  Magnetic systems have been extensively studied both from a fundamental
physics perspective and as building blocks for a variety of applications. Their
topological properties, in particular those of excitations, remain relatively
unexplored due to their inherently dissipative nature. The recent introduction
of non-Hermitian topological classifications opens up new opportunities for
engineering topological phases in dissipative systems. Here, we propose a
magnonic realization of a non-Hermitian topological system. A crucial
ingredient of our proposal is the injection of spin current into the magnetic
system, which alters and can even change the sign of terms describing
dissipation. We show that the magnetic dynamics of an array of spin-torque
oscillators can be mapped onto a non-Hermitian Su-Schrieffer-Heeger model
exhibiting topologically protected edge states. Using exact diagonalization of
the linearized dynamics and numerical solutions of the non-linear equations of
motion, we find that a topological magnonic phase can be accessed by tuning the
spin current injected into the array. In the topologically nontrivial regime, a
single spin-torque oscillator on the edge of the array is driven into
auto-oscillation and emits a microwave signal, while the bulk oscillators
remain inactive. Our findings have practical utility for memory devices and
spintronics neural networks relying on spin-torque oscillators as constituent
units.
