Effect of Rashba interaction at normal metal/insulator interface on spin-orbit torque of ferromagnet/normal metal/insulator trilayers

Abstract

Based on a spin drift-diffusion model, we theoretically investigate the spin-orbit torque in ferromagnet/normal metal/insulator trilayers with considering the Rashba interfacial spin-orbit coupling at the normal metal/insulator interface. We find that the spin-orbit torque shows the opposite normal-metal-thickness dependences for the bulk spin-orbit coupling effect in the normal metal layer and for the interfacial spin-orbit coupling effect at the normal metal/insulator interface, offering a way to disentangle these two spin-orbit coupling effects. Moreover, we show that the conventional interpretation based on the bulk spin-orbit coupling effect overestimates the spin Hall angle and underestimates the spin diffusion length of the normal metal layer, when the interfacial contribution is non-negligible. Our result, a concise analytic expression of the spin-orbit torque considering both bulk and interface spin-orbit coupling effects, will be useful to design and interpret experiments on spin-orbit torque experiments in ferromagnet/normal metal/insulator trilayers.