thebase follows theheavyexponentialdecay curve of figure 20. On the other hand, if the magneticmultilayer is in an applied field and its layers are all aligned,one spin class gets scattered heavily in every magnetic layer,whereas the other class has a passport to travel through thestructure relatively unscathed and the density (with E > EC)versus distance of this privileged class follows the thin curve.It may thus be seen that for parallel magnetic alignment, morespins with energy greater than EC impinge on the collectorbarrier and the collected current is correspondingly higher.Onceagain,liketheJohnsondevice,wehaveatransistorwhoseelectrical characteristics are magnetically tuneable. This time,however, the working voltages and the magnetic sensitivity

are sufficiently large that, with help from some conventionalelectronics, this is a candidate for a practical working device.It may be seen from comparison of the two traces of

figure 20 that there is a trade-off to be made in determining theoptimum base thickness. A thin base allows a large collectorcurrent harvest but affords little magnetic discrimination.A thick base, on the other hand, means a large factor betweenthe collector currents corresponding to the two magnetic statesof the multilayer but an abysmally small current gain (the lowcurrent gain has always been the Achilles heel of metal basetransistors, and is probably the main reason for their fall fromfavour as practical devices despite their good high frequencyperformance due to the absence of charge storage in the base).

An interesting feature of the Monsma transistor is that thetransmission selection at the collector barrier is done on thebasis of energy. Thus thescattering processesin thebase whichdetermine collected current are the inelastic ones. Elasticcollisions which change momentum, but not energy, are ofless significance (though spin transmission at the interfaceis confined to a cone of k-vectors whose incident angleslie within certain limits). This contrasts with the functioningof a spin-valve-type system in which all momentum changingcollision processes have the same status in determining deviceperformance [76].

7.2. Spin transport in semiconductors

The Monsma transistor represents a very important step in theevolution of spin electronics. It is thefirst combination of spin-selective materials with semiconductors. However, as yet, the

R135


16/35

Topical Review

semiconductor is used only to generate barriers and to shieldthe spin-dependent part of the device from electric fields. Torelease the full potential of hybrid spin electronics, we needto make devices which exploit spin-dependent transport in thesemiconductor itself.

7.3. The SPICE transistor

The current gain of a conventional bipolar transistor [77, 78]is, in part, due to the screening action of the junctions eitherside of the base which absorb the bias voltages and leavethe base region relatively free of electric fields. The currentwhich diffuses across the base is primarily driven by carrierconcentration gradient and to a rather lesser extent by electricfield. The randomness associated with concentration-drivencurrent flow helps to improve the current gain. The carriersinjected by the emitter are forced to wander towards the basealong the top of an extended cliff in voltage, at the bottom ofwhich lies the collector. Of order, say, 99% of the carriersstumble over the cliff and are swept out the collector and theremaining 1% make it to the base connection; this gives a verysatisfactory current gain = Ic/Ib of 99.

Implementing spin-polarized current transport in asemiconductor enables a new concept in spin transistordesignthe spin-polarized-injection current emitter (SPICE)device in which the emitter launches a spin-polarized currentinto the electric field screened region and a spin-selectiveguard-railalongthetopofthecliffdeterminesifthesepolarizedcarriers are allowed to fall into the collector or not. Thuswe have a device with a respectable current gain from whichpower-gain may easily be derived, but whose characteristicsmayagain be switched by manipulating the magnetic guardrailvia an externally applied magnetic field. A wide variety ofdesignsarepossiblewhichanswertothisgeneralprinciple. Forexample, the emitter and collector interfaces may be realizedby pn junctions, Schottky barriers or spin-tunnel junctionsand the geometry of the device may be adjusted to allow agreater or lesser degree of electric field driving component tothe diffusion current in the base depending on the application.This design type is analysed in more detail in section 7.13.

7.4. Measuring spin decoherence in semiconductorsby

direct injection

The crucial question which needs to be answered in order to

realize this kind of spin transistor is whether spin transportis possible at all in semiconductors, and, if so, whether it ispossibleoverthesortofphysicaldimensionsonwhichatypicaltransistor is built. In other words, we need an estimate of thespin diffusion length in a typical semiconductor. A subsidiaryquestion concerns the role of dopants in the semiconductor andwhether they introduce spin-orbit scattering which militatesagainst the spin transport by reducing the spin-flip times.

Animmediatewaytoaddressthisquestionistodirectspininject into a semiconductor [77] and observe the polarizationof the current which emerges on the other side. Figure 21shows such an experiment. Doped channels of silicon withvarious dopant types and concentrations and of different

lengths (from 1 to 64 m) were contacted at each endwith differentially magnetizable cobalt pads of well-definedmagnetizing behaviour. The transport results shown in

Figure 21. Geometry of an experiment (dimensions in microns) toinvestigate the possibility of spin injection across aFM/semiconductor interface (a). The transport curves (b) suggestthat the spin diffusion length is of order tens ofm, but that thespin-injection process at the interface is highly inefficient.

figure 21 are insensitive to magnetic field direction, haveeven symmetry (thereby eliminating AMR and Hall effectas a possible cause) and they are compatible with theobserved domain magnetization processes for the cobalt pads.They appear to correspond to spin transport through thesemiconductor, and as such they correlate well with earlierexperiments [79] using nickel injectors.

7.5. Spin injectioninterface effects

Interestingly, however, the spin transport effects are of theorder of a few per cent at best, yet the effect decays onlyvery slightly with silicon channel length and was still wellobservable for 64 m channels. The message would seem tobe that the spin diffusion length in silicon is manytensofm atthe least, but that the spin-injection process at the metal/siliconinterface is highly inefficient (see below).

7.6. Measuring spin decoherence in semiconductors by

optical polarized carrier generation

A very beautiful direct measurement of semiconductor spindiffusion length has been performed by avoiding the spin-injection problem [8082, 84] and generating the spin-polarized carriers in the semiconductor itself (figure 22).Gallium arsenide was used as the host which has the propertythat, when pumpedwith circularly polarizedlight, theselectionrules are such as to populate the conduction band withpredominantly one spin type.

These spins can be made to precess by application of asmall magnetic field. The resulting precessing magnetization

is then detected using optical Faraday rotation using a probebeam from the same optics as provides the pump. Themagnetization drifts under the application of a driving electric

R136


17/35

Topical Review

Figure 22. Lateral drag of spin coherence in gallium arsenide measured by Faraday rotation as shown in (a). Additional population iscreated every time a pulse hits the sample as shown in (b). The electrons in each new population drift along the magnetic field and the spatialextent of each spin population can be assessed as shown in (c). Spin transport can be observed on length scales exceeding 100m (afterKikkawa and Awschalom [84]).

field and the spatial decay in precession signal gives a measureof the spin diffusion length. The results are of order manytens of m, in accordance with the silicon direct injectionexperiment discussed above.

Thus it would seem beyond doubt that the spin diffusionlength in semiconductors is adequate for the design andrealization of SPICE-type transistor structures, providedthat means are provided for efficient delivery of the initialspin-polarized current.

7.7. Allowed non-equilibrium spin configurations in a

semiconductor

The origins of the differences in spin diffusion betweensemiconductors and metals are: (i) the much greater spinrelaxation lifetime in semiconductors, (ii) the ineffectivenessof screening in semiconductors relative to metals and (iii) thepossibility of controlling whether carriers in a band aredegenerate or not by small perturbations (e.g. electric fieldsor doping). In recent work Flatte and Byers [83] consider theconsequences of the latter two factors in order to gain insightinto the different behaviour of spin diffusion in doped andundoped semiconductors.

Their findings show that spin diffusion in doped and

intrinsic semiconductors is qualitatively different. Thebasic reason for this is as follows: whereas a spin packetin an intrinsic semiconductor must be a multiple-band

disturbance, involving inhomogeneous distributions of bothelectrons and holes, in a doped semiconductor a single-banddisturbance is possible. Therefore, for n-doped non-magneticsemiconductors the single-band spin-packet excitations arepossible in the conduction band whose diffusion constantis much larger than for spin packets in undoped materials,since the relatively immobile holes are no longer involved.This explains the anomalously large spin diffusion recentlyobserved in n-doped GaAs at 1.6 K [84].

In n-doped FM and semi-magnetic semiconductors themotionof spin packets polarizedantiparallel to theequilibrium

carrier spin polarization is predicted to be an order ofmagnitude faster than for parallel polarized spin packets.These results are reversed for p-doped semiconductors. Theresulting different sub-band density profiles are summarizedin figure 23.

7.8. Spin injection into three-dimensional semiconductors

Although it has been experimentally established beyondreasonable doubt that spin diffusion lengths in semiconductorsare more than adequate [84] to enable construction ofsemiconductor spin-electronic devices, high yield direct spininjection from FM metals into semiconductor has so fareluded

experimenters. To date, attention has focused on injectioninto two-dimensional semiconductors since this is the idealsystem for realization of the Datta and Das [85] proposed

R137


18/35

Topical Review

Figure 23. Spin sub-band density profile of (a) charge polarizationpackets in an n-doped semiconductor, (b) spin polarization packetsin an undoped semiconductor and (c) spin polarization packets in ann-doped semiconductor (after Flatte and Byers [83]).

Figure 24. Ferromagnetic/semiconductor interface.

transistor. Experiments have been performed which purportto show spin injection into two-dimensional semiconductors

[86] though their interpretation is considered ambiguous insome quarters [8789]. More recently, theoretical workhas appeared [90, 91] which explains why direct injectioninto two-dimensional semiconductors is expected to bedisappointing.

The fundamental problem is seen in figure 24 where in theabsence of interface scattering the electrochemical potentials(and hence ) are continuous at the interface. This meansthat thespin-accumulationdensity (whichscales as thepseudo-densityofstates[91])isverysmallinthesemiconductor:hencealso is the spin-polarized current through the interface whichfeeds it.

Rashba [92] has proposed that spin-tunnel injection is a

solution to the semiconductor spin-injection problem. Recenttheories conclude that spin-tunnel injection is efficient becauseit releases us from having to satisfy the boundary conditions

on electrochemical potential continuity and, in so doing, com-pletely changes the physics of the problem. However, in con-trast to popular thinking, Borges et al [91] point out that, incertain circumstances, the tunnelling configuration is capableof delivering the worst spin injection of all due to the reversal

of the chemical potential divergences either side of the tunnelbarrier. This situation arises for the case of very thin or discon-tinuous tunnel barriers which is precisely the case expected ifrealization of a metal semiconductor direct contact is marredby oxidation or other surface contamination. In this case bothdirect-injected and tunnel-injected currents exist and competewith each other since their spin polarizations are opposed.

7.9. Methods of increasing direct spin-injection efficiency:

the promise of magnetic semiconductors

With these problems in mind, it is interesting to examine theresults of an experiment which injects spin-polarized carriersfrom a magnetic semiconductor into a normal semiconductorlightemitting diode(LED)structure [9396]. The polarizationof the injected carriers is dependent on the magnetizationdirection of the magnetic semiconductor which supplies them.This is reflected in the polarization of the light emitted by theLEDits polarization is related to the spin of the electronswhich cause it via the selection rules as discussed in theexperiment illustrated in figure 25.

The polarization of the light emitted correlates wellwith the hysteresis loop for the magnetic semiconductor anddecays with temperature exactly as the magnetic momentof the magnetic semiconductor, leaving little doubt thatsuccessful spin injection has been achieved. The percentageinjection achieved here is more favourable that has beenpossible by direct injection from metals and it may be thatmagnetic semiconductors have an important role to play infuture spin-electronics development, notwithstanding the non-negligible materials problems which they pose. Very recentdevelopments [97,98] would seem to promise workable high-temperature magnetic semiconductor materials.

Otherwise, experiments suggest that spin-tunnel injectioninto semiconductors is a promising technique which offershigher injection efficiency than direct spin injection [99].Further results in this area are imminent.

7.10. Conditions for high-efficiency spin injection

Itmaybeseen[91]thatthegreatenemyofOhmicspininjectionis loss of polarization in the FM/PM structure, either by spinflipping at the interface or within a spin diffusion length of theinterface. The key to success is then to suppress this spin fliploss insofar as is practical. The origin of interface spin flip isa difficult subject, as yet incompletely understood. However,recipes may be offered for spin-flip suppression in the FMspin-accumulation layer.

First, for Ohmic contact between a FM and a PMmaterial with a similar density of states, the spin-flip lossesare comparable in the two accumulations and the injectionefficiency is high, hence the success of the early metalmetalGMR devices.

However for direct Ohmic contact between FM and PMwith a small density of states such as a semiconductor, spin-flip loss in the FM dominates and spin-injection efficiency is

R138


19/35

Topical Review

Figure 25. Electrical spin injection into an epitaxially grown FM semiconductor is shown in (a); (b) shows the photoluminescence of thedevice as a function of energy. In (c) the polarization of the emitted optical radiation decays in accordance with the variation of thesemiconductor magnetization with temperature (after Ohno et al [95]).

Figure 26. Position dependence of the electrochemical potentials and near a HMF-N interface. The dashed line in N represents0; in the HMF, 0 = F (after van Son et al [100]).

poor. Theexceptionisthecaseofthehalf-metallicferromagnetwhere FM spin-flip loss is suppressed by the complete absenceof final states for spin flipping.

Analysis of interfacesbetween half-metallic ferromagnetsand paramagnets is subtly different. The equations again takethe form of equation (9) except that we assume the sameD for each spin channel but different and where is vanishingly small. The current continuity condition thendemands that the values of and are weighted in theratio of the densities of states /. In practice this means is undeviated, whereas deviates over a spin diffusionlength to match its PM equivalent at the interface. Themost important consequence is that spin-flip loss is totallysuppressed in the FM and this has interesting consequencesfor FM semiconductor spin injection (see section 7.8).

If the FM is not a half-metallic ferromagnet, thendifferenttacticsmustbeusedtoimplementhigh-efficiencyspininjection into the semiconductor which do not involve direct

Ohmic contact. In the Ohmic contact case the polarization ofthe injected current is defined in the bulk FM and the gameis not to lose it (by spin flip in the FM) before it arrives inthe PM. The new approach is to insert a thin layer of somematerial between FM and PM which takes over the role ofdefining the injected polarization independently of what ishappening in the bulk FM and delivers that polarization intactto the PM. Usually this intermediate layer is a tunnel barrier ofsome variety. In the next section we consider three particularcases of the intermediate layer configuration: a non-magnetictunnelling barrier, a magnetic tunnelling barrier anda Schottkybarrier.

7.11. Viable semiconductor spin-injection configurations

As discussed above, spin injection by direct Ohmic contactbetween FM and semiconductor is unsatisfactory except inthe extreme case of a HMF. Viable alternatives include FMinjection with intermediate layers and/or spin filters.

7.11.1. Non-magnetic tunnel barrier. The simplest interme-diate layer injector is a FM/non-magnetic tunnel bar-rier/semiconductor sandwich (figure 27). Comparison ofthe electrochemical potential diagram for this configurationwith that of figure 24 shows that insertion of the interme-diate layer changes the physics beyond recognition. Thekey to the successful operation of the new arrangement isthat the voltage dropped on the tunnel barrier is very largecompared with the electrochemical potential divergences andhence totally controls the injected current and its polariza-tion. Indeed, for the FM type chosen in this example (D =D, d d, s = s), the relative signs of the FMand semiconductor spin accumulations are actually inverted

between figure 24 and figure 27. Spin-flip loss still occursin the FM spin accumulation but is now of no consequencesince the injected polarization is now independent of D, D

R139


20/35

Topical Review

Figure 27. FM/tunnel barrier/semicond

Date post:	03-Apr-2018
Category:	Documents
Upload:	gokaran-shukla
View:	217 times
Download:	0 times

Review on Spin _electronics

Documents