We formulate a theory of the ac spin Hall magnetoresistance in a bilayer system consisting of a magnetic insulator such as yttrium iron garnet and a heavy metal such as platinum. We derive expressions for the dc voltage generation based on the drift-diffusion spin model and quantum mechanical boundary condition at the interface that reveal a spin-torque ferromagnetic resonance (ST-FMR). We predict that ST-FMR experiments will reveal valuable information on the current-induced magnetization dynamics of magnetic insulators and the ac spin Hall effect.

The evolution of information technology has been driven by the discovery of new forms of large magnetoresistance (MR), such as giant magnetoresistance (GMR) 1,2 and tunnelling magnetoresistance (TMR) 3,4 in magnetic multilayers. Recently, new types of MR have been observed in much simpler bilayers consisting of ferromagnetic (FM)/nonmagnetic (NM) thin films 5-10 ; however, the magnitude of MR in these materials is very small (0.01 ~ 1%). Here, we demonstrate that NM/FM bilayers consisting of a NM InAs quantum well conductive channel and an insulating FM (Ga,Fe)Sb layer exhibit giant proximity magnetoresistance (PMR) (~80% at 14 T). This PMR is two orders of magnitude larger than the MR observed in NM/FM bilayers reported to date, and its magnitude can be controlled by a gate voltage. These results are explained by the penetration of the InAs two-dimensional-electron

The spin-torque ferromagnetic resonance (ST-FMR) in a bilayer system consisting of a magnetic insulator such as Y 3 Fe 5 O 12 and a normal metal with spin-orbit interaction such as Pt is addressed theoretically. We model the ST-FMR for all magnetization directions and in the presence of field-like spin-orbit torques based on the drift-diffusion spin model and quantum mechanical boundary conditions. ST-FMR experiments may expose crucial information about the spin-orbit coupling between currents and magnetization in the bilayers.

We report the observation of current-induced spin torque resonance in yttrium iron garnet/platinum bilayers. An alternating charge current at GHz frequencies in the platinum gives rise to dc spin pumping and spin Hall magnetoresistance rectification voltages, induced by the Oersted fields of the ac current and the spin Hall effect-mediated spin transfer torque. In ultrathin yttrium iron garnet films, we observe spin transfer torque actuated magnetization dynamics which are significantly larger than those generated by the ac Oersted field. Spin transfer torques thus efficiently couple charge currents and magnetization dynamics also in magnetic insulators, enabling charge current-based interfacing of magnetic insulators with microwave devices.

We theoretically study the magnetoresistance (MR) of two-dimensional massless Dirac electrons as found on the surface of three-dimensional topological insulators (TIs) that are capped by a ferromagnetic insulator (FI). We calculate charge and spin transport by Kubo and Boltzmann theories, taking into account the ladder-vertex correction and the in-scattering due to normal and magnetic disorder. The induced exchange splitting is found to generate an electric conductivity that depends on the magnetization orientation, but its form is very different from both the anisotropic and the spin Hall MR. The in-plane MR vanishes identically for nonmagnetic disorder, while out-of-plane magnetizations cause a large MR ratio. On the other hand, we do find an in-plane MR and planar Hall effect in the presence of magnetic disorder aligned with the FI magnetization. Our results may help us understand recent transport measurements on TI|FI systems.