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We investigate the magnetization dynamics of a pair of ferromagneticinsulators (FMIs) deposited on the surface of a topological insulator (TI). Dueto the nonlinear nature of the underlying physics and intrinsic dynamics, theFMIs can exhibit oscillatory behaviors even under a constant applied voltage.The motion of the surface electrons of the TI, which obeys relativistic quantummechanics, provides a mechanism of direct coupling between the FMIs. Inparticular, the spin polarized current of the TI surface electrons can affectthe magnetization of the two FMIs, which in turn modulates the electrontransport, giving rise to a hybrid relativistic quantum/classical nonlineardynamical system. We find robust phase and anti-phase locking between themagnetization dynamics. As driving the surface electrons of a TI only requiresextremely low power, our finding suggests that nano FMIs coupled by a spinpolarized current on the surface of TI have the potential to serve as thefundamental building blocks of unconventional, low-power computing paradigms.

Phase locking of a pair of nano ferromagnetic oscillators on a topological insulator