Theory of unidirectional spin Hall magnetoresistance in   heavy-metal/ferromagnetic-metal bilayers
  Recent experiments have revealed nonlinear features of the magnetoresistance in metallic bilayers consisting of a heavy-metal (HM) and a ferromagnetic metal (FM). A small change in the lon- gitudinal resistance of the bilayer has been observed when reversing the direction of either the applied in-plane current or the magnetization. We attribute such nonlinear transport behavior to the spin-polarization dependence of the electron mobility in the FM layer acting in concert with the spin accumulation induced in that layer by the spin Hall current originating in the bulk of the HM layer. An explicit expression for the nonlinear magnetoresistance is derived based on a simple drift-diffusion model, which shows that the nonlinear magnetoresistance appears at the first order of spin Hall angle (SHA), and changes sign when the current is reversed, in agreement with the experimental observations. We also discuss possible ways to control the sign of the nonlinear magnetoresistance and to enhance the magnitude of effect. 
Steven S.-L. Zhang and Giovanni Vignale
cond-mat.mes-hall cond-mat.mtrl-sci