Spin torques due to various linear spin-orbit coupling in semiconductor and graphene systems in the adiabatic limit

¹ Department of Mathematics, School of Science, Hangzhou Dianzi University - Hangzhou 310018, PRC
² Computational Nanoelectronics and Nano-device Laboratory, Electrical and Computer Engineering Department, National University of Singapore - 4 Engineering Drive 3, Singapore, 117576, Singapore
³ Information Storage Materials Laboratory, Electrical and Computer Engineering Department, National University of Singapore - 4 Engineering Drive 3, Singapore, 117576, Singapore
⁴ Data Storage Institute, A*STAR (Agency for Science, Technology and Research) - DSI Building, 5 Engineering Drive 1, Singapore, 117608, Singapore
⁵ Department of Physics, School of Science, Hangzhou Dianzi University - Hangzhou 310018, PRC
⁶ Center for Integrated Spintronic Devices, Hangzhou Dianzi University - Hangzhou 310018, PRC

^(a) muze7777@hdu.edu.cn

Received: 4 November 2016
Accepted: 23 May 2017

Abstract

We use the gauge formalism to investigate the current-induced spin dynamics in ferromagnetic media with spatially varying local magnetization, which is coupled to various material systems exhibiting linear spin-orbit coupling (SOC) effects, such as semiconductor and graphene materials. We perform a gauge transformation to the system, and obtain a gauge field (vector potential) in the adiabatic limit, i.e., strong coupling between the spin of the conduction electrons to the magnetization. The gauge field interacts with the applied current, resulting in a current-driven effective magnetic field and the corresponding spin torque acting on the magnetization of the FM media. We find that the current-driven spin orbit torque in various linear SOC systems and graphene systems can be described by a unified way. We propose a generalized Landau-Lifshitz-Gilbert (LLG) equation which includes this effective field term.