University of Groningen Charge and spin transport in Nb ......4 Chapter 4 Electric ﬁeld control of...

University of Groningen

Charge and spin transport in Nb-doped SrTiO3 using Co/AlOx spin injection contactsKamerbeek, Alexander

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4

Chapter 4

Electric field control of spin lifetimes inNb:SrTiO3 by spin-orbit fields

Abstract

We show electric field control of the spin accumulation at the interface of the oxide semi-conductor Nb:SrTiO3 with Co/AlOx spin injection contacts at room temperature. Thein-plane spin lifetime τ‖ as well as the ratio of the out-of-plane to in-plane spin lifetimeτ⊥/τ‖ is manipulated by the built-in electric field at the semiconductor surface, withoutany additional gate contact. The origin of this manipulation is attributed to Rashba Spin-Orbit Fields (SOFs) at the Nb:SrTiO3 surface and shown to be consistent with theoreticalmodel calculations based on SOF spin flip scattering. Additionally, the junction can beset in a high or low resistance state, leading to a non-volatile control of τ⊥/τ‖, consistentwith the manipulation of the Rashba SOF strength. Such room temperature electric fieldcontrol over the spin state is essential for developing energy-efficient spintronic devicesand shows promise for complex oxide based (spin)electronics.

This chapter is based on:

A. M. Kamerbeek, P. Hogl, J. Fabian, T. BanerjeePhys. Rev. Lett. 115, 136601 (2015).

4

74 4. Electric field control of spin lifetimes in Nb:SrTiO3 by spin-orbit fields

4.1 Introduction

Recent demonstrations of electrical injection and detection of spin accumulation inconventional semiconductors enhances the prospects for realizing a spin based Field-Effect-Transistor (S-FET) [1–5]. A key requirement for S-FETs is the possibility tomanipulate spin transport in the semiconducting channel by an electric field, at roomtemperature, which till date remains elusive. An attractive way to realize this is theintegration of a gate electrode which tunes the spin-orbit coupling in the semicon-ducting channel via an electric field perpendicular to it [6, 7].

In this context, the emerging class of oxide materials and their heterostructuresprovide an attractive platform for designing electronic interfaces [8–11]. Exploitingtheir intrinsic correlation effects allows tuning of key transport properties such ascharge density, mobility, permittivity and ferromagnetism, essential for electric fieldtuning of (spin)electronic transport. Although electric control of magnetism in engi-neered interfaces of oxide materials have been predicted and demonstrated [12, 13],electric field control of spin transport in oxide semiconductors is largely unexplored,in spite of theoretical predictions of long spin lifetimes in n-doped SrTiO3 [14].

In this work, we demonstrate a strong influence of the built-in electric field, closeto the interface, on the spin lifetimes in an oxide semiconductor - Nb-doped SrTiO3.Semiconducting SrTiO3 is a commonly used substrate in oxide electronics and ex-hibits much richer electronic states, as compared to conventional p-band semicon-ductors, due to the narrow bandwidth of the d-orbital derived conduction bands. Weobserve a strong dependence of the Hanle line shape on the applied bias, unlike inother electrical injection and detection experiments with conventional semiconduc-tors such as Si, Ge or GaAs, using a three-terminal geometry [3, 4, 15]. We find thatthe extracted in-plane spin lifetime changes by an order of magnitude from 3 to 15ps, with decreasing electric field strength at the spin injection interface.

Similarly, the spin voltage anisotropy V⊥/V‖ (the voltage generated by out-of-plane V⊥ over in-plane spins V‖) exhibits a systematically increasing trend (from 0.5to 0.75) when decreasing the interface electric field. These observations are shownto be consistent with a theoretical model, where the spin lifetime is determined byspin flip events due to a Rashba Spin-Orbit Field (SOF). We further demonstrate, thepossibility to modestly modulate the SOF strength, by using the electro-resistanceeffect prevalent at metal/Nb:SrTiO3 interfaces. These results are a first demonstrationof realizing control (via an electric field tuned SOF) over the spin accumulation in asemiconductor at room temperature, a vital ingredient for spin logic.

4

4.2. Results 75

4.2 Results

For this work, 0.1 wt% Nb-doped SrTiO3 (Nb:SrTiO3) single crystal substrates fromCrystec GmbH are used. SrTiO3 has a perovskite crystal structure which becomesn-type conducting by doping Nb5+ at the Ti4+ site. The crystal has a very largepermittivity εr of∼300 at room temperature and is a non-linear dielectric [16]. Typicalroom temperature electron mobilities µ are around 10 cm2/Vs which results in acharge diffusion constant Dc of around 0.2 cm2/s using the Einstein relation σ =nqµ = q2νDc with n the charge carrier density, µ the mobility and ν(E) the densityof state = 0.615 states/Ry·cel (obtained from Ref. [17]). Here I would like to point outthat this estimate of D is a purely theoretical estimate and values one or even twoorders of magnitudes larger have been used in the work of Ref. [18] 1

The measurement schematic of the three-terminal geometry is shown in Fig. 4.1(a).Prior to deposition of the spin injection contacts of Co/AlOx in an e-beam evaporatoran in-situ O2 plasma is used to clean the Nb:SrTiO3 surface. The spin injection contactsare formed by ∼10 A Al, which is in-situ plasma oxidized followed by subsequentgrowth of 20 nm of Co. The contact sizes range from 50×200 up to 200×200 µm2 andare separated by at least 100 µm. A sketch of the energy landscape at the interface isgiven in Fig. 4.1(b). The charge transport across the junction is dominated by fieldemission through the tunnel barrier and Schottky barrier [19].

Room temperature Hanle measurements are performed by sourcing a constantbias current between contact 1 and 2 and measuring the change in voltage betweencontacts 2 and 3 while applying a perpendicular to plane magnetic field. At zero fieldthe injected spins point in-plane due to the in-plane magnetization of Co. The resultsare shown in Fig. 4.1(c) for negative current bias (spin injection) and Fig. 4.1(d) forpositive current bias (spin extraction).

As shown in Fig. 4.1(d), with increasing positive bias the lineshape shows a sys-tematic trend of narrowing. In this regime an upturn of the spin voltage starts toappear at higher fields, (as marked by V⊥), while this is not observed at low positivebias or negative bias. The applied field rotates the magnetization of Cobalt out-of-plane (completed around 1800 mT) which coincides with saturation of the lineshape.

When spin drift is neglected, the change of the spin voltage in a three-terminalHanle measurement can be described as follows:

∆V = V⊥ cos2(θ) +V‖ sin2(θ)√

2

√1 +

√1 + (ωLτ‖)2

1 + (ωLτ‖)2, (4.1)

with ωL = (egB/2m∗), the Larmor precession term (g = 2,m∗ = me), θ = θ(B) the

1This is based on the following: they mention a theoretical upper limit of RsA = 0.5 kΩ µm2 = ρλ. With acarrier density of∼2× 1019 cm−3, ρ should be between 0.01 and 0.1 Ω cm. Using their experimental upperlimit for τ = 100 ps we find they must have used Ds = 25 (ρ = 0.1 Ω cm→ λ = 0.5 µm) and 2500 cm s−1 (ρ= 0.01 Ω cm→ λ = 5 µm). They do not mention why they used these values (assuming this is correct).

4


angle between the surface normal and the magnetization vector of cobalt which is afunction of the applied magnetic field (see Fig. 4.1(a) right top), τ‖ the in-plane spinlifetime, V⊥ and V‖ the spin voltage developed by the out- and in-plane spin accumu-lation, respectively. The out(in)-plane spin voltage is given by V⊥,‖ = P 2Rsλ

⊥,‖sf /2W

with the out(in)-plane spin relaxation length λ⊥,‖sf =

√Dsτ⊥,‖ and W the contact

width. If the polarization of the electron P and the sheet resistance RS do not stronglydepend on magnetic field the relation between spin voltage and spin lifetime anisotropybecomes V⊥/V‖ =

√τ⊥/τ‖. The solid lines in Fig. 4.1 are fits using Eq. 7.1 which show

good agreement with the data.The fit values for τ‖, V‖, V⊥ and their ratio are plotted as a function of the junc-

tion voltage as shown in Fig. 4.2. We plot the extracted parameters against junctionvoltage instead of bias current as the junction voltage relates to the electric field atthe interface. Both the in- and out-of-plane spin voltage show a superlinear trendfor increasing positive voltage while a saturating (smaller) spin voltage is observedat negative voltage (Fig. 4.2(a)). This is consistent with the observed change of τ‖ asshown in Fig. 4.2(b). To obtain an order of magnitude estimate of λ‖ we can assumeDs =Dc and find it is around 10 nm. The spin voltage anisotropy, defined as V⊥/V‖, atpositive bias shows an increasing trend with positive junction voltage and saturatesaround +500 mV (Fig. 4.2(c)). As the fit to the Hanle lineshape is quite insensitive toa large change in the anisotropy ratio both at low positive and negative bias there isno clear restriction on the fit ratio of V⊥/V‖ (hence the increased error at low positivebias). Given the trend in Fig. 4.2(c) we have set V⊥ = 0.5 V‖ at negative bias whichcan be considered as the upper limit of the ratio (see Supplemental Material [20] fordetails).

Note that Eq. 7.1 implies that for low spin lifetimes (τ‖ ωL|B = MS ) the cobaltmagnetization is rotated from in- to out-of-plane by the magnetic field while thespins are hardly dephased. Therefore the voltage purely reflects the difference inspin voltage generated by in- versus out-of-plane spins. To illustrate this, we havesimulated the change of the lineshape using Eq. 7.1 in Fig. 4.1(e). We vary the in-planespin lifetime from 50, 5, 2.5 to 0.5 ps, set V⊥ = 0.5 V‖ and the saturation magnetizationMS of the cobalt electrode at 1800 mT. The overall shape corresponds very well to theobserved behavior in Fig. 4.1(c) and (d).

The observed response as shown in Fig. 4.2 is different from the findings in Si,Ge or GaAs [3, 4, 15] and even those based on oxides such as the LaAlO3/SrTiO3

2 DEG or highly n- or p-doped SrTiO3 [18, 21, 22]. From the Hanle measurements,we observe a linewidth which is an order of magnitude broader and interestingly,exhibits a systematic evolution over the measured bias range. This systematic changeof the in-plane spin lifetime and spin voltage anisotropy with junction voltage hasnot been reported in earlier studies. Recently, it has also been shown that a Lorentzianmagneto-resistance effect can occur when charge transport occurs via defect states

4

4.2. Results 77

0

50

100

-375

-300

-225

-150

-75

0

- I (mA) 5 1 0.3 0.2 0.1 0.05

+I (mA) 0.2 0.5 1 3 5

∆V

µV)

(∆V

µV

)(

Magnetic Field (mT)-2000 -1000 0 1000 2000

∝ V||

-2000 -1000 0 1000 20001.00.80.60.40.20.0

Magnetic Field (mT)

2.5

50 5 0.5

∆V (

arb.

)

∝ V

VCoMAlOx

Nb:SrTiO3

(a)

1 32

Co AlOX Nb-SrTiO3

EF+eV-eV

(b)

(c)

(d)

(e)

B Mθx

Figure 4.1: (a) Three terminal device schematic, right top defines the angle θ as in Eq. 7.1. (b)Potential energy diagram at the spin injection interface. (c) Three-terminal Hanle measure-ments at negative bias and (d) at positive bias. Narrowing of the linewidth and the appearanceof an upturn in ∆V at higher magnetic fields is observed with increasing positive bias. Around1800 mT ∆V saturates as M has rotated out-of-plane. (e) Simulation of Hanle measurementusing Eq. 7.1 shows good agreement with the observed trend in panel c and d when assuming achanging spin lifetime. The numbers are the spin lifetime in ps used to simulate the lineshapes.

inside the tunnel barrier in the presence of random local magnetic fields [23]. We em-ploy similar Co/AlOx contacts but observe much broader linewidths and systematiclineshape changes with bias. Therefore, we attribute the observed response to spinaccumulation in the semiconductor (see Supplemental Material [20] for extendeddiscussion).

We believe that in our devices, the observed response deviates from the reportedworks due to the difference of the potential landscape at the spin injection interface.

4


750

500

250

0

-25020

15

10

5

-400 -200 0 200 400 600 -400 -200 0 200 400 600

1

0.75

0.50

0.25

0

V⊥

/ V||

Junction Voltage (mV) Junction Voltage (mV)

τ ⊥/τ

||

∆V

µV)

( τ ||

(ps)

1

0.75

0.50

0.25

0

0

(a)

(d)

(c)

(b)

V⊥

V||

Figure 4.2: Spin voltages and lifetime obtained from fits to Hanle data from several devicesas function of junction voltage. (a) In-plane (V‖) and out-of-plane (V⊥) spin voltage. (b) In-plane spin lifetime τ‖. (c) The ratio of the out/in-plane spin voltage. (d) The spin lifetimeanisotropy. It increases systematically with junction voltage. Different symbols represents datafrom different devices in panel b, c and d.

We have tailored the interface such that an appreciable built-in electric field exists atthe semiconductor surface due to the thin Schottky barrier. This field can be increasedor decreased by applying a negative or positive bias to the junction (See Fig. 4.1(b)).

spin-drift The presence of spin-drift can broaden the Hanle lineshape and hencelead to a bias dependent in-plane spin lifetime. Due to the low semiconductor resis-tivity, low mobility and thick semiconductor bulk spin-drift effects are not expected.This can be shown using a rough calculation. Similar to the in-plane spin diffusionlength λ

‖sf =

√Dsτ‖ a spin-drift length λd = Ds/vd can be defined [24]. Spin drift

does not play a role when λd λ‖sf . To estimate vd = µE = 1 cm s−1 where we used µ

= 10 cm2 V−1 s−1 and estimated the electric field E = ρI/A = 0.01× 5× 10−3/ 5× 10−4

= 0.1 V cm−1 with ρ the semiconductor channel resistivity in Ω cm, I the bias currentin A and A the contact area in cm2.

4

4.2. Results 79

0.1 1 10 1000.00

0.25

0.50

0.75

1.00

Z

= 0 Z = 1

Z = 10

J sf

λα

Junction Voltage (V)0.8 0.6 0.4 0.2 0.0 -0.2 -0.4

0.0

0.1

0.2

0.3

0.4

1/τ

(ps-1

)increasing E

Figure 4.3: Calculated normalized spin-flip current Jsf as function of Rashba spin-orbit cou-pling λα. In-plane (dashed lines) and out-of-plane (solid lines) magnetization with spin polar-ization P = 0.4 and bias voltage eV/µF = 0.05 for different barrier potential Z. Inset: Exper-imental in-plane spin-flip rate 1/τ‖. Reducing the junction voltage from positive to negativeincreases the internal electric field.

We then find λd = 0.2 cm which is much larger than the estimated λ‖sf of 10 nm.

Furthermore, as stated in the published manuscript [25] the increase of the spin life-time due to spin drift effects are ruled out as the lifetime should increase with reversebias, opposite to what we observe [24, 26–28]. We would like to point out that thiscomment is slightly misleading since spin drift will always lead to a broadening ofthe measured Hanle curves, irrespective if this is up- or down stream. This can beseen by inspecting the solution to the Bloch equation including spin-drift which onlycontaines squared terms of the drift-velocity. A more correct statement would be thatthe asymmetric change of the extracted spin lifetime is not compatible with spin-drifteffects as the extracted in-plane spin lifetime using Eq. 7.1 in case of spin-drift effectsshould be symmetric as function of applied current bias.

The observed increase of τ‖ and τ⊥/τ‖ with bias occurs when decreasing the elec-tric field strength at the interface. The most likely mechanism driving such changesis spin-orbit fields (SOFs). Large (electric field tunable) Rashba effects have been ob-served for 2DEGs at the LaAlO3/SrTiO3 interface or SrTiO3 surface [29–31]. Due tobreaking of the crystal inversion symmetry, it is expected that a Rashba like SOF isalso present at such spin injection interfaces. To ascertain the influence of RashbaSOFs at the interface, we consider a model with ferromagnet (z < 0) and normalmetal (z > 0) semi-infinite regions separated by a flat interface at z = 0, with poten-tial barrier and Spin-Orbit Coupling (SOC) scattering [20]. From the model we extract

4


spin-flip probabilities for electrons tunneling through the interface. These results areindicative of the experimentally observed spin dephasing of steady state spin accu-mulation induced by Rashba SOFs and allow a qualitative comparison of the maintrends of characteristic quantities. The model Hamiltonian reads H = H0 +HB with

H0 = −~2

2∇[

1

m(z)

]∇− µ(z)− ∆xc

2Θ(−z)m · σ. (4.2)

where H0 contains the kinetic energy and the Zeeman splitting in the ferromagnet.The unit magnetization vector is m = [sin Θ cos Φ, sin Θ sin Φ, cos Θ], σ are the Paulimatrices, ∆xc is the exchange spin splitting in the ferromagnet (Stoner model), m(z)

is the effective mass and µ(z) the chemical potential. The interfacial scattering is mod-eled as HB = (V0d+ w · σ) δ(z), where V0 and d are the barrier height and width [32],while w = α(ky,−kx, 0) is the Rashba SOC field [33, 34]. For simplicity, we considerequal Fermi wave vector kF and mass m in all regions [20]. The normalized spin-flipprobability current along the interface is [20]

Jsf = Pjtr−σ

jtrσ + jtr−σ

∣∣∣∣σ=↑

+ (1− P )jtr−σ

jtrσ + jtr−σ

∣∣∣∣σ=↓

(4.3)

with the spin polarization P = (∆xc/2) /µF with µF the chemical potential in theferromagnet and the transmitted probability current jtrσ , where σ =↑ (↓) correspondsto spin parallel (anti-parallel) to m. The strength of the potential barrier is denotedby Z = V0dm/

(~2kF

)and the strength of Rashba SOC by λα = 2αm/~2.

The calculated spin-flip currents are shown in Fig. 4.3. With increasing SOC thespin-flip current first slowly increases, shows a rapid upturn and finally saturates. Thetransitions at certain λα between these three trends depend on the potential barrier Z.In our experiments, the tunnel barrier employed corresponds to Z ≈ 10 [35]. Usingthe proportionality of spin-flip current and spin-flip rate, Jsf ∼ 1/τ , we compare thecalculated trend to the experiment (inset Fig. 4.3). An increase of 1/τ is observedwhen going from positive to negative junction voltage, corresponding to an increaseof the interface electric field. The similar trend of the model calculations and theexperimental 1/τ plot strongly indicates the presence of Rashba SOFs which areamplified by the applied voltage. In the model we tune the SOC strength by thephenomenological parameter λα [20].

This hypothesis is further strengthened by the anisotropy of the spin lifetimeτ⊥/τ‖. In absence of a Rashba SOF a ratio τ⊥/τ‖ = 1 is expected while the theoreticalminimum, at strong Rashba SOFs, is τ⊥/τ‖ = 0.5. As shown in Fig. 4.2(d) τ⊥/τ‖ indeedexhibits an increase from∼0.25 to 0.55 consistent with a decreasing SOF strength. Theratio however is largely below the theoretical limit of 0.5, indicating other anisotropicspin dephasing mechanisms to be present.

4

4.2. Results 81

0 200 400 600 8000.00

0.25

0.50

0.75

1.00

V / V

||

Junction Voltage (mV)

0

5

10

15

20

τ (p

s)

Figure 4.4: Bias dependent change in the spin voltage anisotropy (V⊥/V‖) (black circles, leftaxis) and the in-plane spin lifetime (τ‖) (red triangles, right axis). Both show an increasing trendwith increasingly postive bias however the effect saturate at a different bias. This differencesuggests the presence of an additional contribution to the spin voltage anisotropy.

tunneling anisotropic spin polarization A mechanism which is likely present isthe anisotropy of the tunnel spin polarization (TASP) when the magnetization of thecobalt layer is in- versus out-of-plane. Generally this is not very large however itcan be hard to distinguish TASP from anisotropic τ . For instance, in graphene it isshown that an anistropy in the spin voltage exists which is attributed to a differencebetween τ‖ and τ⊥ however a possible contribution from TASP is not discussed [36].More recently Guimaraes et al. showed a modulation of τ⊥/τ‖ by varying the electricfield in the channel [37]. However, a ratio of τ⊥/τ‖ ≈ 0.75 is seen when the electricgate field is zero. This is explained by invoking intrinsic remnant SOC fields butagain TASP could also contribute to this difference. For instance a TASP of ∼25% hasbeen observed for (Ga,Mn)As/GaAs spin Esaki diodes [38]. For normal transitionmetal ferromagnets a relatively large TASP could be present in the current systemsince the electric fields at the cobalt surface can be very large due to the large relativepermittivity of SrTiO3 [39] (also see chapter 6).

The presence of Rashba-SOF spin flip scattering is based on the simultaneousobservation of a junction voltage dependence of τ‖ as well as the ratio V⊥/V‖. In Fig.4.4 the trend of τ‖ (red triangles) and V⊥/V‖ (black circles) with positive bias is plottedin the same graph. The solid black line and dashed red line indicate the overall trendof the data. Although there is some scatter in the spin lifetime data the two trendssaturate a distinctly different junction voltages. The change in τ‖ saturates around400 mV - 450 mV while the spin voltage anisotropy saturates slightly above 600 mV.This difference suggests the presence of an additional contribution to the spin voltageanisotropy. The fact that this mechanism reduces the spin voltage anisotropy would

4


be consistent with a TASP of the cobalt injector as the electric field at its surface alsoreduces with increasing positive bias. This would lead to a reduced influence of theelectric field on the spin resolved density of states possible reducing the overall TASP.Note that additional evidence for the saturation of τ‖ at 400 mV is given by the biasdependence of the inverted Hanle effect as shown in chapter 5.3.

tunneling anisotropic magneto-resistance As discussed in chapter 6 and 7 the ob-served tunneling anisotropic magneto-resistance (TAMR) for Co/(AlOx/)Nb:SrTiO3

junctions leads to a reduction of the junction voltage with increasing out-of-planemagnetic field. This could in principle significantly reduce the spin voltage anisotropyratio. However, the TAMR effect present in these junctions at room temperature ismost likely small. This is based on the facts that 1) the lineshape at large negativebias does not suggests a large TAMR effect to be present (see chapter 5.1.4) and 2)the voltage dependence of the spin signal at negative bias does not show the linearor even supralinear scaling observed for TAMR as discussed in chapter 6. Rather thespin voltage shows a strong sublinear, saturating, character with increasing negativebias (see Fig. 4.2(a)).

Another possible candidate is an intrinsic in-plane magnetic field component atthe Nb:SrTiO3 surface. There is considerable evidence for such room temperatureinterface magnetism in related systems [10, 40–42]. We want to point out that usingthe standard Lorentzian form of the spin dephasing expression in Eq. 7.1, commonlyused for three-terminal geometries [3], does not affect the trend of the spin lifetimeanisotropy but shifts the ratio down over the whole range by ∼0.125. A more exten-sive discussion on the consequence of model choice is given in chapter 5.1.1.

Such a pronounced effect of a Rashba like SOF on the spin accumulation couldoriginate from a large Rashba coefficient α. However, due to the electron correlationeffects in SrTiO3 other factors might also play a role and lead to an enhanced sensi-tivity on SOF. For instance, we believe most charge diffusion to occur in the x − yplane even though the electrons are not confined in the z-direction due to the banddispersion close to the Fermi level. The conduction bands of n-doped SrTiO3 consistof the t2g state derived from the dxy,yz,xz orbitals of the Ti. In bulk these orbitals aredegenerate but at an interface this degeneracy can be lifted [10, 43, 44]. The dxy bandis shown to move down in energy while the dyz, xz orbitals move up. The dxy derivedband has light effective mass in the x− y plane and heavy effective mass along the zdirection [43, 45]. Due to the very short spin relaxation length most of the spin voltageis generated in this near interface region and the strong anisotropy of the effectivemasses causes predominant diffusion of the spins in the x-y plane.

effective mass and g-factor In general the band structure of bulk SrTiO3 is rela-tively complicated, the band structure at the surface of doped SrTiO3 or at an inter-

4

4.2. Results 83

0 2 4 6 8

/ τ ||

Magnetic Field (mT)

Current Bias (mA)

0

125

250

375

0.3

0.6

0.40.5

-2000 20000-1000 1000

τ∆V

µV

)(

101.0

1.1

1.2

Rat

io

(b)

(a) LRS HRS

(c)

Figure 4.5: (a) Three terminal Hanle measurements in the low (squares) and high (circles)resistance state at +7.5 mA. A clear modification of the Hanle lineshape is observed. (b) Ratioof the out-of-plane/in-plane spin lifetimes as a function of bias current. A clear systematicincrease of the ratio is observed when the junction is set to the high resistance state. (c) Theratio of HRS over LRS τ⊥/τ‖ as in (b). At larger bias currents the electro-resistive control overthe spin lifetime reduces consistent with Fig. 4.2(b) and (d) (dotted line is a guide to the eye).

face considerably more so as argued above. Therefore it is complicated to determinethe effective mass and up to certain extend the g-factor for the system current inves-tigated. Since the spin lifetime obtained from fitting is determined by the productof ωL = (egB/2m∗) and τ any deviation of m∗ or g from the values used will leadto a change in the fit value of τ . Many reports show m∗ is larger than me (for highNb doping some times as large as 5 to 10 me). Any change in m∗ would result ina change of the spin lifetimes by the same factor. In principle m∗ in the inter-facialregion could depend on the local electric field and hence the junction voltage. Notehowever that changes in m∗ are not directly expected to cause an anisotropy of thespin lifetime for in- versus out-of-plane spins.

Finally, we demonstrate the ability to manipulate the spin accumulation using theelectro-resistance effect present in the junction. Such electro-resistance effects, wherethe junction resistance can be switched from high to low, are well known to occur inmetal/Nb:SrTiO3 junctions [46]. In the pristine state the device is in the High Resis-tance State (HRS). It can be switched back and forth between a Low Resistance State(LRS) and HRS by applying a large positive or negative bias, respectively. Hanle mea-

4


(a) (b)

200 300 400 500 600 7005

10

15

20 LRS HRS

τ || (ps)

Junction Voltage (mV)200 300 400 500 600 700

0.5

0.6

0.7

0.8 LRS HRS

∆V ⊥

/∆V ||


Figure 4.6: (a) Spin voltage anisotropy as function of postive junction voltage for LRS (blackcircles) and HRS (red triangles). The LRS and HRS data points collapse on a single line sug-gesting that it is the change in junction voltage which drives the non-volitile control over thespin voltage anisotropy. (b) The in-plane spin lifetimes for LRS and HRS do not collapse onthe same line exactly but do show the proper dependece on junction voltage. The differenceof the lifetimes in HRS and LRS state suggests the presence of an additional spin dephasingmechanism which is stronger in the LRS.

surements at the same current bias (+7.5 mA) in the LRS and HRS state are shownin Fig. 4.5(a). A clear modulation of the Hanle lineshape is observed. Fits to theHanle data using Eq. 7.1 show a systematic increase of the spin lifetime anisotropy asshown in Fig. 4.5(b). The increased voltage in the HRS decreases the electric field atthe interface as it effectively acts as an added positive bias. The increase of the ratiois in line with a decreased SOF strength and indicates a non-volatile way of control-ling the Rashba SOFs. In Fig. 4.5(c) the ratios of the values in Fig. 4.5(b) are shown(i.e. the ratio of τ⊥/τ‖ for the HRS over LRS). The effectiveness of electro-resistivecontrol reduces at higher bias consistent with Fig. 4.2(b) and (c). (See SupplementalMaterial [20] for details).

in-plane spin lifetime dependence on resistance state Apart from the anisotropyof the spin voltage, the in-plane spin lifetime also shows a dependence on the re-sistance state. In Fig. 4.6 the spin voltage anisotropy is plotted in panel (a) and thein-plane spin lifetime τ‖ in panel (b) both as function of the junction voltage. As canbe seen in panel (a) the spin voltage anisotropy is completely determined by thejunction voltage as both the data points for LRS and HRS fall in a single trend. Forthe in-plane spin lifetime a similar trend is observed, at higher voltage it increasesregardless of the resistance state. However, it’s absolute value depends slightly on theresistance state. The dotted lines in panel (b) are least square fits to the data points.The difference in τ‖ suggests that when altering the resistance state a dephasingmechanism other than the electric field controlled spin-flip scattering is contributing.The resistive switching is most likely related to the trapping/detrapping of electrons

4

4.3. Conclusions 85

in defect states (for instance oxygen vacancy related) or the movement of oxygenvacancies. The presence of oxygen vacancies has been linked to inducing magneticmoments via localized Ti3+ states [47–50]. Hence, trapping/detrapping charge onthe electronic states associated with the oxygen vacancies could lead to alteration ofthe Ti3+ state density, changing the local magnetic fields. Please note that, as shownin the next chapter, the junction response when applying an in-plane magnetic fieldsuggests that the limitation of the spin lifetime at large positive bias originates fromthe presence of large local magneto-static fields.

4.3 Conclusions

We demonstrate a wide tunability of the spin accumulation, achieved by the built-inelectric field in an oxide semiconductor, Nb:SrTiO3, at room temperature, withoutany additional design complexity of a gate contact. We show that the manipulation ofthe built-in electric field leads to a large change in the spin lifetime and its anisotropywhich we explain with the field tuning of the Rashba SOF strength. The general trendsare confirmed by a theoretical spin-flip model based on interfacial spin-orbit fields.The strong SOF effects on the electron spins in SrTiO3 show promise for electric fieldcontrol over the spin state, a prerequisite for developing a S-FET.

Acknowledgments

We would like to acknowledge J. G. Holstein, H. M. de Roosz and H. Adema for tech-nical support. A. M. K. and T. B. acknowledge financial support from the NetherlandsOrganization for Scientific Research NWOVIDI program and the Rosalind FranklinFellowship.

4.4 Supplemental Material

Uniqueness of Fit - Loss of fit restriction for V⊥/V‖ forHanle curves without shoulders

When the spin lifetime becomes low (τ‖ ≈ ωL|B=MS) the linewidth of the Hanle

curves becomes wide enough such that the distinct shoulders disappear. When thisoccurs (the derivative of the Hanle curve no longer changes sign anywhere within thefull field range) it is not possible to define a unique ratio for V⊥/V‖. This is becausethe linewidth is only very slightly modified while changing the anisotropy ratioappreciably. This is clearly visible in Fig. 4.7 where we show forced fits for several

4


fixed ratios of V⊥/V‖ to data with clear shoulders, only one ratio results in a goodfit (top panel). However, when the same is done for the broad linewidths observedat very low positive bias or negative bias the goodness of fit is nearly the same forall ratios chosen. Hence we set a fixed spin voltage ratio, in the negative bias regime,for the fits as no shoulders are observed. A value of V⊥ = 0.5 × V‖ is set in thisregime, as the trend of the data indicates this as the upper bound value. Note thatchoosing a different ratio does not change the trend of the in-plane spin voltage(V‖) or lifetime (τ‖) on junction voltage but only shifts the overall value slightly. Theanalysis regarding electric field effects on the spin voltage/lifetime anisotropy ismainly focused on the postive junction voltage region where the ratio is well defined.

The origin for this insensitivity of the linewidth on the ratio can be understoodby looking more in-depth at the Hanle equation. When the lifetime is large (τ ωL) the dominant term in the equation at low magnetic fields (Bzapplied MS) isthe Lorentzian like decay of the spin voltage on applied magnetic field. At higherfields the upturn is then described by the sine and cosine terms and the sizes ofin and out-of-plane spin voltage. However, when the spin lifetime becomes low(τ . ωL) the sine and cosine terms become more dominant in determining the lineshape over the whole field region. In this latter case, the spin lifetime is low enoughsuch that little in-plane spin dephasing occurs while the magnetization of cobaltrotates significantly. In the extreme case it is possible to observe a Magneto-Resistance(MR) signal originating from the spin accumulation while the in-plane spins are notdephased by the applied magnetic field. The MR originates from the inequality of in-and out-of-plane spin voltage (V⊥ 6= V‖). For perfect out-of-plane alignment of theexternal magnetic field this would result in a parabolic MR.

Discussion related to Impurity assisted Tunnel Magneto-Resistance mechanism

It has been shown that the Lorentzian MR originating for impurity-assisted TMR(iaTMR) is strongly related to the number of impurity states involved in the hoppingcharge transport process through the barrier [23]. The number of phonon-assistedhops through a chain of N impurities leads to a temperature dependent resistance.The observation of the iaTMR signal is only present when a significant increase of thejunction resistance with temperature (T(4K)/T(300K) & 5 is observed as in Ref. [23].In Fig. 4.8 we show the change of the junction resistance normalized to the room tem-perature resistance as function of temperature. This shows the change in normalizedresistance at both a low and intermediate junction voltage of 52 and 302 mV whichcorrespond to a junction current around 200 µA and 1.8 mA, respectively. An increaseof around 1.6-1.7 is observed when decreasing the temperature from 295 to 4 K. Thisis well within the regime where no iaTMR effect was reported in their studies. Such

4

4.4. Supplemental Material 87

-300-200-100

0

-1500 -750 0 750 15000

50

100 0 0.35 0.55 0.7 0.9

∆V

( µV

)

Ratio V / V| |

∆V ( µ

V)

Magnetic Field (mT)

Figure 4.7: (top panel) Hanle measurement at positive bias current showing the characteristicshoulders, the upturn of the spin voltage above ∼ 1000 mT. Several fits with different fixedratios of the out/in-plane spin voltage are shown. Only one specific ratio fits the data well.(bottom panel) Hanle measurements at negative bias. Due to the low in-plane spin lifetimethe in- and out-of-plane spin voltage results in a merged curve without the shoulders. A largespread in spin voltage ratios results in approximately equally good fits.

weakly insulating behavior is however attributed to tunneling transport through thebarrier [51].

Furthermore, the linewidth of the iaTMR effect is related to (random) internalmagnetic fields at the impurity sites. We employ a tunnel barrier of similar material,hence we do not expect significant differences in the origin of any random magneticfields originating from inside the AlOx tunnel barrier. The much broader linewidthsobserved in this study are inconsistent with such an iaTMR mechanism, as we use thecommonly employed Co/AlOx injector stack, for which iaTMR results in much nar-rower linewidths similar to those observed in Ref. [23]. Therefore, the magnetic fieldresponse observed in the studied junction is likely to originate from semiconductingNb:SrTiO3. It is still possible that a broadened line width is observed due to nuclearfields originating from for instance Sr or Ti acting on defects in the AlOx barrier. How-ever, the observed linewidths are also considerably broader than those reported forspin injection into the 2 DEG at the LaAlO3 [21] or into Nb:SrTiO3 [18] where a thickMgO barrier is employed. The abundance of isotopes with nuclear magnetic momentfor La (99.91 %) and Al (100 %) is also much higher than Ti (∼12.8%) and Sr (∼7%)hence smaller nuclear fields for Nb:SrTiO3 are expected compared to the La and Al inthe 2DEG study or Al in the AlOx tunnel barrier. Therefore, considerable lineshapebroadening due to nuclear fields is unlikely. Note that in both these studies the tunnelbarrier resistance dominates the junction resistance and is much larger than in the

4


0 100 200 300

1.0

1.2

1.4

1.6

1.8Vbias (mV)

52 302

Temperature (K)

R(T)

/R(3

00K)

Figure 4.8: Normalized junction resistance at low (red circles) and intermediated (blacksquares) junction bias showing a weak increase of the junction resistance with decreasingtemperature. The weak temperature dependence is well within the range where the iaTMRmechanism was observed in Ref. [23].

present study. Furthermore, no anisotropy (meaning V‖ = V⊥) or bias dependenceof the lineshape should exist for the iaTMR mechanism. Hence we conclude that theobserved magneto-resistance is not due to the iaTMR mechanism.

The overall (change in) lineshape is well expressed by the 1 dimensional spin dif-fusion model. Also, the observed trend of the in-plane spin lifetime is very similar tothose calculated for the model system. Therefore we interpret the observed responseas originating from a spin accumulation in the semiconductor close to the interfaceinfluenced by Rashba-like SOFs.

Electro-Resistive switching of the SOF strength

The existence of a large Electro-Resistive (ER) effect at metal/Nb:SrTiO3 interfaces iswell know and is actively explored for realization of memory devices. Although theeffective ER effect is strongly reduced when a thin AlOx tunnel barrier is inserted, itis still present. In Fig. 4.9(a) we show the I −V s obtained for one of the spin injectiondevices when it was set to a High Resistance State HRS, switched to Low ResistanceState (LRS) and finally back to HRS. We observe the same resistive switching behavioras that observed for Co/Nb:SrTiO3 interface i.e. at large positive bias the resistancereduces while at negative bias it increases. In our experiments we slowly ramp toa certain (high) junction bias and wait at this bias for considerable time to set the

4


0 1 20

100

200

300 HRS LRS HRS

Current (mA)

Volta

ge (m

V)

0 2 4 6 80.3

0.4

0.5

0.6

200 300 400 500 600 7000.3

0.4

0.5

0.6

Current Bias (mA)

τ ⊥ /τ

||


(a) (c)

1 10 100 1000 10000105

120

135

150

165

HRS

LRS

Res

ista

nce

(Ω)

Time (sec)

(b)

Figure 4.9: (a) Current-Voltage measurements of the junction in the intial HRS (red line),switched to the LRS (dotted black line) and set back to the HRS (dash blue line). (b) Timedependence of the junction resistance in HRS and LRS at low injection current (+1mA). A slowdecay towards from LRS to HRS is observed. (c) Extracted spin lifetime ratio as function of biascurrent for LRS (squares) and HRS (circles). (d) Extracted spin lifetime ratio as function of thejunction voltage at constant bias currents for LRS (squares) and HRS (circles). The collapse ofthe ratios in a single trend indicates that the driving mechanism is the change in backgroundjunction voltage, consistent with an effective modulation of the SOF strength.

system from HRS to LRS or vice versa. This is to prevent breakdown of the tunneland Schottky barrier in the system by application of a sudden large bias.

The decay of the LRS back to the HRS involves a slow process as shown Fig. 4.9(b).To indicate that the change in the extracted spin lifetime anisotropy indeed relatesto the change of the junction voltage we plot the ratio as a function of current bias(top panel) and junction voltage (bottom panel) in Fig. 4.9(c). The change in the ratiowhen in HRS (red circles) falls nicely in the trend observed for the LRS (black squares)indicating that the junction voltage drives the change. The increased voltage in theHRS effectively decreases the electric field at the interface and hence reduces the SOFstrength. Also note that the lineshape is not influenced by switching from HRS toLRS at negative bias (not shown). This is expected as in this regime the change of thein-plane spin lifetime with increasing Rasbha SOC strength has already saturated.

Spin flip rates at the ferromagnet/insulator/normal metalinterface due to interfacial Rashba spin-orbit fields

In the manuscript we compare experimentally measured characteristic spin dephas-ing quantities of steady state spin accumulation to spin-flip probability currents froma theoretical model describing ferromagnet/normal metal (F/N) tunnel heterojunc-tions (Fig. 4.10). The tunnel barrier comes from a thin insulating or semiconducting

4


\sectionParameters of the system

\sectionDependence of differential conductance on energy

\subsectionFerromagnetic system

\subsectionHalf metallic system

\sectionAngular dependence

\subsectionTunneling magnetoresistance and tunneling anisotropic magnetoresistance

\subsectionFerromagnetic system

[001] [ 010]

[100]

(b)

Fermi surface

4s

1 el

ectr

on

5 electrons 5 electrons

3d 3d

(b)

4.46 electrons 5 electrons

0.54

elec

tro

n

0.54 hole

3d 3d

Ф

ϴ

m

Normal metal

Ferromagnet

I

Superconductor

Normal metal V

[001]

Figure 4.10: Scheme of F/N junction. The unit vector of the magnetization in the F region ism, current flow is denoted by I .

layer between the F and N electrodes. We consider Rashba spin-orbit coupling (SOC)which arises from structure inversion asymmetry of the junction and discuss a simpli-fied model for very thin tunnel barriers which approximates the barrier and spin-orbitcoupling fields (SOFs) by delta functions.

We choose F (z < 0) and N (z > 0) semi-infinite regions separated by a flatinterface at z = 0, with potential and SOC scattering. The model Hamiltonian reads

H = H0 +HB , (4.4)

with

H0 = −~2

2∇[

1

m(z)

]∇− µ(z)− ∆xc

2Θ(−z)m · σ. (4.5)

There, m = [sin Θ cos Φ, sin Θ sin Φ, cos Θ] is the unit magnetization vector, σ are Paulimatrices, ∆xc is the exchange spin splitting in the F region (Stoner model),m(z) is theeffective mass, and µ(z) the chemical potential. The interfacial scattering is modeledas

HB = (V0d+ w · σ) δ(z), (4.6)

where V0 and d are the barrier height and width, while w = α(ky,−kx, 0) is theRashba SOC field [33, 34]. Assuming the in-plane wave vector k|| being conserved,we can write Ψσ(r) = Ψσ(z)eik||r|| . The solution in the F and N region for incomingelectrons with spin σ is

ΨFσ =

eikσz√kσχσ + rσ,σe

−ikσzχσ + rσ,−σe−ik−σzχ−σ, (4.7)

4


and

ΨNσ = tσ,σe

iqzχσ + tσ,−σeiqzχ−σ, (4.8)

with the spinors

χTσ =

(σ

√1 + σ cos Θ

2e−iΦ,

√1− σ cos Θ

2

), (4.9)

where σ =↑ (↓) corresponds to a spin parallel (antiparallel) to m in F. The wavevectors in the F and N regions are kσ =

√k2F + 2mF /~2 [E + σ∆xc/2]− k2

|| and q =√q2F + 2mN/~2E − k2

||.

The reflection and transmission coefficients can be found by applying appropriateboundary conditions at the interface and solving the corresponding system of linearequations. The probability for an incoming electron with spin σ to be transmitted asa particle with the same spin σ is

Tσ,σ(E,k‖) = Re(q |tσ,σ|2

). (4.10)

For transmission with flipped spin, the probability reads

Tσ,−σ(E,k‖) = Re(q |tσ,−σ|2

). (4.11)

The normalized spin-flip current along the interface is

Jsf = Pjtr−σ

jtrσ + jtr−σ

∣∣∣∣σ=↑

+ (1− P )jtr−σ

jtrσ + jtr−σ

∣∣∣∣σ=↓

, (4.12)

with the transmitted probability current

jtrσ ∝∫d2k‖Tσ,σ(eV,k‖), (4.13)

jtr−σ ∝∫d2k‖Tσ,−σ(eV,k‖), (4.14)

and spin polarization P = (∆xc/2) /µF . The strength of the potential barrier is de-noted by Z = V0dm/

(~2kF

)and the strength of Rashba SOC by λα = 2αm/~2. For

simplicity, we consider equal Fermi wave vector kF and effective massm in the F andN region.

In the manuscript we discuss the dependence of the spin-flip current on thestrength of SOC. In the model we tune the SOC strength by changing the RashbaSOC parameter which is a phenomenological parameter and has no explicit depen-dence on the applied bias voltage in the calculations. Whereas in the experiment the

4


10-3

10-2

10-1

100

J sf

λα = 0.1

λα = 1

λα = 10

λα = 100 10

-3

10-2

10-1

100

0 0.02 0.04 0.06 0.08eV / µ

F

10-8

10-6

10-4

10-2

100

J sf

0 0.02 0.04 0.06 0.08 0.1eV / µ

F

10-8

10-6

10-4

10-2

100

Z = 0 Z = 1

Z = 10 Z = 100

(a)

(c) (d)

(b)

Figure 4.11: Calculated normalized spin-flip current Jsf as function of bias voltage eV/µF .Magnetization is in-plane with spin polarization P = 0.4 for different spin-orbit coupling λα.From (a) to (d), the strength of the potential barrier Z is increased.

0.01 0.1 1 10 100Z

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

J sf

λα = 0.1

λα = 1

λα = 10

λα = 100

Figure 4.12: Calculated normalized spin-flip current Jsf as function of potential barrier ZMagnetization is in-plane with spin polarization P = 0.4 and bias voltage eV/µF = 0.05 fordifferent spin-orbit coupling λα.

junction voltage both changes the energy distribution of the tunneling electrons aswell as the electric field strength at the surface of the semiconductor. In the experi-ment it is the change of the electric field in the semiconductor surface region whichinfluences the Rashba SOC strength. To investigate if the change in energy distribu-tion of the tunneling electrons would significantly influence the spin flip probabilitywe analyze the bias voltage dependence of the calculated spin-flip current, where

4


0.1 1 10 100λ

α

0

0.2

0.4

0.6

0.8

1

J sf

Z = 0Z = 1Z = 10

FK

= 2

Figure 4.13: Comparison of calculated normalized spin-flip current Jsf as function of RashbaSOC λα for equal Fermi wave vectors (solid lines) and a mismatch FK = 2 (dashed lines).Magnetization is out-of-plane with spin polarization P = 0.4 and bias voltage eV/µF = 0.05

for different barrier strength Z.

bias voltage is unrelated to the Rashba SOC strength but relates to the changes in theenergy distribution of the tunneling electrons due to the change in the Fermi energyof the biased electrode.

In Fig. 4.11 the normalized transmitted spin-flip current, calculated from Eqs. (4.12)-(4.14), is presented as a function of bias voltage for in-plane magnetization. The spin-flip current shows a very weak dependence on bias voltage. Hence, we can simulatethe change of Rashba SOC strength due to decreasing or increasing the junction volt-age in the experiment and with this the electric field in the semiconductor surfaceregion by tuning only the phenomenological Rashba SOC parameter λα in the calcu-lations.

The amplitude of the spin-flip current is remarkably reduced compared to thecase of a metallic point contact [Z = 0, Fig. 4.11(a)] and a tunnel contact [Z & 10,Fig. 4.11(c-d)] since mainly spins of electrons with large in-plane momentum k‖ areflipped, but their transmission is particularly suppressed for strong tunnel barriers. InFig. 4.12, the dependence of the spin-flip current on the potential barrier Z is shown.First, it is nearly independent of the barrier strength, for high barriers the spin-flipcurrent goes as Jfs ∝ 1/Z2. The range of Z, in which the two limiting cases are valid,depends on the strength of Rashba SOC.

In the manuscript we assume equal Fermi wave vectors and effective masses inthe ferromagnet and the normal metal region. If we take into account different Fermiwave vectors, parametrized by FK = qf/kF , the results are only slightly modified andshow exactly the same trends (see Fig. 4.13 for FK = 2). The same is true for differenteffective masses when SOC is of moderate strength. For high SOC a mismatch of theeffective masses leads to a decrease instead of a saturation as in the case of equal

4


0.1 1 10 100λ

α

0

0.2

0.4

0.6

0.8

1

J sf

Z = 0Z = 1Z = 10

FM

= 5

Figure 4.14: Comparison of calculated normalized spin-flip current Jsf as function of RashbaSOC λα for equal effective masses (solid lines) and a mismatch FM = 5 (dashed lines). Mag-netization is out-of-plane with spin polarization P = 0.4 and bias voltage eV/µF = 0.05 fordifferent barrier strength Z.

masses, exemplified in Fig. 4.14 for FM = mN/mF = 5. Analog results are obtainedfor in-plane magnetization. The ratio between in-plane and out-of-plane spin-flipcurrents is not affected by mismatch. Since the anisotropy of the effcitive mass canbe very large in Nb-doped SrTiO3 a large value (FM = 5) is chosen to exemplify theeffect on the spin-flip current. The experimental setup compares to Z ≈ 10, for whicha reduction in the spin-flip current is observed at very large λα ≈ 30. Comparisonwith the experiment shows that the spin-orbit strength lies below this region.

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