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 behavior of the resistance due to an interplay between the Hanle effect and the spin mixing at the interface. We describe an unusual negative magnetoresistance originating from a nonlocal Hanle effect. Our theory provides a useful tool for understanding the experiments on heavy metals in contact with magnetic insulators of different kinds, and it enables the spin Hall magnetoresistance effect to be used as a technique to study magnetism at interfaces.
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