Theory of spin Hall magnetoresistance

TL;DR

This paper develops a theoretical framework for understanding spin Hall magnetoresistance (SMR) in multilayer systems involving insulating ferromagnets and normal metals with spin-orbit coupling, explaining experimental observations and predicting effects in spin valves.

Contribution

It introduces a comprehensive theory of SMR in multilayer structures, incorporating spin-diffusion and boundary conditions, and predicts enhanced effects in certain configurations.

Findings

Explains experimental SMR in N|F bilayers.

Predicts increased SMR in collinear F|N|F spin valves.

Shows control of SMR and spin torques via magnetic configuration.

Abstract

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 non-equilibrium 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.