Microscopic theory of spin Hall magnetoresistance

We consider a microscopic theory for the spin Hall magnetoresistance (SMR). We generally formulate a spin conductance at an interface between a normal metal and a magnetic insulator in terms of spin susceptibilities. We reveal that SMR is composed of static and dynamic parts. The static part, which is almost independent of the temperature, originates from spin flip caused by an interfacial exchange coupling. However, the dynamic part, which is induced by the creation or annihilation of magnons, has an opposite sign from the static part. By the spin-wave approximation, we predict that the latter results in a nontrivial sign change in the SMR signal at a finite temperature. In addition, we derive the Onsager relation between spin conductance and thermal spin-current noise.