Phase Locking of a Pair of Ferromagnetic Nano-oscillators on a Topological Insulator

We investigate the magnetization dynamics of a pair of ferromagnetic insulators (FMIs) deposited on the surface of a topological insulator (TI). Because of the nonlinear nature of the underlying physics and intrinsic dynamics, the FMIs can exhibit oscillatory behaviors even under a constant applied voltage. The motion of the surface electrons of the TI, which obeys relativistic quantum mechanics, provides a mechanism of direct coupling between the FMIs. In particular, the spin-polarized current of the TI surface electrons can affect the magnetization of the two FMIs, which in turn modulates the electron transport, giving rise to a hybrid relativistic quantum and classical nonlinear dynamical system. We find robust phase and antiphase locking between the magnetization dynamics. As driving the surface electrons of a TI requires only extremely low power, our finding suggests that nanoscale FMIs coupled by a spin-polarized current on the surface of a TI have the potential to serve as the fundamental building blocks of unconventional, low-power computing paradigms.