Nonlinear effects for spin waves in DMI systems: enhancement of harmonic generation and the development of frequency combs

We theoretically examine the effect of the Dzyaloshinskii-Moriya Interactions (DMI) on the nonlinear behavior of spin waves. In specific, we investigate how DMI influences harmonic generation, where a wave at a frequency, f, generates waves at frequencies of 2f, 3f, or higher. We consider a narrow magnetic stripe with interfacial DMI present and an external field perpendicular to the length of the stripe, i.e. the typical nonreciprocal geometry. We study the spin wave motion in two ways: 1) We artificially move the spins from their equilibrium direction and study the resulting motion and 2) we drive the system with a spatially uniform oscillating magnetic field. The resulting differential equation for the time-development of the spin system is calculated numerically through a 2nd order Runge-Kutta scheme, with exchange, DMI, demagnetizing fields, and external fields present. Surprisingly, we find that in the magnetic system only the 3rd and 5th harmonics are strongly generated. We compare these results with the case where DMI is absent, and find that both the 3rd and 5th harmonics are increased when DMI is present, with the 5th harmonic increased by a factor of over 100. More importantly, with DMI and at higher power levels, each of these frequencies develops a nearby frequency comb leading to multiple generated frequencies.