Theory of spin Hall magnetoresistance

TLDR

The spin Hall magnetoresistance arises from concurrent spin Hall and inverse spin Hall effects, making it a non‑equilibrium proximity phenomenon. The authors develop a theoretical framework for SMR in F|N multilayers comprising an insulating ferromagnet (e.g., YIG) and a spin‑orbit coupled normal metal (e.g., Pt). They calculate SMR using spin‑diffusion theory for the normal metal, applying quantum‑mechanical boundary conditions at interfaces expressed through spin‑mixing conductance for both bilayer and trilayer structures. The theory reproduces the measured SMR in N|F bilayers, predicts a larger SMR in F|N|F spin valves with collinear magnetizations, and shows that SMR and spin‑transfer torques in trilayers can be tuned by the 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.