Interface-Enhanced Spin-Orbit Torques and Current-Induced MagnetizationSwitching of Pd=Co=AlOx Layers

Abhijit Ghosh, Kevin Garello, Can Onur Avci, Mihai Gabureac, and Pietro GambardellaDepartment of Materials, ETH Zürich, Hönggerbergring 64, CH-8093 Zürich, Switzerland

(Received 25 July 2016; revised manuscript received 29 October 2016; published 6 January 2017)

Magnetic heterostructures that combine large spin-orbit torque efficiency, perpendicular magneticanisotropy, and low resistivity are key to developing electrically controlled memory and logic devices.Here, we report on vector measurements of the current-induced spin-orbit torques and magnetizationswitching in perpendicularly magnetized Pd=Co=AlOx layers as a function of Pd thickness. We find sizabledampinglike (DL) and fieldlike (FL) torques, on the order of 1 mT per 107 A=cm2, which have differentthicknesses and magnetization angle dependencies. The analysis of the DL torque efficiency per unitcurrent density and the electric field using drift-diffusion theory leads to an effective spin Hall angle andspin-diffusion length of Pd larger than 0.03 and 7 nm, respectively. The FL spin-orbit torque includes asignificant interface contribution, is larger than estimated using drift-diffusion parameters, and, further-more, is strongly enhanced upon rotation of the magnetization from the out-of-plane to the in-planedirection. Finally, taking advantage of the large spin-orbit torques in this system, we demonstrate bipolarmagnetization switching of Pd=Co=AlOx layers with a similar current density to that used for Pt=Co layerswith a comparable perpendicular magnetic anisotropy.

DOI: 10.1103/PhysRevApplied.7.014004

I. INTRODUCTION

Spin-orbit torques (SOTs) generated by current injectionin normal-metal/ferromagnet (NM/FM) bilayers haveattracted considerable attention as a method to inducemagnetization switching of thin FM films and magnetictunnel-junction devices [1–7]. Although the bulk or inter-face origin of the spin current giving rise to the dampinglike(DL) and fieldlike (FL) SOT components is a matter ofdebate [8–11], it has been established that the strongestSOTs are found in NMs with large spin-orbit coupling, andhence a large spin Hall effect (SHE) and a small spin-diffusion length (λ), such as the 5d metals Pt, W, and Ta[12–19]. For this reason, the 4d metals have been largelycast aside in the quest for large SOTs, even though severalstudies of the SHE in these materials show sizable spin Hallangles, of the order of γSH ∼ 0.01 [20–24].Pd-based heterostructures constitute an apparent excep-

tion to this trend: recent studies of ½Pd=Co�N multilayers[25] and Pd=FePd=MgO trilayers [26] evidenced DL andFL effective fields of the same order of magnitude or largerthan those found in Pt- and Ta-based structures, reaching upto more than 10 mT for an injected current density ofj ¼ 107 A=cm2. The effective spin Hall angle required tomodel the SOTs according to spin-diffusion theory is γSH >1 in ½Pd=Co�N [25] and γSH ≈ 0.15 in Pd=FePd=MgO [26],which is substantially larger than previous estimates of γSHin Pd [20–24]. This comparison calls for further inves-tigations of the SOTs resulting from Pd as well as of thepossibility of using Pd to induce magnetization switching,which has not been reported to date.In this work, we present a study of current-induced SOTs

and magnetization switching in Pd=Co=AlOx trilayers with

varying Pd thicknesses. We focus on the simple trilayerstructure to avoid the complexity resulting from multipleinterfaces and current paths in ½Pd=Co�N multilayers, whichcomplicate the analysis and interpretation of the experimentaldata [25]. Our study is based on the harmonic Hall voltagemethod tomeasure SOT [14–16,27,28] and includes a detailedmagnetotransport characterization as well as the analysis ofmagnetothermal contributions to the Hall resistance [14,29].We report strong DL and FL SOT amplitudes and efficientmagnetization switching for this system, combined with largeperpendicular magnetic anisotropy (PMA) and relatively lowresistivity.We further observe a distinct thickness dependenceof the DL and FL torques and discuss different models toaccount for the SOT efficiency. The main results are summa-rized at the end of this paper.

II. EXPERIMENT

Our samples are Tað0.8 nmÞ=PdðtPdÞ=Coð0.6 nmÞ=AlOxð1.6 nmÞ layers grown on thermally oxidized Sisubstrates by dc magnetron sputtering in an Ar pressureof 2 × 10−3 Torr. The Al cap layer is oxidized for 37 sunder a partial O2 pressure of 7 × 10−3 Torr in order toincrease the PMA of Co=Pd. The Ta seed layer is used toimprove the uniformity of Pd; because of its high resistivityand reduced thickness, such a layer plays a negligible rolein the generation of SOTs, as we confirm by measuringPd=Co=AlOx structures grown with a Ti seed. The rmsroughness measured by atomic-force microscopy is foundto vary between 0.15 nm (tPd ¼ 1.5 nm) and 0.13 nm(tPd ¼ 8 nm). The as-grown layers are patterned using UV

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lithography and dry etching into Hall bars with a widthw ¼ 10 μm and a length L ¼ 50 μm, as shown in Fig. 1(a).For the magnetotransport characterization, the samples

are mounted in the gap of an electromagnet producing afield Bext and allowing for rotating the current directionrelative to the magnetization (m). The experiments areperformed at room temperature using an ac current I ¼I0 sinðωtÞ with an amplitude I0 and a frequencyω=2π ¼ 10 Hz. I0 ranges between 3 and 14 mA in sampleswith tPd ¼ 1.5 and 9 nm, respectively, and is adjustedin order to keep the current density flowing through Pdbetween jPd ¼ 1 × 107 and 1.5 × 107 A=cm2. The har-monic Hall-voltage measurements are performed by takingthe Fourier transform of the ac Hall resistance recordedfor 10 s at each value of the applied field and current. Thefirst harmonic Hall resistance is analogous to a dc Hallmeasurement and is given by

RωH ¼ RAHE cos θ þ RPHE sin2 θ sinð2ϕÞ; ð1Þ

where RAHE and RPHE are the anomalous and planar Hallcoefficients, and θ and ϕ represent the polar and azimuthalangles of the magnetization, respectively.Current-induced effects are characterized by measuring

the second harmonic Hall resistance, R2ωH , which arises

from the mixing of the ac current with the Hall effectmodulated by the oscillations of the magnetization inducedby the DL and FL torques [14–16,27,28]. This termaccounts for the SOT effective fields, which are propor-tional to I, as well as for magnetothermal effects that areproportional to I2 [14,16,29]. Following Ref. [29], we have

R2ωH ¼ ½RAHE − 2RPHE cos θ sinð2ϕÞ�

d cos θdBext

BIθ

sinðθB − θÞ

þ RPHEsin2θ2 cosð2ϕÞBext sin θB

BIϕ þ R2ω∇T; ð2Þ

where BIθ and BI

ϕ are the polar and azimuthal componentsof the current-induced effective fields, respectively,including both SOT and the Oersted field, and R2ω∇T ∝ð∇T ×mÞ · y is the thermal Hall resistance associated withthe anomalous Nernst effect. The latter is caused by theunintentional out-of-plane and in-plane temperature gra-dients ∇T produced through Joule heating and asymmetricheat dissipation in the trilayer [29].To separate the SOT contributions from R2ω∇T , we

exploit the different behaviors of BIθ;ϕ and R

2ω∇T as a functionof Bext, as explained in detail in Ref. [29] and theSupplemental Material [30]. Finally, in order to explicitlyshow the relationship between BI

θ and BIϕ in Eq. (2) and the

DL and FL SOT effective fields, we express the latter inspherical coordinates [14]:

BDL ¼ BDLθ cosϕeθ − BDL

ϕ cos θ sinϕeϕ; ð3Þ

BFL ¼ −BFLθ cos θ sinϕeθ − BFL

ϕ cosϕeϕ; ð4Þ

where the coefficients BDLθ , BFL

θ , BDLϕ , and BFL

ϕ represent thepolar and azimuthal amplitudes of the DL and FL SOTs.In the “isotropic torque” limit usually considered in theSOT literature, Eqs. (3) and (4) are obtained by projectingBDL ¼ BDL

0 ðm × yÞ and BFL ¼ BFL0 ½m × ðm × yÞ� onto

the unit vectors eθ and eϕ and by assuming BDLθ;ϕ ¼ BDL

0

and BFLθ;ϕ ¼ BFL

0 .General models and SOT vector measurements, however,

have shown that BDLθ;ϕ and BFL

θ;ϕ can be functions of themagnetization orientation [14,31,32]. In such a case, as inthe present work, the four unknown coefficients in Eqs. (3)and (4) must be determined by four independent measure-ments of R2ω

H as a function of Bext, applied in plane alongϕ ¼ 0°,�45°, and 90°. All of the SOT values reported in thiswork are normalized to jPd ¼ 1 × 107 A=cm2 for ease ofcomparison with data in the literature.

III. RESULTS

A. Resistivity and magnetic anisotropy

Figure 1(b) shows the resistance of the Pd=Co=AlOxlayers as a function of Pd thickness. Using a simpleparallel-resistor model and assuming that the conductivityof Co remains constant across the series, we find that theresistivity of Pd varies approximately as ρPd ∝ 1=tPd [insetof Fig. 1(b)]. This result is in line with previous inves-tigations of the resistivity of Pd thin films [33], which issimilar to that of Pt [34] and significantly smaller than that

FIG. 1. (a) Schematic of the experimental geometry and scan-ning electron micrograph of a Pd=Co=AlOx Hall bar. (b) Resis-tance as a function of Pd thickness. (Inset) Pd resistivity as afunction of inverse thickness. The solid line is a linear fit. (c) Firstharmonic Hall resistance Rω

H of three representative samples as afunction of an external field applied at θB ¼ 84° and ϕ ¼ 0°.(Inset) Detail of the low-field region of the 4-nm sample. (d) RAHEas a function of Pd thickness. (Inset) Anisotropy field BK .

ABHIJIT GHOSH et al. PHYS. REV. APPLIED 7, 014004 (2017)

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of β-W and β-Ta films. The Hall resistance RωH is shown in

Fig. 1(c) as a function of Bext applied at an angle θB ¼ 84°relative to the sample normal. As is customary in SOTinvestigations of PMA materials, the external field isslightly tilted off plane in order to prevent the formationof magnetic domains. Accordingly, we observe that themagnetization loops are reversible as long as m does notswitch direction, as expected for a coherent rotation of themagnetization, and that Rω

H decreases with an increasingBext as m tilts away from z. When ϕ ¼ 0° or 90°, Rω

H isproportional to m · z, which allows us to derive the angleθ ¼ cos−1ðRω

H=RAHEÞ as a function of the applied field. Weobserve also that the maximum amplitude of Rω

H decreaseswith an increasing Pd thickness owing to the decreaseof the AHE resulting from current shunting through Pd[Fig. 1(d)]. Our data indicate that both the AHE and thePHE are roughly proportional to t−3Pd rather than toρPd=tPd ∝ t−2Pd , as would be expected for a parallel-resistormodel of the Co and Pd layers. This result suggests that theAHE and the magnetoresistance are enhanced at the Pd=Cointerface relative to bulk Co, in agreement with studies ofthe AHE in ½Co=Pd�N multilayers [35].The inset of Fig. 1(d) shows the effective magnetic

anisotropy field calculated by using the macrospin approxi-mation: BK ¼ Bextðsin θB= sin θ − cos θB= cos θÞ. We findthat BK varies between 0.7 and 0.9 T, with no systematicvariation as a function of Pd thickness and independentlyof the in-plane direction of the magnetization. Thecorresponding uniaxial magnetic-anisotropy energy isthus Ku ¼ BKMs=2þ μ0M2

s=2¼ ð1.5� 0.1Þ× 106 J=m3,where Ms ¼ 1.27 × 106 A=m is the saturation magnetiza-tion measured by a superconducting quantum interferencedevice. Interestingly, Ku for Pd=Co=AlOx is comparable orlarger relative to ½Pd=Co�N multilayers [36–38], which weattribute to the top oxide layer favoring strong PMAthrough the formation of Co─O bonds [39,40].

B. Spin-orbit torques

The SOT measurements are performed by analyzingthe second harmonic Hall resistance that arises due to themixing of the ac current with the ac oscillations of themagnetization induced by the DL and FL torques [Eq. (2)].Because the DL torque is larger when m is oriented in thex-z plane, whereas the FL torque tends to align m towardsy, measurements taken at ϕ ¼ 0° (ϕ ¼ 90°) mainly reflectthe strength of the DL (FL) effective fields. Figures 2(a)and 2(b) show R2ω

H measured at ϕ ¼ 0° and ϕ ¼ 90° afterthe subtraction of R2ω∇T [30]. These curves are, respectively,odd and even with respect to magnetization reversal,reflecting the different symmetry of BDL and BFL [14].Similarly to the Rω

H case, we observe that the amplitude ofR2ωH decreases with an increasing Pd thickness, which limits

the signal-to-noise ratio and, consequently, the range of ourSOT measurements to tPd ≤ 8 nm. Figures 2(c) and 2(d)

show the effective fields BDLθ and BFL

θ as a function of θ,obtained by R2ω

H using Eqs. (2)–(4). We find that the DLand FL fields have the same sign as measured forPt=Co=AlOx [1,14,41] and increase as the magnetizationrotates towards the plane of the layers. Compatibly with theuniaxial symmetry of the system, the angular dependenceof the DL and FL fields can be modeled by a Fourier-seriesexpansion of the type BDL;FL

θ ¼ BDL;FL0 þ BDL;FL

2 sin2θþBDL;FL4 sin4θ þ � � �, whereas the azimuthal components are

only weakly angle dependent and are approximated byBDL;FLϕ ≈ BDL;FL

0 [14]. The values of the zeroth-, second-,

and fourth-order BDL;FLθ coefficients are obtained by fitting

the data in Figs. 2(c) and 2(d) according to this expansion.Additionally, we present data obtained using the small-angle approximation [28], which yields accurate valuesfor BDL;FL

0 when θ ≈ 0° [stars in Figs. 2(c) and 2(d)]. Thisapproximation is valid as long as R2ω

H varies linearlywith the applied field, as shown in the insets ofFigs. 2(a) and 2(b), and is equivalent to Eq. (2) in this limit.Figures 3(a)–3(c) report the isotropic and angle-

dependent SOT amplitudes as a function of tPd, normalizedto jPd ¼ 107 A=cm2. To obtain the isotropic FL SOTcomponent, BFL

0 , the Oersted field is calculated as BOe ¼μ0jPdtPd=2 [open triangles in Fig. 3(a)] and subtracted fromthe total FL effective field derived from R2ω

H (open dots).

The coefficients BDL ðFLÞ0 , shown in Fig. 3(a), represent the

magnetic field induced by the DL (FL) torque when m∥z,whereas BDL ðFLÞ

2þ4 , shown in Fig. 3(b), represents the angle-

dependent contributions, and BDL ðFLÞ0þ2þ4 , shown in Fig. 3(c),

represents the total amplitude of the field when m∥xðyÞ.

FIG. 2. Second harmonic Hall resistance R2ωH as a function of

applied field at (a) ϕ ¼ 0° and (b) ϕ ¼ 90°. (Insets) R2ωH in the

small-angle limit (θ ≤ 7°). (c) BDL and (d) BFL extracted from thedata in (a) and (b), respectively, as a function of the polarmagnetization angle θ. The BDL and the BFL obtained using thesmall-angle approximation are indicated by a star.

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For comparison with literature data, we plot also the SOTefficiency (right scale), defined by

ξDL ðFLÞj ¼ 2e

ℏMstCo

BDL ðFLÞ

jPd; ð5Þ

which represents the ratio of the spin current absorbed bythe FM to the charge current injected in the NM layer[12,42]. Remarkably, we find that the ratio BDL

0 =jPdincreases with an increasing tPd, whereas BFL

0 =jPd has anonmonotonic dependence on tPd. This finding is the firstindication that the interface and bulk contributions to thetwo torques differ in magnitude. Moreover, we observethat the SOT efficiency depends on the orientation of themagnetization relative to the current direction. Specifically,the angular dependence of the FL SOT is much strongerthan that of the DL SOT [Fig. 3(b)], such that the total FLtorque is larger than the total DL torque when themagnetization is tilted in plane [Fig. 3(c)].Next, we analyze the SOT amplitudes normalized by the

applied electric field BDL;FL=E, shown in Figs. 4(a)–4(c).The motivation for this analysis is that the resistivity of Pdis strongly thickness dependent, as shown in Fig. 1(b).Therefore, even within a single sample, the current is nothomogeneously distributed across the Pd layer. Moreover,the current profile in Pd can vary from sample to sample ina way that is not described by a simple parallel-resistormodel. The electric field E ¼ ρj ¼ ρPdjPd, on the otherhand, is the primary force driving the charge and spincurrents [9] and is constant throughout the thickness of thewhole sample, which makes it a practical unit for thickness-dependent studies of SOT [15,42]. Accordingly, in analogy

with Eq. (5) and for the purpose of comparing the SOT indifferent systems, we define the SOT efficiency per unitelectric field [42]

ξDL ðFLÞE ¼ 2e

ℏMstCo

BDL ðFLÞ

E¼ ξDL ðFLÞ

j

ρPd: ð6Þ

Figure 4(a) shows that the thickness dependence of theelectric-field-normalized SOT is very different from that ofthe current-normalized SOT: BDL

0 =E increases in an almostlinear way in the whole range of tPd, while BFL

0 =E has amonotonic dependence on tPd and extrapolates to a nonzerovalue at tPd ¼ 0. The angular amplitudes BDL

2þ4=E, on theother hand, are very small relative to BDL

0 =E and onlyweakly thickness dependent, contrary to the FL compo-nents BFL

2þ4=E, which have a strong dependence on tPd, asshown in Fig. 4(b). The implications of these results arediscussed below.

C. Discussion of spin-orbit torquedependence on Pd thickness

We discuss first the thickness dependence of the isotropicDL torque BDL

0 =jPd in terms of the drift-diffusion approachwidely employed in the analysis of SOT and spin-pumpingexperiments. Assuming that the spin current flowing fromthe NM into the FM is uniquely due to the bulk SHE of theNM and is entirely absorbed at the NM-FM boundary [12],the simplest drift-diffusion model gives a dependence of thetype ξDLj ¼ γSH½1 − sechðtPd=λÞ�. A fit according to thisfunction [gray line in Fig. 3(a)] yields γSH ¼ 0.03 andλ ¼ 2 nm, with an incertitude of about 10%.

BD

L,F

L/j

(m

T/1

07 A c

m-2

)

DL,

FL

j

tPd (nm)

BD

L,F

L/j

(m

T/1

07 A c

m-2

)

DL,

FL

j

tPd (nm)

BD

L,F

L/j

(m

T/1

07 A c

m-2

)(a)

BFL +BOe0

BFL, FL0 j

BDL, DL0 j

DL,

FL

j

fit

tPd (nm)

BOe

BDL , DL0+2+4 j

BDL , DL2+4 j

BFL , FL2+4 j

BFL , FL0+2+4 j

(b)

(c)

FIG. 3. SOT fields per unit current density as a function of tPd. (a) Isotropic amplitudes BDL0 =jPd and BFL

0 =jPd, corresponding toperpendicular magnetization. (b) Angle-dependent amplitudes BDL

2þ4=jPd and BFL2þ4=jPd. (c) Total amplitudes for in-plane magnetization,

BDL0þ2þ4=jPd and BFL

0þ2þ4=jPd. The SOT efficiency ξDL ðFLÞj is shown on the right scale.

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There are, however, several reasons that caution againstdrawing conclusions from such a simplified model. First,within drift-diffusion theory, one should take into accountthe spin backflow into the NM [8,43] and spin-memory lossat the NM/FM interface [44,45]. Second, as pointed out inRef. [42], drift-diffusion models assume constant ρNM, γSH,and λ throughout the NM layer, whereas the strong depend-ence of ρNM on tNM typical of ultrathin films [Fig. 1(b)]invalidates this hypothesis. Third, both first-principles elec-tronic calculations [10,11] and optical measurements [46]suggest the existence of an “interface SHE,” which can besignificantly larger than the bulk SHE. This interface SHE isascribed to the current carried by interface states, similar tothe Rashba-Edelstein effect [47]. Additionally, spin-dependent scattering at the FM/NM interface can also leadto a spin-polarized current and generate DL and FL SOTs[48,49]. Keeping track of all of these effects together leads toan overparametrized problem, which makes it difficult todraw a firm conclusion on either γSH or λ.An alternative approach is to consider the SOT values

normalized by the applied electric field. According to drift-diffusion theory and including spin backflow [8], the SOTefficiency per unit electric field due to the bulk SHE isgiven by

ξDLE ¼ 4λγSHρ

sinh2�

t2λ

�

×2λG2

i coshðtλÞ þGr½2λGr coshðtλÞ þ 1ρ sinhðtλÞ�

½2Giλ coshðtλÞ�2 þ ½2λGr coshðtλÞ þ 1ρ sinhðtλÞ�2

;

ð7Þ

ξFLE ¼ 4λγSHρ

sinh2�

t2λ

�

×1ρGi sinhðtλÞ

½2Giλ coshðtλÞ�2 þ ½2λGr coshðtλÞ þ 1ρ sinhðtλÞ�2

;

ð8Þwhere ρ and t are the resistivity and thickness of thenormal-metal layer (Pd, in our case), while Gr and Gi arethe real and imaginary parts of the spin-mixing conduct-ance. The gray line in Fig. 3(c) is a fit of BDL

0 =E accordingto Eq. (7), which gives a spin Hall conductivity σSH ¼γSH=ρ ¼ ð4� 1Þ × 105 Ω−1m−1 and λ ¼ ð7� 1Þ nm,assuming ρ∞Pd ¼ 1.4 × 109 Ωm for the bulk Pd resistivity(measured for a 30-nm-thick Pd film), and the spin-mixingconductance calculated for a permalloy/Pd interface, Gr ¼7.75 × 1014 Ω−1m−2 and Gi ¼ Gr=7 [50]. Although λ ¼7 nm is in good agreement with recent first-principlescalculations of Pd [51], σSH exceeds the intrinsic value of2.1 × 105 Ω−1 m−1 calculated for bulk Pd [50], and γSH ¼ρ∞PdσSH ≈ 0.055 is consistently larger than previouslyreported for Pd/permalloy bilayers in spin-pumping experi-ments [20–24,44,50]. An even larger estimate of σSH isobtained if we use Gr to 5.94 × 1014 calculated for a Co=Ptinterface [8]. This analysis suggests that extrinsic orinterface-related effects may enhance the DL SOT inPd=Co=AlOx relative to what is expected from the bareSHE of Pd. The amplitude of the DL SOT, however,remains smaller than reported for Pt=Co=AlOx [14] andPt=Co=MgO [42]. We remark that the observed variation ofthe torques cannot be related to changes of the film

(a)B

DL,

FL / E

(10

-7 T

V-1

m

)

t Pd (nm)

DL,

FL

E(1

05 Ω

-1m

-1)B

FL, FL0 E

B DL, DL0 E

fit

(b) B DL ,

DL2+4 E

B FL ,

FL2+4 E

(c)

B D

L,F

L / E

(10

-7 T

V-1

m

)

t

Pd (nm)

DL,

FL

E(1

05 Ω

-1m

-1)

B DL , DL0+2+4 E

B FL ,

FL0+2+4 E

B D

L,F

L / E

(10

-7 T

V-1

m

)

t Pd (nm)

DL,

FL

E(1

05 Ω

-1m

-1)

FIG. 4. SOT fields per unit electric field as a function of tPd. (a) Isotropic amplitudes BDL0 =E and BFL

0 =E, corresponding toperpendicular magnetization. (b) Angle-dependent amplitudes BDL

2þ4=E and BFL2þ4=E. (c) Total amplitudes for in-plane magnetization,

BDL0þ2þ4=E and BFL

0þ2þ4=E. The SOT efficiency ξDL ðFLÞE is shown on the right scale.

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roughness [52], which is approximately constant across thewhole Pd=Co=AlOx series. We also note that a refinementof the drift-diffusion model that considers a thickness-dependent λ rescaled such that the product ρPdλ is constantand equal to the bulk value ρ∞Pdλ

∞, consistent with theElliott-Yafet mechanism of spin relaxation [42], givesσSH ¼ ð5� 2Þ × 105 Ω−1 m−1 and λ ¼ ð18� 8Þ nm,showing that the fitted values of σSH and λ are stronglymodel dependent. Even such a refined model, however,does not take into account the interface enhancement of theSHE [10,11,48,49] and cannot justify the presence of alarge FL SOT.A similar analysis can be performed on BDL

0þ2þ4, corre-sponding to the SOT efficiency for the in-plane magneti-zation [Fig. 3(c)]; the main result in this case is a reductionof λ by 20%–40% relative to the out-of-plane casediscussed above. Such a result is not so surprising if oneconsiders that spin diffusion in the limit of tPd ≥ λ isstrongly influenced by the NM/FM interface, where spin-orbit coupling is responsible for inducing anisotropicelectron scattering processes. For the same reason, onemay expect also the spin-mixing conductance and spin-memory loss to depend on the magnetization direction.We now discuss the thickness dependence of the FL

SOT, which is qualitatively different than the DL SOT. TheBFL0 =jPd ratio [full dots in Fig. 3(a)] has a nonmonotonic

behavior as a function of tPd, with a minimum around3.5 nm. This behavior compounds the FL SOT thicknessdependence with the uneven current distribution in thePd=Co bilayer. Analyzing the ratio BFL

0 =E [full dots inFig. 4(a)] obviates the problem of the current distribution,revealing a monotonic increase of BFL

0 =E with an increas-ing tPd. Unlike BDL

0 =E, however, BFL0 =E extrapolates to a

nonzero value at tPd ¼ 0, evidencing a significant contri-bution from the Pd=Co interface akin to a Rashba-Edelsteinmagnetic field [41,53]. Moreover, an attempt to fit ξFLEusing the SHE drift-diffusion theory [Eq. (8)] adding aconstant term for the interface contribution yields a σSHabout one order of magnitude larger than that derived fromthe analysis of ξDLE . Similar considerations apply to BFL

0þ2þ4.The comparison between BFL

2þ4 and BDL2þ4 in Fig. 4(b) further

shows that the FL torque has a stronger anisotropiccomponent relative to the DL torque, and that suchanisotropy is thickness dependent. This finding is incontrast to the standard form of the SOTs derived fromthe bulk SHE using either the drift-diffusion model or theBoltzmann transport equation, exemplified by Eqs. (7)and (8), which predict only the existence of the isotropicterms BDL

0 and BDL0 [8]. Although there is presently no

theory providing a complete description of the torqueanisotropy in realistic FM-HM systems including bothbulk and interfacial spin-orbit coupling, a possible explan-ation is that the angular dependence of the torques arisesfrom anisotropic spin-dependent scattering at the FM/HM

interface or inside the FM, which affects the amplitude ofthe nonequilibrium spin currents in the bilayer.The observation of a thickness-independent FL SOT and

of strongly enhanced DL and FL amplitudes relative tothose expected from the bulk SHE of Pd leads to theconclusion that interface effects contribute significantly tothe current-induced SOTs in Pd=Co=AlOx. Such effectsare ubiquitous, but they may be particularly evident in Pdbecause of the reduced bulk SHE compared to 5d-metalsystems. The standard drift-diffusion theory of the SHE[8,43], which is routinely used to extract γSH and λ fromspin-pumping and SOT measurements, does not accountfor interface terms, thickness-dependent spin-diffusionparameters, or angle-dependent SOT.Similarly, two-dimensional models of the Rashba-

Edelstein effect do not properly describe the spin-accumulation profile in FM/HM layers and neglect thebulk SHE of the HM [53]. More recent theoretical workconsequently points out the need to include the bulk- andinterface-generated spin accumulation on the same footingin three-dimensional models of electron transport [48,49].A key prediction of the latter work is that interfacialspin-orbit scattering creates substantial spin currents thatflow away from the FM/HM interface, generating both DLand FL torques. The thickness dependence of the twotorques differs, with the interfacial FL torque being nearlythickness independent and the interfacial DL torqueincreasing with the thickness of the NM layer [49]. Thisfinding is qualitatively consistent with the resultsreported in Fig. 4, namely, a FL torque comprising athickness-independent term and a DL torque that isstrongly thickness dependent. In this scenario, both torqueswould include bulk and interface contributions of compa-rable magnitude. Another prediction of this theory is thatthe interfacial scattering amplitudes depend on the mag-netization direction, which naturally leads to anisotropicSOT as well as magnetoresistance [48,49].In this respect, it is interesting to draw a parallel between

the angular dependence of the SOT and magnetoresistancein metallic FM/HM bilayers. Figures 3 and 4 show that theSOT amplitude increases strongly whenm is tilted towardsthe y direction and only moderately when m is tiltedtowards the x direction. This behavior is similar to that ofthe magnetoresistance in FM/HM layers, which showsmuch greater change when m is rotated in the y-z planerelative to rotations in the x-z plane [54,55]. Exploring thisconnection goes beyond the scope of this work, but webelieve that additional studies of the correlation betweenSOTand anisotropic magnetoresistance [19] may help us tounderstand transport at interfaces with spin-orbit coupling.

D. Magnetization switching

Finally, we address the question of whether the SOTsprovided by Pd are sufficient to reverse the magnetizationof the Co layer in a controlled way. To our knowledge,

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SOT-driven switching using 4d-metal layers has not yetbeen reported. Figure 5(a) shows the results of a typicalswitching experiment, performed by injecting 0.3 s longcurrent pulses of positive and negative polarity in aPdð4 nmÞ=Coð0.6 nmÞ=AlOx Hall bar. The plot showsthe change of the Hall resistance after each pulse due toswitching of the magnetization from up to down and viceversa during a single sweep of the in-plane external field,from −0.82 to 0.82 T.An alternative demonstration of current-induced switch-

ing is reported in Fig. 5(b), where the Hall resistance isrecorded as a function of current for a constant in-planefield. As discussed in previous work [1,2], the purpose ofthe in-plane field is to break the symmetry of the DL SOTand univocally determine the switching direction, whichoccurs through the expansion of chiral domain walls [6].Figure 5(c) shows the difference of the Hall resistance ΔRω

Hmeasured after two consecutive current pulses, one positiveand one negative, normalized to its saturation value.Switching is obtained whenever jΔRω

Hj > 0.We observe that the minimum field required to achieve

deterministic switching, Bm, decreases linearly with anincreasing current, as shown in Fig. 5(d), similar toPt=Co=AlOx [1] and Ta=CoFeB=MgO [16]. Such a linearbehavior is found in all samples, albeit with a differentslope, which we attribute to differences in the domainnucleation field. The minimum current density required toachieve deterministic switching depends on tPd and isgenerally smaller in the thicker samples, as expected due

to the overall increase of the SOT with an increasing tPd(Fig. 3). Remarkably, the dc current density required toswitch Pd=Co=AlOx is similar (within a factor of 2) to thatused to switch Pt=Co=MgO and Pt=Co=AlOx dots withcomparable PMA [2,5], which is in agreement with therelatively large SOT efficiency reported in this work.

IV. CONCLUSIONS

We performed magnetotransport, magnetic-anisotropy,and SOT vector measurements of Pd=Coð0.6 nmÞ=AlOxlayers as a function of Pd thickness. We found that thePMA of Pd=Co is reinforced by optimum oxidation of theAl capping layer relative to Pd=Co multilayers, yielding amagnetic anisotropy energy of ð1.5� 0.1Þ × 106 J=m3,which is nearly independent of tPd. Current injection inPd=Co=AlOx leads to sizable DL and FL SOTs that havethe same order of magnitude, about 1 mT per 107 A=cm2,but different thicknesses and angular dependence.The analysis of the DL SOT yields a relatively large

effective spin Hall angle for Pd, γSH ≈ 0.03–0.06, or a spinHall conductivity σSH ¼ ð4� 1Þ × 105 Ω−1 m−1, depend-ing on the model used to fit the data. The DL spin-torqueefficiency per unit electric field is on the order of105 Ω−1m−1, only a factor of 2 smaller relative toPt=Co=MgO layers of comparable thickness [42]. γSH isenhanced compared to Pd/permalloy bilayers [20–24], butit is significantly smaller than that reported for ½Pd=Co�Nmultilayers [25] and Pd=FePd=MgO [26].Additionally, our data evidence a strong FL SOT, with an

interface contribution that extrapolates to a finite value attPd ¼ 0, and up to a threefold enhancement of the FL SOTefficiency when the magnetization rotates from the out-of-plane to the in-plane direction transverse to the current.Overall, our results indicate that SOT models based on one-dimensional drift-diffusion theory and a bulk SHE do notadequately capture the SOT dependence on Pd thickness,at least based on a single set of σSH, λ,Gr, andGi parameters.A possible scenario is that spin currents driven by interfacialspin-orbit scattering add up to the spin currents induced bythe bulk SHE of Pd [49], resulting in the nontrivial thicknessand angle dependence of the SOT observed here.Finally, we report bipolar magnetization switching in

Pd=Co=AlOx for jPd ¼ 3–6 × 107 A=cm2, depending onthe Pd thickness and in-plane applied field. These resultsshow that Pd=Co=oxide layers with relatively low resis-tivity can be used to combine strong PMA with efficientcurrent-induced magnetization switching, opening the pos-sibility of using Pd as an alternative material to Pt, Ta, andW in SOT devices.

ACKNOWLEDGMENTS

This work was supported by the Swiss National ScienceFoundation (Grant No. 200021-153404) and the European

FIG. 5. (a) Change of the Hall resistance due to magnetizationswitching induced by positive and negative current pulses withamplitude jPd ¼ 4.75 A=cm2 (I ¼ 11 mA) as a function of theexternal field Bext in Pdð4 nmÞ=Coð0.6 nmÞ=AlOx. The externalfield is applied in-plane parallel to the current direction(θB ¼ 89.7°, φ ¼ 0°). (b) Hall resistance as a function of jPdat a constant Bext ¼ 0.2 T. (c) Normalized difference of the Hallresistance measured for I > 0 and I < 0 in (a) as a function ofBext. Similar curves are shown also for different values of jPd.(d) Minimum switching field Bm as a function of jPd and tPd.

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Commission under the Seventh Framework Program(spOt project, Grant No. 318144). We thank JunxiaoFeng and Luca Persichetti for performing the roughnessmeasurements.

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Supplementary Information

SEPARATION OF THE THERMAL AND SPIN-ORBIT TORQUE CONTRIBUTIONSTO THE SECOND HARMONIC HALL RESISTANCE

Abhijit Ghosh, Kevin Garello, Can Onur Avci, Mihai Gabureac, and Pietro GambardellaDepartment of Materials, ETH Zurich, Honggerbergring 64, CH-8093 Zurich, Switzerland

The second harmonic component of the Hall resistance, R2ωH , derives from all the Hall-type voltages that vary

proportionally to I2, namely

V 2ωH = R2ω, SOT

H I +RANE∇T ×m, (1)

where I = I0 sin(ωt) is the ac current injected in the sample, R2ω, SOTH ∼ I is the SOT-modulated Hall resistance,

RANE is the anomalous Nernst effect (ANE) coefficient, and ∇T ∼ I2 is the thermal gradient due to Joule heating.We distinguish two magnetothermal contributions, both due to the ANE and proportional to either the in-planetemperature gradient, ∇Tx, or the out-of-plane temperature gradient, ∇Tz. The first originates from asymmetriesin the structure of the Hall bar, which tends to be hotter in the middle compared to the sides (Fig. 1a). Although∇Tx can be minimized by careful design of the Hall bar, we find that sample-to-sample inhomogeneities, likely dueto the patterning process, result in residual in-plane thermal gradients that need to be accounted for [1]. The secondcontribution is due to the combined effect of the inhomogeneous current distribution in the FM/HM bilayer andthe asymmetric heat dissipation towards the substrate and air sides of the sample [2]. The second harmonic Hallresistance is thus given by

R2ωH =

V 2ωH

I= R2ω, SOT

H +R2ω∇Tx

+R2ω∇Tz

, (2)

where

R2ω∇Tx

=RANEI∇Txmz =

RANEI∇Tx cos θ, (3)

R2ω∇Tz

=RANEI∇Tzmx =

RANEI∇Tz sin θ cosϕ. (4)

We recall that θ and ϕ are the polar and azimuthal angle of the magnetization, respectively, whereas θB and ϕB arethe polar and azimuthal angle of the applied magnetic field Bext. Moreover, because of the uniaxial symmetry of thesystem, we have ϕB ≡ ϕ.

The R2ωH signal before thermal correction is shown in Fig. 1b (detail around zero field) and Fig. 3a (full scale) for the

representative case of Pd(2.5 nm)/Co(0.6 nm)/AlOx. At zero field the magnetization is parallel to the z axis, whichimplies that R2ω, SOT and R2ω

∇Tzare null by symmetry, whereas R2ω

∇Txis maximum. Hence, the difference between the

intercept at zero field for the upward and downward field sweep branches in Fig. 1b is equal to 2RANE

I ∇Tx. Using

this factor and extracting θ from the first harmonic measurements, we can reconstruct the entire R2ω∇Tx

signal using

FIG. 1: (a) Schematic of the current-induced in-plane thermal gradient. (b) Detail of the R2ωH signal before subtraction of the

thermal contribution. The orange arrow shows the amplitude of the factor 2RANEI∇Tx.

2

FIG. 2: (a) Schematic of the current-induced out-of-plane thermal gradient. (b) Top: R2ωH as a function of external field applied

at θB = 89.75◦, φB = 45◦. The extended field range shows that R2ωH peaks when Bext ≈ BK and then rapidly decays, following

the behavior of the magnetic susceptibility. Bottom: detail of |R2ωH | at high field (dashed rectangles in the top panel). (c) R2ω

H

is plotted as a function of (Bext −BK)−1 for Bext ≥ 1.7 T.

Eq. 3, as shown in Fig. 3b.

Finding the R2ω∇Tz

signal requires a more elaborate procedure. As described in Ref. 2, the damping-like (DL) SOT

contribution to R2ωH and R2ω

∇Tzhave the same angular dependence, namely sin θ cosϕ. However, whereas the thermal

signal depends only on the orientation of the magnetization and remains constant once the magnetization has saturatedalong the direction of the external field, the DL SOT signal scales with the susceptibility of the magnetization, whichis inversely proportional to the total effective field Bext−BK . Here, Bext is applied in-plane and BK is the anisotropyfield that opposes the in-plane rotation of the magnetization, which includes both the PMA and the demagnetizingfield. Figure 2b shows R2ω

H measured at θB = 90◦ and ϕB = 45◦ as a function of Bext. This measurement extends wellbeyond the usual range included in SOT measurements, delimited by Bext < BK , and shows how R2ω

H decreases withincreasing field, tending towards a constant value determined by R2ω

∇Tz. In this geometry, when the magnetization lies

in-plane at angles θ = 90◦ and ϕ = 45◦, Eq. 2 of the main text simplifies to

R2ωH =

RAHEBDL

(Bext −BK)cos

π

4+RANE∇Tz cos

π

4. (5)

Plotting R2ωH versus (Bext − BK)−1 thus allows us to extract the asymptotic value R2ω

∇Tzas the intercept of R2ω

H

with the ordinate axis in Fig. 2c, whereas the linear slope of R2ωH is equal to the factor RAHEB

DL cos π4 . Notethat it is important to measure at in-plane fields Bext > 1.5BK to reach near saturation of the magnetization andcorrectly evaluate the above coefficients. By using Eq. 4, it is now possible to reconstruct R2ω

∇Tzfor any direction of

m. This signal has the same symmetry as that induced by BDL, with a maximum contribution for ϕ = 0◦ and a nullcontribution at ϕ = 90◦, as shown in Fig. 3c.

Once the thermal coefficients are evaluated, it is straightforward to correct the raw R2ωH data and isolate the SOT

contribution. In Fig. 3 we illustrate the process for the exemplary measurements at ϕ = 0, 90◦. In panel (a) the rawsignal is plotted as a function of external field. From this curve we subtract the reconstructed signals R2ω

∇Tx(b) and

R2ω∇Tz

(c), leading to the pure SOT contribution R2ω, SOTH shown in (d). After these two corrections, the usual SOT

analysis can be carried out using either the full angle method or the small angle approximation, as described in themain text.

The amount of the correction is strongly sample dependent. In the case of Pd/Co/AlOx, neglecting the thermalcontributions to R2ω

H results in an overestimation of the DL and field-like (FL) SOT by about 20-30%. We remarkthat thermal corrections should be applied also when using the small angle approximation [3]. This is obvious for themeasurements of the damping-like torque at ϕ = 0, since R2ω

∇Tzhas a field dependence that adds up to that of the

pure torque (top panels in Figs. 3c and d). However, because of the planar Hall effect, the correction of the DL SOTalso influences the determination of the FL SOT. Unfortunately these points are often neglected in the analysis of theharmonic Hall voltage in the context of SOT.

3

FIG. 3: Separation of the thermal and SOT contributions to R2ωH . The top (bottom) panels refer to the ϕ = 0◦ (ϕ = 90◦)

geometry. (a) R2ωH measured as a function of applied field. (b) R2ω

∇Tx. (c) R2ω

∇Tz. (d) R2ω, SOT

H = R2ωH −R2ω

∇Tx−R2ω

∇Tz.

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[2] Can Onur Avci, Kevin Garello, Mihai Gabureac, Abhijit Ghosh, Andreas Fuhrer, Santos F. Alvarado, and Pietro Gam-bardella, “Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers,” Phys. Rev. B 90,224427 (2014).

[3] Masamitsu Hayashi, Junyeon Kim, Michihiko Yamanouchi, and Hideo Ohno, “Quantitative characterization of the spin-orbit torque using harmonic Hall voltage measurements,” Phys. Rev. B 89, 144425 (2014).