Crystalline Orientation–Dependent Spin Hall Effect in Epitaxial Platinum

We report on the spin Hall effect in epitaxial Pt films with well-defined crystalline (200), (220), and (111) orientations and smooth surfaces. The magnitude of the spin Hall effect has been determined by spin–torque ferromagnetic resonance measurements on epitaxial Pt/Py heterostructures. We observed a 54% enhancement of the charge-to-spin conversion efficiency of the epitaxial Pt when currents are applied along the in-plane < 002 > direction. Temperature-dependent harmonic measurements on epitaxial Pt/Co/Ni heterostructures compared to a polycrystalline Pt/Co/Ni suggest the extrinsic mechanism underlying spin Hall effect in epitaxial Pt. Our work contributes to the development of energy-efficient spintronic devices by engineering the crystalline anisotropy of non-magnetic metals.

In this letter, we detail the growth of epitaxial Pt thin films and Pt/FM heterostructures with (200), (220), and (111) crystalline orientations. In epitaxial films, symmetries of the magnetic interactions will reflect the underlying crystal and interface symmetries where the three orientations studied have four-fold, two-fold, and three-fold surface symmetries, respectively. The symmetries should be reflected in fundamental properties such as interfacial anisotropy (both in-plane and out-of-plane) [37] and Dzyaloshinskii-Moriya interaction (DMI) [38,39]. For low-symmetry systems such as Pt (220) with C 2v , the strength of the DMI may vary in magnitude or sign along different directions [40][41][42][43][44]. Such anisotropic DMI and anisotropy can stabilize novel phases such as antiskyrmions [41].
In this study, we focus on the SHE with the current flowing in various symmetry directions in Pt. By quantitatively evaluating the SOT along in-plane crystalline orientations via spin torque-FMR (ST-FMR) measurements, isotropic and anisotropic SHE have been observed and the role of the crystal symmetry enumerated. Moreover, by performing temperature-dependent harmonic measurements, we further reveal the intrinsic and extrinsic mechanisms underlying the SHE in epitaxial and polycrystalline Pt films. By combining directional-dependent SOT and anisotropic magnetic properties, we anticipate energy-efficient magnetization manipulation in novel spin structures.

SAMPLE GROWTH AND CHARACTERIZATION
Epitaxial Pt films were grown onto single-crystalline MgO (200), MgO (220), and Al 2 O 3 (1120) substrates by DC magnetron sputtering. The vacuum chamber had a base pressure of 8 × 10 −8 Torr and a growth Ar pressure of 2.7 mTorr. Pt (200) was grown on Cr (200)-buffered MgO (200) substrates. The 5-nm-thick Cr (200) seed layers were deposited at 450°C to initiate the epitaxy, followed by Pt (200) deposition at 200°C. Pt (220) and Pt (111) films were grown directly on MgO (220) and Al 2 O 3 (1120) substrates, respectively, at 300°C. The growth procedures have been optimized for both epitaxy and desirable smooth surface conditions. After the Pt growth, the substrate was cooled, and subsequential FM layers were grown in situ at room temperature to minimize the interfacial mixing effect and magnetic dead layers. All samples were capped with a 2-nm-thick amorphous Al 2 O 3 layer to prevent surface oxidation. Following the aforementioned procedure, we prepared a series of epitaxial Pt (10)/ Py (8) (Py, Ni 81 Fe 19 ) samples for ST-FMR measurements and both epitaxial Pt (111) (5)/Co(0.8)/Ni(1) and polycrystalline Pt (15)/ Co(0.8)/Ni(1) samples with perpendicular magnetic anisotropy for harmonic measurements (thickness in nanometer throughout the text unless otherwise stated). Note that the choice of Py as the FM layer is motivated by its wide application as an efficient spin detector [15,[45][46][47][48][49][50] and the usage of Co/Ni is due to its spontaneous perpendicular magnetic anisotropy, a prerequisite for harmonic measurements [51,52].
The crystallographic properties of as-deposited Pt films were evaluated by X-ray diffraction (XRD) measurements. The out-ofplane symmetric θ-2 θ scans of Pt (200), Pt (220), and Pt (111) films are presented in Figures 1A-C, demonstrating the epitaxy growth along the substrates or the seed layers. The clear Laue oscillations of the Pt (111) peak indicate excellent lattice matching and a sharp Al 2 O 3 /Pt interface. Figures 1D-F show the in-plane XRD scan, confirming the characteristic four-fold symmetry of Pt (200) film and two-fold symmetry of Pt (220) film. Note that the Pt (111) sample exhibits a six-fold symmetry, which is attributed to crystal twinning. The relative orientation between the crystalline axis of the Pt thin films and substrates has been verified by both ϕ scans and semi-sphere pole figures, as shown in Supplementary Figure S2-S4. Specifically, for the Pt (200) sample, the in-plane Pt < 002 > aligns with MgO < 002 > and is 45°to the in-plane Cr < 002 > and Pt < 220 > . For the Pt (220) sample, the in-plane Pt < 002 > //MgO < 002 > and Pt < 220 > // MgO < 220 > . For the Pt (111) sample, the in-plane Pt < 220 > is perpendicular to the in-plane Al 2 O 3 < 0001 > . By fitting the low-angle X-ray reflectivity (XRR) data, the surface roughness of the deposited Pt (111), Pt (220), and Pt (200) films are found to be 0.085, 0.25, and 0.37 nm (Supplementary Figure  S1A-C), respectively. The smooth surface condition of the prepared epitaxial Pt thin films contributes to a sharp HM/FM interface, which is the key to reduce inhomogeneous linewidth broadening [53] and improved spin current conductance [54]. We highlight that some previous studies of Pt (220) films observed significant surface roughness [55] which we have ameliorated.

ST-FMR Measurements
We first introduce our ST-FMR measurement technique to characterize the charge-to-spin conversion efficiency J S /J C of the deposited epitaxial Pt films. Figure 2A illustrates the schematic of our ST-FMR measurement setup. In the measurements, a microwave current is applied along specific in-plane crystalline directions in the Pt layer determined by lithography. Due to the combination of the SHE and spin diffusion effects, oscillating spin currents can be generated in the Pt films, transported across the Pt/Py interface, and absorbed by the adjacent Py layer. The out-of-plane Oersted field torque and the in-plane SOT will drive precessional motion of the Py magnetization around the direction of the in-plane effective magnetic field, leading to an oscillatory change in resistance arising from the anisotropic magnetoresistance (AMR) of Py. The largest precession amplitude is found to occur at the ferromagnetic resonance (FMR) frequency of the Py layer. Mixing the oscillatory resistance and the applied RF current will give rise to a DC voltage, which can be detected by a lock-in amplifier with a modulated RF current. Figure 2B shows the optical image of the photolithographically patterned microstrips with varied aspect ratios for impendence matching and two different orientations of the current. Coplanar wave guide (CPW) channels are patterned in certain angles to align with the crystalline orientations in the prepared Pt/Py films. Ti (6)/Au (200) pads are fabricated for symmetric ground-signal-ground contact electrodes by a standard sputtering and lift-off technique. The RF current is applied to the CPW channels via wire bonding from transmission lines to the ground-signal-ground electrodes. The in-plane external magnetic field is oriented 45°relative to the CPWs to improve the magnitude of the measured ST-FMR signals [46]. Measurement of the induced DC voltages takes advantage of a bias tee which separates the input RF microwave currents and the ST-FMR signals. All the ST-FMR measurements presented in this work were performed at room temperature. The measured DC voltage follows a linear dependence on the applied microwave power, as shown in Figure 2C, suggesting the marginal role of the Joule heating effect in our measurements.
The ST-FMR technique provides a quantitative measurement of the J S /J C of the prepared epitaxial Pt films. The lineshape of the Frontiers in Physics | www.frontiersin.org January 2022 | Volume 9 | Article 791736 measured DC voltage can be expressed as a combination of symmetric Lorentzian and antisymmetric Lorentzian [56][57][58]: where the parameter S is the amplitude of symmetric Lorentzian arising from the spin Hall-induced anti-damping SOT exerted on Py, A is the amplitude of antisymmetric Lorentzian resulting from the sum of field-like SOT and Oersted field torque, B 0 is the resonance field, and Δ is the full-width-half-maximum (FWHM) linewidth of the Py layer. The ratio between S and A is directly proportional to J S /J C , which can be further expressed as follows [15]: where μ 0 is the permeability in vacuum; Z is the reduced Planck constant, e is elementary charge; M S is the saturated magnetization of Py, which has been characterized to be 698 kA/m via vibrating sample magnetometry (VSM) measurements (Supplementary Figure S5); M eff is the effective magnetization of Py which can be obtained from fitting the frequency-dependent resonance field by the Kittel formula [59]; and t and d represent the thickness of Py and Pt layers, respectively. Figures 2D-F show the experimental ST-FMR resonance spectrum measured on Pt (200)/Py, Pt (220)/Py, and Pt (111)/ Py samples with microwave frequencies varying from 5 to 11 GHz. Due to the larger saturation field of Py, measurements of the Pt (220)/Py sample are mainly focused in the high-frequency regime. For Pt (220)/Py, the shift of the resonance fields when the RF current applied along different crystalline directions is attributed to the in-plane anisotropy of Py induced by Pt (220) with low symmetry (C 2v ), while in highsymmetry systems (C 4v and C 3v ) of Pt (200) and Pt (111) samples, nearly isotropic Py magnetic properties make the resonance fields independent of the in-plane direction. The experimental results (open dots) were well-fitted with Eq. 1 (solid lines). We note that J S /J C follows a constant value over the whole frequency range of our measurements. It is worth mentioning that the lineshape method based on Eq. 2 only provides an estimation of the upper limit of J S /J C due to the resonance-driven spin pumping effect from Py to Pt as reported in a previous work [46,49].
To independently verify the results obtained from the lineshape method, we also performed linewidth modulation measurements. By applying a DC current to the patterned Pt/ Py microstrip, a static anti-damping torque effectively modulates the Gilbert damping of Py, resulting in a systematic currentdependent variation of the linewidth of the obtained ST-FMR spectra. Based on the spin-transfer torque (STT) model [56], the injected DC spin currents effectively increase (decrease) the damping of the Py layer when the spin polarization is parallel (antiparallel) to the Py magnetization, leading to a broadened (reduced) ST-FMR linewidth [15,60]. Furthermore, reversing the polarity of the external magnetic field that saturates Py magnetization will also lead to the sign change of the observed signals, as illustrated in Figure 3. Quantitatively, J S /J C can be obtained from the slope of the DC-dependent resonance linewidth of Py as follows [15,23,49]: where φ is the angle between DC current and external magnetic field, f is the FMR frequency, c is the gyromagnetic ratio, and J C is the electric current density in the epitaxial Pt layer. Figure 3 presents the results of modulated linewidth as a function of J C in Pt (220)/ Py(8) sample. By four-probe measurement, the longitudinal resistivity ρ xx of Pt (220) and the 8-nm-thick Py films along individual crystalline orientations has been characterized independently on control samples (Supplementary Figure S6).
Thus, J C can be quantitatively calculated from the portion of current distribution based on the parallel resistor model. As shown in Figures 3A,B, when the electric current is along < 002 > , the slope is approximately 54% larger than that when current is along < 220 > . We note that such distinct crystalline orientation-dependent SHE is absent in higher symmetry Pt (200)/ Py and Pt (111)/Py samples. To summarize our ST-FMR results, Table 1 shows the obtained J S /J C of Pt along different crystalline orientations of the prepared epitaxial Pt films. In general, a larger value of J S /J C is observed in the sample with higher ρ xx . In the high-symmetry systems such as square Pt (200) and hexagonal Pt (111) lattice with C 4v and C 3v symmetry, the difference between ρ xx along different in-plane crystalline orientations is less than 5%, within the experimental error. Notably, the isotropic ρ xx yields isotropic J S /J C in Pt (220) and Pt (111) samples. Isotropic J S /J C has been observed in other high-symmetry epitaxial materials, such as SrIrO 3 (0001) [25] and Fe (001)/Pt [61]. In contrast, in the lowsymmetry system (C 2v ) of Pt (220), ρ <002> xx is 11% larger than ρ <220> xx . The obtained value of J S /J C along < 002 > direction is significantly larger than that along < 220 > direction via both lineshape and linewidth methods. We remark that the obtained anisotropic J S /J C on Pt (220) agrees with the results recently reported [30], where enhancement of J S /J C was also observed in Pt when current was along < 002 > direction.
As the thickness of the measured Pt films is greater than the spin diffusion length λ S , the measured J S /J C is mainly contributed by bulk SHE, bulk REE, and interfacial REE [62]. The bulk SHE consists of intrinsic and extrinsic mechanisms, in which orientational-dependent anisotropic ρ xx can be contributed by the intrinsic SOC and intrinsic SHE. On the other hand, different extrinsic scattering events can give rise to anisotropic SHE; however, extrinsic impurity scattering is minor in the undoped, highly crystalline epitaxial Pt. Therefore, we believe that the anisotropic bulk SHE in Pt is mainly driven by the orientation-dependent intrinsic mechanism. This is supported by the fact that since broken space inversion symmetry is absent in Pt crystals, the bulk REE contribution can be ruled out [63]. Last, the interfacial REE is expected to be anisotropic in the Pt (220)/Py interface. Simon et al. demonstrated, for reduced symmetry surface such as Au (110), the anisotropic REE dominates due to the mixing of the surface state with the bulk state [64].
Conclusively, the anisotropy in both intrinsic SHE and interfacial REE could result in anisotropic J S /J C .

Temperature-Dependent Harmonic Measurements
To further understand the resistivity-dependent SHE of the epitaxial Pt films, we performed temperature-dependent harmonic measurements on patterned Pt/Co(0.8)/Ni(1) Hall devices, as illustrated in Figure 4A. Figure 4B shows the characteristic first and second harmonic Hall results measured in the prepared device. For bulk SHE, when a charge current J C flows through the Pt along the x-axis, spin current J S is generated along the z-axis with spin polarization σ along the y-axis. A damping-like SOT τ DL ∼ m × (σ × m) and a field-like SOT τ FL ∼ σ × m produced by the generated spin currents are exerted on the magnetization m of Co/Ni [1,4]. When m reaches an equilibrium position, the effects of these two SOTs   Frontiers in Physics | www.frontiersin.org January 2022 | Volume 9 | Article 791736 can be described equivalently as the damping-like effective field (ΔH DL ∼ m × σ) and field-like effective field (ΔH FL ∼ σ), respectively [1,4]. By applying a 5-mA AC current at a frequency of 161 Hz, the generated ΔH DL(FL) causes an oscillation of m around the equilibrium position. By sweeping an in-plane external magnetic field along the current direction, the field dependence of the first harmonic signal V ω and the 90°out-of-phased second-harmonic signal V 2ω can be measured. The derivatives of the harmonics signal are used to calculate the ratio coefficient B x(y) [20,65,66]: and the ΔH DL(FL) can be extracted as follows [20,65,66]: where ξ is the ratio of the planar Hall resistance R PHE and AHE resistance R AHE . Note that the reported R PHE is typically much smaller than R AHE [66], giving rise to the following approximation: [25,66,67]. Notably, the slope of V 2ωx versus the field along the x axis is much larger than the slope of V 2ωy versus field along the y axis, indicating a negligible contribution from the field-like SOT. Hence, we only consider the damping-like SOT in this work. From ΔH DL , J S /J C can be calculated based on the following equation [68,69]: Figure 4C presents the obtained temperature-dependent J S /J C of epitaxial and polycrystalline Pt films. As mentioned before, the growth condition of Co/Ni on Pt (111) is consistent with the growth condition of Co/Ni on polycrystalline Pt. Furthermore, the saturated magnetization M S of Pt/Co/Ni for both polycrystalline Pt and Pt (111) sample is nearly the same (600 kA/m), suggesting similar surface conditions. We can see that J S /J C measured on Pt (111) at room temperature agrees well with the value obtained from ST-FMR measurements. Also, J S /J C of polycrystalline Pt is about 3 times larger than that of the epitaxial Pt (111), which is comparable with the values reported in other studies [24]. In the temperature range of our measurements, J S /J C of both polycrystalline and epitaxial Pt films decreases monotonically with temperature. Due to the high residual-to-resistance ratio in epitaxial Pt (111), the shunting effect becomes significantly pronounced in the low-temperature regime; thus, the measured anomalous Hall signals coming from Co/Ni become negligibly small below 150 K. In metals with spin-orbit coupling, spin Hall conductivity is predicted to scale with ρ xx linearly or quadratically [70]. The former contribution results from the extrinsic scattering in "clean metals," and the latter one is driven by the intrinsic mechanism in "dirty metals" [70]. Isasa et al. reported that the intrinsic mechanism dominates the SHE in polycrystalline Pt [71], while for the case of epitaxial Pt (111) with significantly reduced resistivity, the weight of extrinsic mechanism is reasonably raised in "cleaner" epitaxial Pt (111). Our results support the previous picture.

CONCLUSION
In summary, we have prepared high-quality epitaxial Pt thin films on a series of substrates. Systematic ST-FMR measurements demonstrate the isotropic nature of SHE in the high-symmetry Pt (200) and Pt (111) films. In contrast, the low-symmetry system such as (220) orientated Pt exhibits the anisotropic SHE behavior that is correlated to the anisotropic resistivity. The temperaturedependent harmonic measurements further suggest that SOT can be a hint for "cleaner" metals with more extrinsic contribution to SHE. The observed crystalline orientation-dependent J S /J C of epitaxial Pt could be readily extended to other Pt/FM heterostructures with a broad range selection of FMs. Our work reveals the underlying mechanism of SHE in crystalline textured metals and broadens the material scope available for developing energy-favorable spintronic devices for next-generation information technologies.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

AUTHOR CONTRIBUTIONS
YX and EF conceived the idea and designed the project. YX fabricated devices and performed characterization. YX and HW performed the measurements. All authors discussed the results and contributed to the final manuscript.