  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 of the SMR signal at a finite temperature. In addition,
we derive the Onsager relation between spin conductance and thermal
spin-current noise.
