Level attraction and exceptional points in a resonant spin-orbit torque system

Level attraction can appear in driven systems where instead of repulsion, two modes coalesce in a region separated by two exceptional points. This behavior was proposed for optomechanical and optomagnonic systems, and recently it was observed for dissipative cavity magnon-polaritons. We demonstrate that such a regime exists in a spin-orbit torque system where a magnetic oscillator is resonantly coupled to an electron reservoir. An instability mechanism necessary for mode attraction can be provided by applying an electric field. The field excites interband transitions between spin-orbit split bands leading to an instability of the magnetic oscillator. Two exceptional points then appear in the oscillator energy spectrum and the region of instability. We discuss conditions under which this can occur, and we estimate the electric field strength necessary for reaching the attraction region for a spin-orbit torque oscillator with Rashba coupling. A proposal for experimental detection is made using magnetic susceptibility measurements.