Theory of spin Hall magnetoresistance (SMR) and related phenomena

Chen, Y.-T.*; Takahashi, Saburo*; Nakayama, Hiroyasu*; Althammer, M.*; Goennenwein, S. T. B.*; Saito, Eiji; Bauer, G. E. W.*

We review the so-called spin Hall magnetoresistance (SMR) in bilayers of a magnetic insulator and a metal, in which spin currents are generated in the normal metal by the spin Hall effect. The associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction. The SMR provides a convenient tool to non-invasively measure the magnetization direction and spin-transfer torque to an insulator. We introduce the minimal theoretical instruments to calculate the SMR, i.e. spin diffusion theory and quantum mechanical boundary conditions. This leads to a small set of parameters that can be fitted to experiments. We discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and Rashba spin-orbit torques, and point out new developments.