Origin of Nonlinear Damping due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

We investigate the physical origin of nonlinear damping due to mode-mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on temperature and applied field angle. We observe a transition in the nonlinear damping of the auto-oscillation modes extracted from the total oscillation power as a function of drive current, which coincides with the onset of power redistribution amongst several modes and the reversal of the slope of the linewidth change vs. drive current from negative to positive for all modes. This indicates the activation of a new relaxation process by nonlinear magnon-magnon scattering between the modes. We also find that both nonlinear damping and threshold current are temperature independent in high drive current regime after the transition, suggesting that the mode coupling occurs dominantly through a non-thermal magnon scattering process via a dipole or exchange interaction rather than via thermally excited magnon-mediated scattering.