Exploring non-Hermitian topology with spin-torque oscillator arrays

Topological phases of matter have emerged as building blocks for new technologies due to their novel electronic and spin transport properties including robust conducting edge states. Recently, the theory of topological phases has been extended to open quantum systems which can be described by a non-Hermitian effective Hamiltonian. Magnonic systems are a natural platform in which to study non-Hermitian topology because they are inherently dissipative, and the injection of spin current into the system provides an external gain mechanism. Dissipation and gain are both described by non-Hermitian Hamiltonian terms. In this talk we show how the magnetization dynamics of a one-dimensional array of spin-torque oscillators can be mapped to a non-Hermitian Hamiltonian with topologically protected edge states. Changing the amount of spin current injected allows it to be tuned to the topologically nontrivial phase. The edge state manifests as an auto-oscillation of a single spin-torque oscillator on the edge of the system despite the uniform injection of spin current across the system. We will discuss the extension of these results to two-dimensional spin-torque oscillator arrays, which can exhibit one-dimensional edge states and present new possibilities for novel spintronic devices.