Intensity distribution, evolution, and dispersion of discrete spin wave modes in nanoscale spin-torque oscillator

Spin wave dynamics form the foundation of spin-torque oscillator (STO) modulation. In addition to the uniform spin wave mode with wave vector k = 0, multiple spin wave modes with different wave vectors and frequencies coexist in the nanoscale STO. To characterize these spin wave modes and the interactions between them, the distribution and evolution of spin wave intensity in k space need to be investigated together with spin wave dispersion of the individual mode, stressing energy degeneracy. To this end, using micromagnetic simulation, we studied the dynamics of the discrete spin wave modes in a nanoscale STO with structure enhancing spin wave propagation. Simulation using the object oriented micromagnetic framework demonstrated that although they were generated with different spin currents, spin wave modes evolved similarly in k space, according to the wave vector. Furthermore, magnetization pinning at the corners of yttrium iron garnet led to two-magnon scattering. This interaction affects spin wave dynamics in two ways: multivalued dispersion occurs with two-magnon scattering and the uniform mode can become weaker than the near-uniform modes (spin wave modes with wave vector close to zero) in the strong excitation region. The latter phenomenon is supported by the results of studies on the spin wave dispersion of the individual mode, which demonstrate the energy degeneracy between the uniform mode and the near-uniform modes.