Oscillatory edge modes in two dimensional spin-torque oscillator arrays

Abstract

Spin-torque oscillators (STOs) are dissipative magnetic systems that provide a natural platform for exploring non-Hermitian phenomena. We theoretically study a two-dimensional (2D) array of STOs and show that its dynamics can be mapped to a 2D, non-Hermitian Su-Schrieffer-Heeger (SSH) model. We calculate the energy spectrum and identify the one-dimensional (1D) edge states of our model, corresponding to auto-oscillation of STOs on the boundary of the system while the bulk oscillators do not activate. We show that tuning the Gilbert damping, injected spin current, and coupling between STOs allows for exploring the edge-state properties under different parameter regimes. Furthermore, this system admits 1D edge states with nonuniform probability density, and we explore their properties in systems of different sizes. Additional symmetry analysis indicates that these states are not topologically protected but are nevertheless confined to the edge of the system, as the bulk is protected by PTsymmetry. These results indicate that 2D arrays of STOs may be useful to explore novel edge-state behavior in dissipative systems.