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Description
Spin-orbit torque (SOT) provides a fast and efficient way to manipulate the magnetization in magnetic devices such as magnetoresistive random access memory (MRAM) [1]. These devices take advantage of the strong spin-orbit coupling (SOC) in the bulk or at the interfaces of heavy metal (HM) layers to generate spin polarized currents. The spin currents are injected into an adjacent ferromagnet (FM), where through spin dephasing the spins align with the magnetization while exerting a torque on the magnetization. In the bulk, the spin currents are generated through the spin Hall effect (SHE) which generates out-of-plane spin currents with in-plane polarization. The HM/FM interface plays a crucial role in the resulting torques as spin-flip scattering can be strong and additional spin currents can be generated through the Rashba-Edelstein effect (REE) at the interface [2]. Typically, the SOTs are modeled by assuming that the spins instantly align with the magnetization in the FM. In this picture, the SOT is determined purely by the spin current on the HM side of the interface, and the interface scattering is captured by the complex spin mixing conductance.
We compare this approach with one that allows for transmission of the transverse spin currents into the bulk by introducing a transmission spin mixing conductance. Furthermore, we explore the addition of the REE through considering spin-flip scattering from a Rashba SOC potential at the interface. In Fig. 1 we show that these two approaches give qualitatively similar results, and with parameter fitting the instant absorption assumption can be a good approximation for bilayers. The addition of the REE yields a stronger field-like torque which does not vanish with decreasing HM thickness in agreement with reported experimental results [3].
Fig. 1 HM thickness dependence of the spin torque in a HM($d_{HM}$)/FM(1.2 nm) bilayer induced by a $10^{12}$A/m$^2$ electrical current. Panel (a) and Panel (b) show the torque generated by the SHE and by both the REE and the SHE, respectively. Dashed lines show the result obtained from considering instant absorption of transverse spin currents.
References
[1] S. Hu et al., “Frontiers in all electrical control of magnetization by spin orbit torque,” Journal of Physics: Condensed Matter, vol. 36, no. 25. IOP Publishing, p. 253001, Mar. 27, 2024. doi: 10.1088/1361-648x/ad3270.
[2] V. P. Amin, P. M. Haney, and M. D. Stiles, “Interfacial spin–orbit torques,” Journal of Applied Physics, vol. 128, no. 15. AIP Publishing, Oct. 21, 2020. doi: 10.1063/5.0024019.
[3] A. Ghosh, K. Garello, C. O. Avci, M. Gabureac, and P. Gambardella, “Interface-Enhanced Spin-Orbit Torques and Current-Induced Magnetization Switching of Pd/Co/AlOx Layers,” Physical Review Applied, vol. 7, no. 1. American Physical Society (APS), Jan. 06, 2017. doi: 10.1103/physrevapplied.7.014004.
