Theory of spin Hall magnetoresistance

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 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.

Modulation of pure spin currents with a ferromagnetic insulator

“…One could take advantage of the spin-mixing conductance concept [5,6] at nonmagnetic metal (NM)/ferromagnetic insulator (FMI) interfaces, which governs the interaction between the spin currents present at the NM and the magnetization of the FMI. This concept is the basis of new spindependent phenomena, including spin pumping [6][7][8][9][10][11][12], spin Seebeck effect [6,13], and spin Hall magnetoresistance (SMR) [6,[14][15][16][17][18]. In these cases, a NM with large spin-orbit coupling is required to convert the involved spin currents into charge currents via the inverse spin Hall effect [19].…”

Effect of quantum tunneling on spin Hall magnetoresistance

“…We adopt the spin diffusion approach of Chen et al 22 to address the effect of the interface spin current in Eq. (6) on SMR, which is briefly summarized below.…”

“…The spin diffusion part has been addressed in detail by Chen et al for the NM/ferromagnetic insulator (NM/FMI) bilayer, such as Pt/Y 3 Fe 5 O 12 (Pt/YIG), and FMI/NM/FMI trilayer 22 . This approach solves the spin diffusion equation in the presence of SHE and ISHE in a self-consistent manner, where the spin current at the NM/FMI interface serves as a boundary condition.…”

“…We focus on the SMR in NM/FMI bilayer realized in Pt/YIG, and the NM/ferromagnetic metal (NM/FMM) bilayer realized in Pt/Co and Ta/Co 14 . The spin diffusion in the NM is assumed to be described by the same formalism of Chen et al 22 , whereas the interface spin current is calculated from the quantum tunneling formalism 26,27 . In the NM/FMM bilayer, we consider an FMM that has long spin diffusion length and a small thickness, such that the spin diffusion effect is negligible and the spin transport is predominately of quantum origin 26 .…”

“…In reverse, the inverse spin Hall effect 9,10 (ISHE) can convert the spin current generated by certain means, for instance spin pumping 11,12 , into an electric signal. A particularly intriguing phenomenon that involves both SHE and ISHE is the spin Hall magnetoresistance [13][14][15][16][17][18][19][20][21][22] (SMR), in which a charge current in an NM causes a spin accumulation at the edge of the sample due to SHE, yielding a finite spin current at the interface to a ferromagnet. Through ISHE, the spin current gives an electromotive force along the original charge current, effectively changing the magnetoresistance of the NM.…”