Spin Hall effect versus Rashba torque: a Diffusive Approach

Abstract

Current-driven magnetization dynamics of single ferromagnets in heavy metal/ferromagnet bilayers has been recently realized. In this work, spin torque induced by so-called Rashba spin-orbit coupling and spin Hall effect are considered within a diffusive model. The dependence of the resulting torque as a function of the thicknesses of the ferromagnet and heavy metal is analyzed. We show that (i) both torques are on the form $\mathbf{T}=T_{||}\mathbf{m}\times \mathbf{y}+T_{\perp }\mathbf{m}\times (\mathbf{y}\times \mathbf{m})$, (ii) the ratio $T_{||}/T_{\perp }$ strongly depends on the thickness of the layers and (iii) the thickness dependence of the spin torque provides an indication of the origin of the (Rashba- or spin Hall effect-induced) spin torque .

7 pages, 7 figures, submitted

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