Current-induced magnetization dynamics in two magnetic insulators separated by a normal metal

We study the dynamics of spin valves consisting of two layers of magnetic insulators separated by a normal metal in the macrospin model. A current through the spacer generates a spin Hall current that can actuate the magnetization via the spin-transfer torque. We derive expressions for the effective Gilbert damping and the critical currents for the onset of magnetization dynamics including the effects of spin pumping that can be tested by ferromagnetic resonance experiments. The current generates an amplitude asymmetry between the in-phase and out-of-phase modes. We discuss superlattices of stacked films of metals and magnetic insulators.