Exceptionally high, strongly temperature dependent, spin Hall


May 2, 2019 - Spin-orbit torques (SOT) in thin film heterostructures originate from strong spin-orbit interactions (SOI) that, in the bulk, generate a...
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Exceptionally high, strongly temperature dependent, spin Hall conductivity of SrRuO3 Yongxi Ou, Zhe Wang, Celesta S. Chang, Hari Nair, Hanjong Paik, Neal Reynolds, Daniel C. Ralph, David A. Muller, Darrell G. Schlom, and Robert Buhrman Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b00729 • Publication Date (Web): 02 May 2019 Downloaded from http://pubs.acs.org on May 5, 2019

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Exceptionally High, Strongly Temperature Dependent, Spin Hall Conductivity of SrRuO3 Yongxi Ou1,2*†, Zhe Wang1†, Celesta S. Chang1,2†, Hari P. Nair3, Hanjong Paik3,4, Neal Reynolds2, Daniel C. Ralph2,5, David A. Muller1,5, Darrell G. Schlom3,5 and Robert A. Buhrman1* 1School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA, 2Department of Physics, Cornell University, Ithaca, New York 14853, USA, 3Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, USA, 4Platform for the Accelerated Realization, Analysis, & Discovery of Interface Materials (PARADIM), Cornell University, Ithaca, New York 14853, USA, 5Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA *email: [email protected]; [email protected] †: These authors contributed equally to this work. Abstract Spin-orbit torques (SOT) in thin film heterostructures originate from strong spin-orbit interactions (SOI) that, in the bulk, generate a spin current due either to extrinsic spin-dependent, skew or/and side-jump scattering, or to intrinsic Berry curvature in the conduction bands. While most SOT studies have focused on materials with heavy metal components, the oxide perovskite SrRuO3 has been predicted to have a pronounced Berry curvature. Through quantification of its spin current by the SOT exerted on an adjacent Co ferromagnetic layer, we determine that SrRuO3 has a strongly temperature (T) dependent spin Hall conductivity  SH , increasing with the electrical conductivity, consistent with expected behavior of the intrinsic effect in the “dirty metal” regime.  SH is very high at low T, e.g.

at 60 K and is largely

unaffected by the SrRuO3 ferromagnetic transition at Tc ≈ 150K, which agrees with a recent theoretical determination that the intrinsic spin Hall effect is magnetization independent. Below Tc smaller non-standard SOT components also develop associated with the magnetism of the oxide. Our results are consistent with the degree of RuO6 octahedral tilt being correlated with the strength of the SOI in this complex oxide, as predicted by recent theoretical work on strontium

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iridate. These results establish SrRuO3 as a very promising candidate material for implementing strong spintronics functionalities in oxide electronics.

Keywords: complex oxide heterostructures, spin-orbit torques, spin Hall conductivity, intrinsic spin Hall effect

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Strong spin-orbit interactions (SOI) in conducting systems have long been a subject of keen fundamental interest and practical importance, accounting, e.g. for the source of the anomalous Hall effect (AHE) in magnetic conductors.1–3 Until recently the direct experimental study of these effects on electron and spin conductivity has been largely limited to magnetooptical studies4,5 and to measurements of the AHE, where the effect of the SOI on electron transport is intertwined with the magnetic properties.1 The development of methods for quantifying the transverse spin Hall conductivity  SH of conducting systems through measurements of the “spin-orbit torques” (SOT)6–10 that the spin current exerts when it impinges on an adjacent ferromagnetic layer, has now established a powerful new technique for studying strong spin-orbit interactions in non-magnetic conductors with high  SH . So far, the search for materials that can provide robust SOT has concentrated on conductors where at least one component is a heavy metal (HM) element, e.g. Pt, W, Bi, Ir,11–18 but it is known that strong SOI can also be found in materials composed of only lighter elements. In particular the Ru ion is understood to be the origin of a quite strong spin-orbit interaction in the conduction bands of the ruthenate class of oxide conductors,19–21 Srn+1RunO3n+1, accounting for the very strong magnetocrystalline anisotropy (MCA) of SrRuO3 (n=  ) in its low temperature ferromagnetic state.19 Band structure calculations have indicated a particularly strong Berry curvature in this material,22,23 which is now understood to be a good predictor of a high intrinsic  SH (strong spin Hall effect, SHE), although AHE measurements did not fully support a dominant role of the Berry curvature in that aspect of ferromagnetic SrRuO3.24 More recently, the spin Hall properties of SrRuO3 has been investigated via inverse spin Hall effect (ISHE) studies of epitaxial SrRuO3/La0.7Sr0.3MnO3 and SrRuO3/Y3Fe5O12 heterostructures,25,26 of which the former work indicated a modest spin Hall angle for SrRuO3 with a maximum value |  SH | 0.027  0.018 at

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190 K, a finding that does not indicate the presence of particularly strong Berry curvature in the SrRuO3 conduction band. We note that the ISHE technique can give values for the spin Hall angle that are quite a bit lower than the values obtained by direct measurements of the torques exerted by the spin Hall effect such as spin-torque ferromagnetic resonance (ST-FMR) measurements8,27 due to the parasitic rectification effects in the ISHE measurements unless painstaking efforts are made.28,29 Also, as we report below, the spin Hall conductivity in SrRuO3 appears to be correlated, as predicted by a recent theoretical effort30 on SrIrO3, with the degree of tilt of the RuO6 octahedra within the material, which if suppressed in a particular sample, due perhaps to a high density of crystalline or point defects, could result in a lower spin Hall conductivity. Here we report ST-FMR measurements of the SOT exerted by high quality SrRuO3 on an adjacent Co thin film layer, with the bilayers grown in situ in a molecular beam epitaxy (MBE) system where the highly ordered SrRuO3 (hereafter SRO) is grown on a SrTiO3 (STO) buffer layer formed on a Si substrate. From these ST-FMR measurements we find that the damping-like SOT that is exerted on the Co layer from RF current flowing in the SRO layer is quite strong at room temperature, indicative of  SH  0.10 at 300 K, and the SOT increases quasi-linearly with decreasing temperature to the lowest temperature studied, ~ 60 K, well below the ferromagnetic Curie temperature Tc of the SRO layer of ~ 150 K. These measurements set lower bounds of

 SH  0.24 and of

for the SRO spin Hall conductivity at 60 K.

Effects of the ferromagnetic transition and the AHE for T ≤ Tc are also clearly evidenced in the temperature dependent SOT.

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Figure 1

(a)

(b)

(c)

(d)

Figure 1 (a) Schematic showing the crystal structure of SrRuO3 on SrTiO3. (b) Low magnification ABF image exhibiting the well-ordered heterostructure of STO/SRO/Co. (c) High magnification HAADF and ABF images of the SRO/Co interface, showing a clearly delineated interface between the deposited Co and the top of the SRO with no indication of interfacial

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disorder that could result from oxidation of the Co surface and reduction of the SRO surface. (d) Resistivity measurements of SRO(10 nm) as a function of temperature. Inset: The derivative of resistivity d  xx / dT versus T. The kink around 150 K indicates the Curie temperature of the SRO.

The fabrication of the oxide/FM heterostructures used in our spin-torque study began with the epitaxial growth of first a 15 nm thick STO buffer layer and then the SRO (4, 6 or 10 nm) on a Si (001) substrate, using a recently refined MBE technique31 (see Supplementary Information (SI)), following by the deposition of a thin film of Co (4 or 6 nm thick) on top of SRO with a 1 nm thick Al capping layer. Figure 1a. provides a schematic representation of the epitaxial heterostructure. We confirmed the quality of the SRO layers by X-ray diffraction (see SI) and by scanning transmission electron microscopy (STEM). Figure 1b shows the low

magnification angular bright field (ABF) image of the STO(15)/SRO(6)/Co(6) heterostructure (thickness of layers in nm). Figure 1c displays high magnification high-angle annular dark-field (HAADF) and ABF STEM images of a SRO(10)/Co(6) sample showing that the Co layer is polycrystalline. As seen clearly in the ABF image, the well-defined atomic positions and clear separation of the layer structures at the SRO/Co interface indicate an abrupt interface, with no sign of interfacial disorder that would indicate an oxidation of the Co surface and a concomitant reduction of the SRO surface.32 We also note that our samples are quite stable over time, yielding essentially the same spin torque results between measurements made over twelve months apart.

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We measured the resistivity of a STO(15)/SRO(10) sample as a function of temperature, with results as shown in Fig.1d. The resistivity of the SRO  xx (T ) shows a strong SRO

temperature-dependent behavior from room temperature down to 4 K, typical of the material.33,34 There is an obvious kink at ~ 150 K in the resistivity, consistent with a change in electron scattering rate due to the ferromagnetic transition of SRO.33 In the inset of Fig.1d, we plot SRO d  xx (T ) / dT as a function of T, from which the Curie temperature can be estimated to be

Tc : 150 K , slightly lower than the Tc in bulk value (~ 160K ), but close to values previously observed in good quality thin SRO films.35 In the SHE a transverse spin current density js is generated in the direction ( zˆ ) normal to the plane of the spin Hall layer with the spin polarization sˆ being in-plane ( sˆy ), orthogonal to the direction ( xˆ ) of the electrical current density jc .  SH  (2e / h) js / jc quantifies the strength of the SHE while the damping-like spin torque efficiency  D  Tint SH as determined for SOT measurements accounts for the less than perfect spin transparency Tint of the interface with the adjacent FM SOT detector.36,37 We note that even for the ideal interface, Tint is less than unity due to the finite spin-mixing conductance of the interface.38 The details of the ST-FMR technique that we used to determine the SOT are provided in the SI along with an example of the ST-FMR signal for one of the SRO/Co samples. Due to the possibility that the spin current from the SRO might have polarization components ( sˆz and/or sˆx ) in addition to the standard SHE sˆy polarization, as we found to be the case at low temperature, as a general procedure we measured the ST-FMR response as the function of the angle  of the Co

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magnetization relative to the RF bias current direction xˆ by varying the orientation of the inplane magnetic field bias from 0 to 360 o relative to xˆ . In ST-FMR, as long as the field-like component of SOT is much weaker than the torque due to the Oersted field, the damping-like spin torque efficiency  D of the SRO/Co heterostructure can be determined from the ratio of the symmetric (S, VS ) and antisymmetric (A,

VA ) components of the FMR response to an applied RF bias current:8,37

D 

VS  e    0 M s tCo dSrRuO3 1  M eff / H res VA  h 

Here e is the electron charge,

(1).

the reduced Planck constant, 0 the vacuum permeability, M s

the saturation magnetization of cobalt, tCo ( dSrRuO3 ) the Co (SRO) thickness, M eff the Co demagnetization field, and H res the resonance field. Table I summarizes  D as determined by ST-FMR measurements for a series of SRO( dSRO )/Co( tCo ) samples at room-temperature (300 K) where only the conventional SOT from the SHE is detected. A substantial  D is found for all three thicknesses of SRO, with  D rising to 0.1 for the SRO(10) samples. Note that for each different SRO thickness,  D is almost identical for the two different Co thicknesses, which indicates that the field-like torque in our SRO/Co is negligible compared to the Oersted field H Oe arising from the RF current flowing in the SRO, since VS / V A would show a nontrivial dependence on tCo if there was a significant field-like torque contribution arising from either an interfacial Rashba-Edelstein effect or from spin rotation during reflection of the incident spin current from the SRO.37 We also note that the

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agreement between the  D values for the 4 nm and 6 nm thick Co samples gives additional support to our conclusion that any “self-Oersted” field that might arise from a non-uniform current flow in the Co, due to a resistivity that might vary differently with distance from one of its two interfaces than from the other, is not a significant factor in our measurements. Table 1: The damping-like spin torque efficiency  D determined from ST-FMR at 300 K for different SRO( dSRO )/Co( tCo ) bilayers. Sample

 D at 300K

SRO(10)/Co(6)

0.10  0.02

SRO(6)/Co(6)

0.05  0.01

SRO(4)/Co(6)

0.05  0.01

SRO(10)/Co(4)

0.10  0.01

SRO(6)/Co(4)

0.06  0.01

SRO(4)/Co(4)

0.05  0.01

Typically, when a HM thickness-dependent  D is observed in measurements of HM/FM heterostructures it is attributed to the fact that the maximum spin current density from the SHE is only approached once the HM thickness is > s , the spin diffusion length.39,40 This would SRO indicate s > 6 nm in our samples, which seems unlikely for SRO at room temperature with

its “bad metal” short mean free path and apparent strong SOI. Moreover a long diffusion length explanation is not consistent with  D being nearly the same for the SRO(4) and SRO(6) samples.

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It is more likely that the SRO electronic structure has a significant dependence on thickness due to a strain effect from the STO/SRO interface that modifies the transport properties of the material, including  SH . To examine this possibility, we performed high resolution STEM to quantify the position-dependent tilt of the RuO6 octahedra in SRO films of two different nominal thicknesses, 6 nm and 10 nm. Results are shown in Fig. 2. The octahedral tilt in the bulk of the thicker SRO is above 20o while it is only about 8o in the thinner SRO sample. A recent theoretical calculation of the spin Hall conductivity of orthorhombic SrIrO3 has concluded that tilting and rotation of the oxygen octahedron in that complex oxide is crucial to the spindependent hopping generating the large spin Hall effect that is predicted, and that this spindependent hopping is not allowed in the perfect cubic perovskite.30 We also note that the measured tilt of both SRO samples drops down to ~ 5o in the last layer adjacent to the Co. This suggests that there could be a diminished spin Hall conductivity near the SRO/CO interface. Thus, while there is no evidence of substantial atomic intermixing at the interface (Fig. 1c), there could still be a non-ideal reduction of Tint due to this suppression of tilt adjacent to the interface. This is because, depending upon the spin diffusion length in the first few SRO layers adjacent to the Co, the spin current density reaching the SRO/Co interface could be less than that generated in the bulk of the thick SRO sample. This would make the spin Hall angle and spin Hall conductivity of the bulk SRO material even larger than indicated by our SOT measurements and the assumption of an ideal Tint .

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Figure 2

(a)

(b)

(c)

Figure 2 (a) ABF image along the [010] zone axis of the SRO orthorhombic crystallographic axis showing small octahedral tilts in the SRO layer within the SRO(6)/Co(6) sample. (b) Similar ABF image of the SRO layer within the SRO(10)/Co(6) sample showing larger octahedral tilts compared to Fig. 2a. (c) The average projected tilt angle for each layer of the SRO(6)/Co(6) and SRO(10)/Co(6) samples determined from the ABF images. The colored diagrams within (a) and (b) depict the tilted octahedra overlaid on the ABF images.

To examine the effect of the strongly temperature (T) dependent electron conductivity of SRO and also the effect of its ferromagnetic transition on the spin current, we performed Tdependent ST-FMR measurements on several SRO(10)/Co(6) samples. For a transverse spin 11

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current of arbitrary spin polarization, the dependence of the SOTs on the magnetization direction results in the following for both the S and A components (see SI):

VS ( A)  VSy( A) cos sin 2  VSz( A) sin 2  VSx( A) sin  sin 2

(2).

In Eq.(2), the first term VSy( A) is determined by the strength of the torques exerted on the FM by the standard SHE-generated spin current ( H Oe ), which represent the in-plane (//) (out-of- plane (  )) torque with symmetry  / /(  ) ( )   S ( A) cos  . The second and third terms denote the STFMR responses that arise from the torques exerted by any incident spin currents with, respectively, sˆz and sˆx polarization (or from the torques exerted by any effective field that is along zˆ or xˆ ). As we discuss below, the signals from our SRO/Co samples are, as expected, dominated by the first term in Eq. (2), but at low T there is also a measurable component whose

 dependence is described by the second term. Figure 3a shows the schematics for  / / and   in the SRO/Co bilayer. y y We show in Fig.3b  D as determined from the VS / V A ratio of the ST-FMR response for

one of our SRO(10)/Co(6) microstrips as a function of T from 300 K to 60 K. Within this T range,

 D increases monotonically and substantially, as T is decreased (a very similar result was obtained with a second sample; see SI). This  D behavior is unusual as the SRO conductivity

 xx (T ) is also increasing with decreasing T (see the inset of Fig.3c). Since we have

 D  Tint (2e / h) SH /  xx , our results indicate a strongly varying  SH (T ) , increasing by as much as 8 times, from room temperature to 60 K, unless Tint is also strongly T-dependent, which we consider unlikely (see SI). With the assumption that Tint is constant, in Fig. 3c we plot the

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Figure 3

(b)

(a)

(d)

(c)

(e)

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Figure 3 (a) Schematic of the SRO/Co spin torque geometry. (b) The SHE-induced damping-like spin torque efficiency  D determined from the angular ST-FMR as a function of T. (c)(d) The eff extracted effective spin Hall conductivity  SH of SRO (c) as a function of T (Inset: the

corresponding T-dependent electrical conductivity of the 10 nm SRO layer measured in the same T range) and (d) as a function of the electrical conductivity of the SRO layer. (e) The dampinglike spin torque efficiency arising from the spin current component with perpendicular spin polarization sˆz , and (inset) the perpendicular effective field, plotted as a function of T.

effective

spin

Hall

conductivity,  SH (T )  Tint SH (T )   h / 2e   DL (T ) xx (T ) eff

of

this

5 1 -1 SRO(10)/Co(6) bilayer showing that it attains the value of 3.2 10  h / 2e   m at 60 K. We eff note again that even though the value that we obtain for  SH is exceptionally high for a material

with no heavy elements and a low carrier density, it is only a lower bound since Tint < 1. Theoretical examinations of the spin Hall effect in normal metals,41–43 and the anomalous Hall effect in ferromagnets,44 have concluded that in the ultraclean region where the carrier lifetime is long, extrinsic skew scattering provides the dominant contribution. In that case the spin Hall angle should be independent of the material’s electrical conductivity  xx . If the carrier lifetime  is reduced, the material enters the clean region where first side-jump and then the intrinsic effect become the dominant contribution as the energy scale set by the decreasing carrier lifetime becomes comparable to the spin-orbit interaction energy. In the clean region the spin Hall conductivity is expected to be more or less independent of  xx . Finally, when  is further decreased the metal begins the transition into the “dirty metal” (or “bad metal”) region 14

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where the carrier mean free path approaches atomic dimensions. There the still dominant intrinsic SHC is expected to decrease rapidly with  (  xx ) until the metal is fully in the carrierhopping regime and the SHC varies even more strongly with  xx . SRO is a dirty or bad metal at eff 300K and in accord with that condition we find, as plotted in Fig. 3d, that  SH increases with

 xx (decreasing T) until the ferromagnetic transition point is reached, where there is an interesting “break” in the slope of the variation, after which the trend continues to the highest electrical conductivity ( : 14 105  1m 1 , 60K) reached in the experiment. Part of the  SH (T ) behavior could alternatively arise from a T-dependent change in the octahedral tilt due to the change in the interfacial strain, but since Co has a slightly higher coefficient of thermal contraction than SRO,45,46 any detrimental strain at the SRO/Co interface should increase with decreasing T. eff In addition to the high  SH (T ) and its strong variation with T, another initially surprising

result is the small effect the paramagnetic-to-ferromagnetic transition of the SRO has on either the ST-FMR measurement or on  D ( js ), (Fig. 3b). If the interface between the SRO and Co is well ordered, exchange coupling should develop between the two ferromagnetic layers below 150 K. However our SRO layers are twinned and as the result each 10 x 20 µm2 sample can reasonably be considered to contain a small ensemble of ~5 µm twinned domains as reported for similar SRO layers.47 Since our devices are patterned so that the RF current flows along the [100] pseudocubic axis, each sample can be expected to include domains where the b-axis of the orthorhombic SRO is oriented either ±45o to the direction of the current flow, and also domains where the b-axis lies 45o out of plane (see SI). This is the easy axis of the very strong MCA of SRO in the FM state, with reported anisotropy fields > 1 Tesla .19 The effect of the exchange 15

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coupling between the Co and those SRO domains with an out-of-plane orientation of the b-axis is apparent in the behavior of the Co demagnetization field below Tc, where the data indicates that the SRO is exerting a, sample-dependent, net interfacial anisotropy field on the Co layer (See SI for more details). Other than this effect on M eff , the exchange coupling does not appear to have any significant effect on the ST-FMR measurement. The angular dependence of the STFMR below Tc shows that the Co magnetization continues to rotate smoothly with the ~ 1000 Oe external bias field, which indicates that the net in-plane pinning field between the multi-domain SRO and the Co is not significant. With respect to  D ( js ), until recently it has generally been expected that any spin current generated by the SHE in a FM would be rapidly dephased due to precession about the local exchange field, and that only a spin current component whose polarization is collinear with the internal magnetization would be retained.48,49 Therefore one interpretation for the persistence of a strong transverse spin current with sˆy polarization well below Tc is that this could be due to the spin diffusion length s in SRO being considerably shorter than the spin dephasing length  dp in the FM state. In a conventional ferromagnet, e.g. Co,

1 nm << s ,40,50 but the lower SRO

exchange energy (field) in combination with its very strong spin-orbit interaction (short s ) could perhaps reverse this relationship resulting in an atypical preservation of a strong spin Hall current below the SRO magnetic transition. A very interesting alternative explanation, however, is provided by a recent work51 which concludes that when a spin current arises from the intrinsic spin Hall effect in a ferromagnetic material the spin current is magnetization-independent and propagates without dephasing, unlike the spin current generated by an extrinsic mechanism, such as skew scattering. Since the intrinsic effect appears to be the dominant contributor to the SRO

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spin Hall conductivity, the largely magnetization-independent behavior of the spin current below the ferromagnetic transition is consistent with that prediction. There is clear evidence of the FM state in the spin torque behavior; that is found in the smaller response of the ST-FMR signal that has the symmetry expected for a spin current with z sˆz polarization, as described by the second term in Eq. 2. In that case VS arises from an in-plane z z field-like spin-orbit torque via a perpendicular effective field H eff and V A is the measure of the

out-of-plane damping-like torque generated by the Co absorption of sˆz spins (see SI). In Fig. 3e z z and its inset we plot as a function of T the spin torque efficiency  D and H eff , respectively, due

to sˆz . Two possible sources of this additional spin torque (spin current) below Tc are the AHE and the anisotropic magnetoresistance (AMR) or planar Hall effect (PHE).49 In both cases, these effects result in a spin current that is polarized parallel to the local magnetization of the ferromagnet, with the spin current flowing either perpendicular to the plane defined by the bias current direction and magnetization direction (AHE) or parallel to the magnetization (PHE).52 Since as discussed above some of the SRO material in each sample should have b-axis oriented

45o out of plane, we would expect the spin current arising from either the AHE or the PHE to have, due to the partial out-of-plane magnetization, an out-of-plane sˆz component. The temperature dependence (Fig. 3e) of the damping-like spin torque attributable to an out-of-plane polarized spin current is not in close accord with that of the AHE in SRO,19 but is quite similar to z the behavior of the strong AMR (PHE) reported for SRO.53 Therefore we tentatively attribute  D

to the absorption by Co of this PHE generated sˆz spin current, with the sharp rise in its amplitude just below Tc, being due to the rapid development of the exchange field that is required to

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z produce this spin orientation from the underlying SHE. The amplitude of  D at 60 K, together

with the value of  xx , indicates a lower bound for the transverse spin conductivity associated with the sˆz polarized spin current of  xyz ≈ s

. The actual value will be

somewhat higher because of the combined effects of the undetermined values of Tint and of the percentage of the twinned SRO material with the b-axis at 45o out of plane. We estimate H Oe per unit current density as generated by the RF current in the SRO to z be ≈ 6 1011 Oe/(Am -2 ) from Ampere’s Law. As can be seen in the inset of Fig. 3e, H eff is only z to be the effective field that is : 15% of H Oe at 60 K. We tentatively ascribe this small H eff

exerted on the SRO magnetization by the limited precession of the spin Hall current about the exchange field in those domains where the easy axis (b) is out of plane, with this field then acting on the Co. We note that there is a clear magnetic interaction between the SRO and the Co as evidenced by the change in the demagnetization field of Co behavior below Tc of SRO (see SI). Since the dimensions ( 20  m 10  m ) of the patterned SRO/Co microstrips used in the STFMR measurements are only somewhat larger than the size (~5 µm) of the twinned domains z z reported in similar SRO layers,47 the details of the  D and H eff signals, and also the behavior of

the Co demagnetization field, should vary somewhat from sample to sample, which is what we observe (see SI). We also analyzed the magnitude of the torques described by the third term in Eq.(2) of the angular dependent ST-FMR signal, but found them either non-existent or much weaker than the other two terms (not shown here). In summary, from ST-FMR measurements we obtain a strong, damping-like SOT attributable to the spin Hall effect in the high-quality SRO/Co bilayers that increases with

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decreasing temperature and continues to do so well below the Curie temperature of the SRO, 5 1 -1 with the lower bound of the spin Hall conductivity rising to  SH   h / 2e  3 10  m at 60 K.

The variation of spin Hall conductivity with mean carrier lifetime, as indicated by the electrical conductivity, is consistent with the expected dirty metal behavior of the intrinsic spin Hall effect below, but in the vicinity of the clean metal regime. The minimal effect of the ferromagnetic transition on the spin Hall conductivity is in accord with the recently predicted magnetization independence of the spin current arising from the intrinsic spin Hall effect. We also observed spin torques attributable to a smaller spin current being emitted by the SRO in the FM state with out-of-plane polarization as might be expected from spin currents generated by the strong AMR previously reported for SRO films. The correlation we find between atomic structure and the strength of the spin Hall effect suggests that the degree of RuO6 octahedral tilt is key to maximizing the spin Hall conductivity of SRO, as predicted recently for strontium iridate. Finally this work clearly establishes that quite strong SOT functionality can be realized in complex oxide electronics.

Supplementary Information Additional details on the MBE growth, XRD and STEM characterization of the STO/SRO/Co thin film heterostructures, analysis and examples of the ST-FMR measurements, and the temperature dependent demagnetization field of the Co layers.

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Authors contributions: Y.O. and R.A.B conceived and designed the experiment. Z.W, H.P.N and H.P. grew the samples with guidance from D.G.S. Z.W. performed the transport measurement. C.S.C performed the STEM measurements and analyzed the STEM images with help from D.A.M. Y.O. fabricated the samples. Y.O. with the assistance of N.R performed the ST-FMR measurements and analyzed the data. Y.O. and R.A.B wrote the manuscript, and all authors contributed to the final version. Competing interests: The authors declare that they have no competing interests.

Acknowledgement: This work was supported by, and also made use of the Shared Facilities of, the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR1719875). This work also made use of the Cornell NanoScale Facility/National Nanotechnology Coordinated Infrastructure which is supported by the NSF (ECCS-1542081). Z.W., H.P.N. and D.G.S. gratefully acknowledge the support from a GRO ‘functional oxides’ project from the Samsung Advanced Institute of Technology and support from the W.M. Keck Foundation. H.P. acknowledges support by the National Science Foundation (Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM)) under Cooperative Agreement No. DMR-1539918. C.S.C. and electron microscopy characterization were supported by the Department of Energy (DE-SC0002334).

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