We present a theory of the spin Hall magnetoresistance (SMR) in multilayers made from an insulating ferromagnet F, such as yttrium iron garnet (YIG), and a normal metal N with spin-orbit interactions, such as platinum (Pt). The SMR is induced by the simultaneous action of spin Hall and inverse spin Hall effects and therefore a nonequilibrium proximity phenomenon. We compute the SMR in F|N and F|N|F layered systems, treating N by spin-diffusion theory with quantum mechanical boundary conditions at the interfaces in terms of the spin-mixing conductance. Our results explain the experimentally observed spin Hall magnetoresistance in N|F bilayers. For F|N|F spin valves we predict an enhanced SMR amplitude when magnetizations are collinear. The SMR and the spin-transfer torques in these trilayers can be controlled by the magnetic configuration.

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We experimentally investigate and quantitatively analyze the spin Hall magnetoresistance effect in ferromagnetic insulator/platinum and ferromagnetic insulator/nonferromagnetic metal/platinum hybrid structures. For the ferromagnetic insulator, we use either yttrium iron garnet, nickel ferrite, or magnetite and for the nonferromagnet, copper or gold. The spin Hall magnetoresistance effect is theoretically ascribed to the combined action of spin Hall and inverse spin Hall effect in the platinum metal top layer. It therefore should characteristically depend upon the orientation of the magnetization in the adjacent ferromagnet and prevail even if an additional, nonferromagnetic metal layer is inserted between Pt and the ferromagnet. Our experimental data corroborate these theoretical conjectures. Using the spin Hall magnetoresistance theory to analyze our data, we extract the spin Hall angle and the spin diffusion length in platinum. For a spin-mixing conductance of 4 × 10 14 −1 m −2 , we obtain a spin Hall angle of 0.11 ± 0.08 and a spin diffusion length of (1.5 ± 0.5) nm for Pt in our thin-film samples.