  We present a theory of the spin Hall magnetoresistance of metals in contact
with magnetic insulators. We express the spin-mixing conductances, which govern
the phenomenology of the effect, in terms of the microscopic parameters of the
interface and the spin-spin correlation functions of the local moments on the
surface of the magnetic insulator. The magnetic field and temperature
dependence of the spin-mixing conductances leads to a rich behaviour of the
resistance due to an interplay between the Hanle effect and spin mixing at the
interface. Our theory provides a useful tool for understanding the experiments
on heavy metals in contact with magnetic insulators of different kinds, and it
predicts striking behaviours of magnetoresistance.
