  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 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 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.
