Electric field induced exceptional points and mode attraction in a spin-orbit torque oscillator

In spin-orbit torque oscillators, spin magnetic moment is transferred from conducting electrons inside a material with spin-orbit coupling to a magnetic oscillator, which modifies its dynamic and dissipative properties. We consider resonant spin-orbit torque system in applied electric field and demonstrate that this system can realize exceptional points in the energy spectrum of the magnetic oscillator. This requires balance of the dissipations in the electron and magnetic systems and special symmetry requirements. We show that if the oscillator realizes two exceptional points, it enters so-called mode attraction regime, which in some way is reminiscent of the mode synchronization. In this regime, the real part of the oscillator frequency is locked with the frequency of the interband electron transitions inside the material with spin-orbit coupling. We estimate electric field needed to reach the attraction regime for a spin-orbit torque oscillator with Rashba coupling and make proposals for experimental detection using the magnetic susceptibility measurements. We also demonstrate that the exceptional points in this system can be electrically controlled that may have utility in electric-field switching of the oscillator modes.