Composition dependence of spin–orbit torques in PtRh/ferromagnet heterostructures

Spin currents generated by the spin Hall effect and/or interfacial spin–orbit coupling effect can exert torque on the magnetization. This so-called spin–orbit torque (SOT) has been demonstrated to effectively switch the magnetization,^1–6 drive domain wall motion,^7–9 and cause precession of magnetization.¹⁰ The conversion efficiency of charge current to spin current is characterized by the effective spin-torque efficiency or spin Hall conductivity, which can be extracted by spin-torque ferromagnetic resonance (ST-FMR), inverse spin Hall, magneto-optic Kerr, second-harmonic, and planar Hall effects.^11–19 So far, various materials have been utilized to study spin–orbit torques. First of all, heavy metals such as Pt, Ta, W, and Hf have been extensively utilized as a spin source as the strength of spin–orbit coupling is expected to be stronger in heavier elements.^1–9 Second, interfacial Rashba systems such as Bi/Ag²⁰ and Bi₂Se₃/Ag²¹ have been studied. Third, topological insulators are proposed to have a large effective spin-torque efficiency originated from spin-momentum locking and can even switch the magnetization.^22–28 Recently, two-dimensional materials such as transition metal dichalcogenides WTe₂, MoTe₂, PtTe₂, and TaS₂ have been explored.^29–33 

From a technological point of view, the spin–orbit torque magnetic random access memory (SOT-MRAM) is a candidate of next generation non-volatile memory because of its fast speed and low power consumption.³⁴ The power consumption for switching the magnetization per unit volume is proportional to $ρSS⋅jSS2$⁠, where ρ_SS is the resistivity of the spin source and j_SS is the critical current density flowing through the spin source, which is inversely proportional to the effective spin-torque efficiency of the spin source. Therefore, a spin source with a high conductivity and large effective spin-torque efficiency, that is, a large spin Hall conductivity, is desirable. Studies have been carried out in alloying heavy metals such as Bi, Pb, Pt, Ir, and Ta to increase the effective spin-torque efficiency.^35–39 In particular, PdPt and AuPt alloys have been demonstrated to have a large effective spin-torque efficiency.^40,41 Realizing deterministic SOT switching of the magnetization with perpendicular anisotropy requires inversion symmetry breaking that is typically realized by applying an external magnetic field along the current direction, which hinders the real application of SOT devices. Several techniques such as exchange-bias field,^42,43 lateral structure asymmetry,⁴⁴ out-of-plane polarized spin currents,^29,30,45 and some other techniques were proposed to realize field-free SOT switching.^46–49 

In this work, we systematically study the SOT in the PtRh/ferromagnet heterostructures. Pt has a large intrinsic spin Hall conductivity and relatively low resistivity. Rh is a 4d transition metal with a face-centered cubic structure and has a relatively low resistivity as well. We first use the dc-biased ST-FMR technique^11,33,50 to quantify the effective damping-like and field-like spin-torque efficiency. Then, we perform second-harmonic and current-induced SOT switching measurements. We find a large spin Hall conductivity of 3.8 ×10⁵ ℏ/2e Ω⁻¹ m⁻¹ for Pt_0.9Rh_0.1 with a relatively low resistivity of 46.9 µΩ cm, indicating that PtRh could be a useful spin source.

The multilayer structure of Si substrate/Ta (2)/Pt_xRh_1−x (6)/Py (2)/MgO (2)/Ta (1.5) (thicknesses in nanometers, x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1), where Py is Ni₈₁Fe₁₉, is deposited for ST-FMR measurements by magnetron sputtering at a base pressure of 5 × 10⁻⁹ Torr. Pt_xRh_1−x is deposited by co-sputtering Pt and Rh targets. For the Pt concentration x ≥ 0.5, the power of Pt is fixed at 60 W, and the power of Rh is varied to adjust the composition. For the Pt concentration x ≤ 0.4, the power of Pt is tuned, while the power of Rh is fixed at 60 W. The films are patterned into rectangular strips with a dimension of 70 × 10 µm² by lithography and Ar ion etching. The coplanar waveguide (CPW) with the gap between the signal and the ground electrode of 15 µm is fabricated by sputtering and lift-off processes.

In order to investigate the second-harmonic based spin-torque efficiency and the SOT switching properties, we also deposit perpendicular magnetic anisotropy (PMA) Co on top of the PtRh alloy. The film structure of thermally oxidized Si substrate/Ta (2)/Pt_xRh_1−x (6)/Co (0.8)/Pt (0.3)/MgO (2)/Ta (1.5) (thicknesses in nanometers, x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1) is prepared. Then, the films are annealed at 300 °C with an external field of 5 kOe applied perpendicular to the films for 0.5 h in order to enhance the PMA of the Co layer. After that, the films are fabricated into Hall-bar devices with a channel width of 10 µm using optical lithography and Ar etching, and the electrodes are patterned using lithography and lift-off processes.

Figure 1(a) shows the XRD characterization results of the thermally oxidized Si substrate/Ta (2)/Pt_xRh_1−x (20) (thicknesses in nanometers, x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1). With the increase in Rh concentration, the (111) peak of the PtRh alloy shifts from 39.5° to 41.1° and the peak intensity also decreases. Utilizing Bragg’s law, the lattice constant (c) of Pt and Rh are determined to be 3.951 and 3.804 Å, respectively, which is comparable to the lattice constant of bulk Pt (3.924 Å) and Rh (3.803 Å). The resistivity of 6 nm thick PtRh films as a function of the Pt composition (x) measured by the four probe method is shown in Fig. 1(b).

Figure 2(a) shows the schematic of ST-FMR devices and the measurement configuration. A rf current is applied to devices, and an external field is simultaneously swept in the xy plane with an angle of 38° with respect to the x direction.^27,30,37 The rf charge current generates a transverse rf spin current in Pt_xRh_1−x, which is injected into the adjacent Py layer and exerts oscillating SOTs on the Py magnetic moments. At the same time, the additional dc current can also generate spin currents and exert SOT on Py, which modifies the resonance field H_res and effective damping α_eff = |γ|/(2πf)·(W − W₀). Here, γ is the gyromagnetic ratio, f is the rf current frequency, W is the linewidth, and W₀ is the inhomogeneous linewidth broadening. These torques together with the Oersted field cause the precession of Py magnetization, and the anisotropic magnetoresistance of the device also oscillates with the same frequency. As a result, the oscillating resistance and charge current produce a dc mixing voltage (V_mix), which is detected by a lock-in amplifier. We apply rf currents with a fixed frequency of 4–6.5 GHz and a nominal microwave power of 13 dBm to ST-FMR devices while sweeping the external field (H_ext) from −1.1 to 1.1 kOe.

Typical ST-FMR dc mixing voltages for Pt_0.9Rh_0.1/Py samples are shown in Fig. 2(b). Figure 2(c) shows that the H_res and f follows the Kittel equation $f=γ2πHres(Hres+Meff)$⁠, where M_eff is the effective magnetization. We extract the M_eff of 0.665 T. The effect of dc current on the ST-FMR data is shown in Fig. 2(d), and the linewidth decreases (increases) and the resonance field increases (decreases) after applying 2 mA (−2 mA) dc current. Figure 2(e) depicts the linear relationship between the linewidth W and dc current. The effective damping-like spin-torque efficiency can be calculated by $ξDL=2eℏ(Hres+Meff/2)μ0MstFsinφΔαeffΔjPtRh$⁠,^11,33,50 where e is the electron charge, μ₀ is the vacuum permeability, ℏ is the reduced Planck constant, M_s and t_F are the saturation magnetization and layer thickness of Py, φ denotes the external field direction with respect to the x direction, and j_PtRh is the current density passing through the PtRh layer. We find that the effective damping-like spin-torque efficiency of Pt_0.9Rh_0.1 is 0.081 ± 0.008.

The field-like torques generated by the dc current together with the dc current induced Oersted field shift the resonance field as shown in Fig. 2(f). The dc current induced Oersted field is calculated by Ampère’s law, H_Oe = 0.5j_PtRht_PtRh, where t_PtRh is the thickness of PtRh. By subtracting the contribution from the Oersted field, the effective field-like spin-torque efficiency can be obtained by $ξFL=2eℏμ0MstFHFLjPtRh$⁠, where H_FL is the field-like effective field extracted from the shift of the resonance field by subtracting the contribution of the Oersted field.⁵⁰ We find that the effective field-like spin-torque efficiency of Pt_0.9Rh_0.1 is 0.017 ± 0.002. The calculated ξ_DL and ξ_FL are shown in Figs. 2(g) and 2(h), respectively, with different compositions. For pure Rh and Pt, the ξ_DL is 0.038 ± 0.006 and 0.074 ± 0.006, respectively. The ξ_DL of the PtRh alloy increases up to 0.081 ± 0.008 for Pt_0.9Rh_0.1. The ξ_FL increases from 0.005 ± 0.004 for pure Rh to 0.018 ± 0.003 for pure Pt.

We then investigate the second harmonic based ξ_DL of PtRh/Co. The device structure and measurement setup are depicted in Fig. 3(a). Utilizing the anomalous Hall effect (AHE), we can detect the PMA of the samples. We apply the current of 0.5 mA and measure the Hall voltage while sweeping the external field along the z and x directions. As shown in the left column of Fig. 3(b), for samples with x ≥ 0.3, the square AHE loops obtained by sweeping the external field along the z direction (H_z) indicate good PMA of the Co layer. On the other hand, samples with x ≤ 0.2 show in-plane anisotropy (IPA). When the in-plane magnetic field (H_x) is large enough to align the magnetization on the xy plane, the AHE resistance approaches zero in the right column of Fig. 3(b), as the AHE resistance is proportional to the z component of Co magnetization. The saturation field with H_x can be used to estimate the anisotropy field, which increases with an increase in the Pt composition. We extract the coercive field (H_c) and AHE resistance (R_AHE) summarized in Fig. 3(c). With the increase in Pt concentration, both H_c and R_AHE tend to increase overall.

Second-harmonic measurements are exploited to determine the ξ_DL of PtRh. We apply the ac current along the x direction and record the in-phase first and out-of-phase second-harmonic Hall voltages while sweeping the external field in the xz plane with 2° tilted with respect to the x axis. Corresponding results for the Pt_0.9Rh_0.1/Co sample are shown in Figs. 3(d) and 3(e). The first harmonic voltage (⁠$Vxy1ω$⁠) in Fig. 3(d) shows a typical parabolic curve for the Co magnetization pointing up or down, while the second-harmonic signals (⁠$Vxy2ω$⁠) in Fig. 3(e) show straight lines for the up and down Co magnetization. The damping-like effective field (H_DL) can be determined by $HDL=−2∂Vxy2ω∂Hx/∂2Vxy1ω∂Hx2$⁠.¹³ Here, we note that the planar Hall correction is not considered in our analysis as it might overestimate the spin-torque efficiency, as discussed in Ref. 40. We estimate the H_DL for different applied ac currents. As shown in Fig. 3(f), H_DL linearly increases with the current density and the slope can be used to extract the effective damping-like spin-torque efficiency through ξ_DL = (2eM_st/ℏ)·H_DL/j_PtRh. The spin Hall conductivity (σ_SH) is calculated using σ_SH = (ℏ/2e)ξ_DL/ρ_PtRh, where ρ_PtRh is the resistivity of the PtRh alloy. The ξ_DL and σ_SH using the second-harmonic measurements for the PtRh alloy are summarized in Fig. 3(g). As the Pt concentration increases, both ξ_DL and σ_SH increase overall. The largest ξ_DL is 0.18 ± 0.01 and the largest σ_SH is 3.8 ± 0.12 ×10⁵ ℏ/2e Ω⁻¹ m⁻¹ for Pt_0.9Rh_0.1. It is worth mentioning that the ξ_DL measured by the second-harmonic measurements is larger than that of dc-biased ST-FMR. This might be due to the interface transparency.⁵¹ We also measure harmonic signals by sweeping the external field in the yz plane with 2° tilted with respect to the y axis in order to extract the field-like torque, but the signal is negligible, as shown in the inset of Fig. 3(e).

We next study the SOT switching of PtRh/Co heterostructures. A current pulse with a pulse width of 150 µs and different amplitudes is applied along the x direction of the Hall bar devices, and the Hall voltage is probed while a fixed magnetic field is applied along the current direction to break the symmetry. Figures 4(a) and 4(b) show the deterministic magnetization switching of Pt_0.9Rh_0.1/Co samples. For positive external fields, the Co magnetization favors down for positive currents and favors up for negative currents, manifesting clockwise switching, whereas for negative external fields, the switching is anticlockwise, which is a typical SOT switching feature of positive spin-torque efficiency materials. As expected, the critical current density (j_c) reduces as the amplitude of external fields increases. We extract the j_c for devices with different compositions under the external field of 250 Oe and summarize the results in Fig. 4(c). With an increase in the Pt composition (x), j_c increases. For micrometer size devices, SOT switching is governed by SOT-assisted domain wall propagation, and thus, the critical current density is proportional to M_sH_c/ξ_DL.^7,39,52 The M_s data of samples with different Pt concentrations are shown in Fig. 4(c). It increases and then slightly decreases as the Pt concentration increases. Using the measured M_s, H_c, and ξ_DL values, we normalize the value of M_sH_c/ξ_DL with different compositions and define as J_c. As shown in Fig. 4(d), the J_c follows the same trend as the measured j_c. Table I shows a comparison of the ξ_DL, ρ, and σ_SH of various materials. The σ_SH of Pt_0.9Rh_0.1 is larger than most of the spin sources and close to that of Pd_0.25Pt_0.75, and the ρ of Pt_0.9Rh_0.1 is smaller than that of Pd_0.25Pt_0.75 and close to the value of pure Pt.

We have studied the SOT in the PtRh alloy. Utilizing dc-biased ST-FMR and second-harmonic measurements, we determine the effective spin-torque efficiency and spin Hall conductivity of the PtRh alloy. We find that the spin Hall conductivity of Pt can be enhanced by alloying with Rh. The spin Hall conductivity is 3.8 ×10⁵ ℏ/2e Ω⁻¹ m⁻¹ for Pt_0.9Rh_0.1 with a relatively low resistivity of 46.9 µΩ cm. The critical SOT switching current density increases with an increase in the Pt composition, which can be explained by SOT-assisted domain wall propagation. With a large spin Hall conductivity and small resistivity, PtRh could be a promising spin source for SOT applications.

This research was supported by the SpOT-LITE programme (A*STAR Grant No. 18A6b0057) through RIE2020 funds from the Singapore and Samsung Electronics’ University R&D program (Exotic SOT materials/SOT characterization).

G.S. and H.Y. designed the experiments. G.S. and Q.Y. prepared the film samples. G.S. and Y.L. fabricated the devices. G.S., E.L., and K.C. carried out the ST-FMR, second harmonic, SOT switching, and XRD measurements. G.S. and H.Y. analyzed data and wrote the manuscript. H.Y. supervised the research. All authors contributed equally to this manuscript.

The data that support the findings of this study are available from the corresponding author upon reasonable request.