Crystal orientation dependence of spin-orbit torques in Co/Pt bilayers

In ferromagnet/heavy metal (FM/HM) bilayers with large spin-orbit coupling, charge current injection generates current-induced torques on the ferromagnet due to bulk (spin Hall) and interfacial (Rashba-type) effects. These spin-orbit torques (SOTs) can switch the magnetization and manipulate the magnetic textures such as domain walls in both in-plane and perpendicularly magnetized heterostructures.^1–7 Due to the technological relevance and fundamental interest, a wide variety of FM and HM combinations have been examined.^3,7–12 Among these, Co/Pt is considered as one of the model heterostructures in SOT studies due to the perpendicular magnetic anisotropy and the strong spin-orbit coupling inherent to this system.^1,13–17 It has been revealed that in FM/Pt bilayers, the spin Hall effect (SHE) of Pt^18–23 provides a major contribution to the SOTs.^16,17 Considering that the spin relaxation mechanism in Pt depends on its crystal structure,^24–26 one may expect that the SOTs induced by Pt likewise depend on the crystallographic texture and the grain morphology. For instance, the Elliot-Yafet mechanism^27,28 can be modulated by periodic crystal structures, producing different SHE depending on the direction of charge current relative to the crystal symmetry directions. Likewise, the Rashba effect in metal systems might also generate distinct effective magnetic fields depending on the Pt crystallographic orientation.

In this Letter, we investigate the dependence of current-induced SOTs in Co/Pt bilayers on the crystal structure of the Pt layer. Current-induced effective magnetic fields are evaluated using harmonic Hall voltage measurements. The damping-like (DL) torque is found to be lower when Co is grown on an epitaxial Pt film as opposed to a polycrystalline Pt layer. On the other hand, the field-like (FL) torque has a comparable value in both films. Current-induced magnetization switching measurements reveal critical currents whose relative magnitudes are in agreement with different DL-SOT strengths.

We sputtered AlOx(2 nm)/Co(1 nm)/Pt(5 nm) layers on single crystal MgO(100) and MgO(111) substrates. To obtain the desired epitaxy, we heated the substrate and kept the temperature at 200 °C during the Pt deposition.^24,29,30 The substrate was then allowed to cool to room temperature before subsequent deposition of the Co film to minimize interfacial mixing. Finally, an AlOx capping layer was grown at room temperature. X-ray diffraction (XRD) measurements in symmetric θ-2θ geometry were performed to evaluate the crystal structure as shown in Fig. 1(a). We observe that the XRD spectra of layers grown on MgO(111) exhibit only Pt(111) peaks, indicating epitaxial (111) growth templated by the MgO substrate. On the other hand, we observe both Pt(100) and Pt(111) peaks in the XRD spectra of films grown on MgO(100), indicating a polycrystalline film structure with no preferred crystallographic orientation. Furthermore, the peaks of Pt(111) on the MgO(100) substrate are broader than that in the Pt grown on MgO(111), evidencing the distorted structure of Pt(111) in the former. These suggest that Pt on MgO(100) cannot follow the substrates' structures fully and relaxes to the more energetically favorable bulk phase of (111) after a few monolayers. Co films tend to have (001) orientation which has the same structure as Pt(111). Therefore, we conclude that the entire Co/Pt bilayer is epitaxial on MgO(111), and for the layers grown on MgO(100), Co and Pt near the Co interface are polycrystalline (see supplementary material). In the text below, we denote the epitaxial film grown on MgO(111) as “epi-Co/Pt” and the polycrystalline film grown on MgO(100) as “poly-Co/Pt.”

Polar magneto-optical Kerr effect measurements on continuous films show square hysteresis loops with coercivity of the order of 50 mT, confirming perpendicular magnetic anisotropy (PMA) in both samples [Fig. 1(b)]. Similarly, the prepared films were patterned into $5 μm$-wide symmetric Hall cross structures using standard photolithography and Ar ion milling. Figure 1(c) schematically shows the device and measurement geometry, including coordinate system definitions. The resistivity is found to be 29 $μΩ cm$ for poly-Co/Pt and $23 μΩ cm$ for epi-Co/Pt, with the difference being attributed to reduced bulk scattering due to high structural order on the latter. In order to evaluate SOTs, we performed harmonic Hall voltage measurements with an a.c. current density amplitude $jc=1×1011 A/m2$ and a frequency f = 19.47 Hz. Hall resistance was measured vs applied external magnetic field $Bext$ oriented at an angle $θB=80°$ and two different in-plane angles, $φ=0°$ and $90°$ [Fig. 1(c)]. The small out-of-plane field component was used to avoid domain nucleation at high fields and ensure coherent single-domain magnetization rotation. These measurements allow for the quantification of the effective magnetic fields generated by DL and FL-SOT as well as the PMA of the Co film. The first harmonic Hall resistance (⁠$Rf$⁠) is given by^5,7,9,13

Here, $RA$⁠, $RP$⁠, $θ$⁠, and $φ$ correspond to the anomalous Hall resistance, the planar Hall resistance, and the polar and azimuthal angles of magnetization, respectively. $Rf$ measured at $φ=0°$ is shown in Fig. 1(d) for both the poly-Co/Pt and epi-Co/Pt films. In this configuration, $RP$ is negligible and the signal is predominantly given by $RAcosθ$⁠, which allows us to quantify the magnetization angle $θ=cos−1(Rf/RA)$ accurately. Then, we estimate the effective perpendicular anisotropy field $Bk$ by using a single-domain model in which $Bk=Bext(sinθB/sinθ− cosθB/cosθ)$⁠. The estimated $Bk$ is nearly equal (⁠$∼1.3 T$⁠) in both films, allowing us to compare SOTs by using both the harmonic and switching measurements directly.

The second harmonic Hall resistance $R2f$ is given by^4,9,31–33

Here, $Bθ$ and $Bφ$ are the polar and azimuthal components of the SOT effective field. $R∇T$ is the thermoelectric contribution to $R2f$⁠, which arises from the Joule heating induced thermal gradient along the out-of-plane direction.⁴ To discuss the contribution of SOT in $R2f$⁠, $R2f,SOT(=R2f−R∇T)$ is obtained after subtraction of $R∇T$ (see supplementary material for details). $Bθ$ and $Bφ$ are composed of effective fields induced by the DL-SOT $BDL$ and the FL-SOT $BFL$ whose contributions depend on $Bext$ and $φ$ as follows:

Here, $BDL,FLθ=BDL,FL0+BDL,FL2sin2θ+BDL,FL4sin4θ+⋯$ and $BDL,FLφ≈BDL,FL0$ are the polar and azimuthal components of $BDL$ and $BFL$⁠. Note that we include both the constant (⁠$BDL,FL0$⁠) and the magnetization angle dependent contributions (⁠$BDL,FL2, BDL,FL4$⁠, etc.) to the SOTs, as was first described in detail by Garello et al.¹³ $R2f$ shows strong θ dependence due to the different dominant SOT contributions in these two geometries.

Figures 2(a) and 2(b) show $R2f,SOT$ at $φ=0°$ and $φ=90°$ in poly-Co/Pt and epi-Co/Pt, respectively. $R2f,SOT$ is odd (even) with respect to $Bext$⁠, when $φ=0°$ (⁠$φ=90°$⁠), as expected from the symmetries of DL and FL-SOT given above. Data were fitted to Eqs. (2)–(4) in order to extract $BDL$ and $BFL$ quantitatively. At a given $φ$⁠, the effective fields $Bθ$ and $Bφ$ were recursively evaluated until they reproduced the measured $R2f,SOT$ by taking into account the term arising from $RP$⁠.¹³ Here, $RP$ in each sample was obtained by independent measurements by rotating the magnetization in the xy plane using a high in-plane magnetic field (see supplementary material).

The extracted $BDL$ and $BFL$ as a function of magnetization polar angle $θ$ are reported in Figs. 2(c) and 2(d), respectively. We find that $BDL$ is larger in poly-Co/Pt than in epi-Co/Pt over the entire range of $θ$⁠. On the other hand $BFL$ is similar in both poly-Co/Pt and epi-Co/Pt films. We fit the $θ$-dependence of the SOTs, which yield $BDL,poly0≈1.8 mT$⁠, $BDL,epi0≈1.3 mT$ and $BFL,poly0≈BFL,epi0≈1.2 mT$ for poly-Co/Pt and epi-Co/Pt, respectively. From these results, we computed the effective spin Hall angle, which includes the effects of interfacial spin transparency, using the relation $θSHE=2eMStcoBDL/ℏjc$⁠, where e, $MS$⁠, $tco$⁠, and $ℏ$ are the electron charge, the saturation magnetization, the Co thickness and the reduced Planck constant, respectively.^34,35 We find $θSHE,poly≈0.082$ for poly-Co/Pt and $θSHE,epi≈0.059$ for epi-Co/Pt, in a range that has comparable values given in previous reports.^{16,17,20,21,34,36} Consequently, we conclude that $BDL0$ in epi-Co/Pt is approximately 1.3 times lower than that in poly-Co/Pt, whereas the FL-SOT shows no significant difference between the two samples.

Our observation that $BDL$ evidently depends on the crystal orientation of Pt, whereas $BFL$ does not, may indicate that different mechanisms are contributing to the two SOT effective fields. In the case of the DL-SOT, generally believed to be dominated by the spin Hall effect in the heavy metal, it has been broadly suggested that scattering events dominated by the Elliot-Yafet mechanism play an important role.^{16,17,19,23,37,38} In the present films, the resistivity of the poly-Co/Pt film is notably larger than in the epi-Co/Pt film, which could suggest that different scattering rates give rise to different effective spin Hall angles. Thus, additional scatterings in the poly-Co/Pt film may lead to enhancement of the extrinsic contribution to the spin Hall angle, ultimately resulting in a larger DL-SOT in the poly-Co/Pt film. However, we note that other factors should also be considered for precise interpretation. For instance, the interface-generated SOTs and dependence of the spin Hall torque on the spin diffusion length also manifest in the effective $θSHE$⁠, and these contributions could be different in the poly-Co/Pt and epi-Co/Pt films.^39–44 Although it is hard to separate bulk and interfacial contributions of SHE, the charge current density is more concentrated at the interface in poly-Co/Pt due to its high resistivity, and therefore interfacial SHE might be also enhanced. However, since the Pt thickness is significantly larger than the spin diffusion length, differences in these parameters are unlikely to be important in the experimentally-observed difference in $θSHE$ between the two films.^{17,23,38,45,46} The FL-SOT, by contrast, seems less sensitive to the bulk crystal orientation of Pt, suggesting that an interfacial mechanism may be dominant in giving rise to this torque component.

Finally, we performed current-induced magnetization switching to compare and contrast with the above findings. For these measurements, we sequentially inject 30 ms-long current pulses and then probe the out-of-plane magnetization by the Hall effect, with the amplitude of the current pulse incremented between each measurement. From this, we construct current-swept magnetization switching curves, as shown in the representative examples in Figs. 3(a) and 3(b). Measurements were performed with an applied field $Bext=±80 mT$ along the current-flow axis, as required for deterministic switching. The observed switching polarities are the same for both samples and are consistent with the literature for Co/Pt. We define the critical current density $jcrit$ to be the current density at which $RH$ crosses zero.

In Fig. 3(c), we plot $|jcrit|$ as a function of $Bext$⁠. We find that $|jcrit|$ gradually decreases with increasing $Bext$ as expected since the energy barrier for magnetization switching is lowered due to magnetization canting. We find that across the measured field range, $|jcrit|$ is approximately 1.3 times smaller for poly-Co/Pt compared to epi-Co/Pt. Since the anisotropy fields are nearly the same for these two samples, this result suggests a weaker DL-SOT in epi-Co/Pt, in quantitative agreement with harmonic SOT measurements.

In conclusion, we investigated SOTs in perpendicularly magnetized epitaxial and polycrystalline Co/Pt bilayers by means of the harmonic Hall effect and current-induced switching measurements. We find that the DL-SOT in epi-Co/Pt is smaller by a factor of 1.3 compared to that of poly-Co/Pt, whereas the FL-SOT is comparable in both samples. As the DL-SOT is predominantly given by the SHE, which results from spin-dependent scattering in the bulk of Pt, we associate the difference in DL-SOT to the difference in the crystal orientations of Pt, which results in different scattering characteristics. In agreement with previous studies, our results suggest that $BDL$ is closely related to Pt resistivity; however, $BFL$ is not. Furthermore, the critical switching currents are different for the two films, with a higher switching efficiency observed in poly-Co/Pt, in good agreement with the DL-SOT estimation. This study highlights the effect of the crystal structure of the nonmagnetic heavy metal on SOTs, which may be important for understanding and engineering SOT-based spintronic devices.

See supplementary material for the XRD spectra of Pt/MgO and a detailed analysis to derive SOTs in epi-Co/Pt and poly-Co/Pt.

This work was supported by the Japan Society for the Promotion of Science with Grants-in-Aid 15H05699, 15H05854, and 15H02099 and by the National Science Foundation under Grant No. ECCS-1408172. The authors thank Hiromu Gamou, Keita Nakagawara, Professor Nobuki Tezuka, Maxwell Mann, Kohei Ueda, and David Bono for technical support.