Temperature effect on the dispersion of spin waves in the ferromagnetic thin film with Dzyaloshinskii–Moriya interaction

Abstract

Ferromagnetic thin films are one of the promising platforms for developing spintronic devices due to the multi-field-controlled diverse dynamic behaviors of spin waves and magnetization topologies like skyrmions. Especially, the short-wavelength spin wave is an excellent information carrier because of the absence of Joule heat and high-speed propagation. However, although the control of spin waves by magnetic field and their interactions is widely studied, the temperature effect on spin waves as a natural feature is still unclear. Here, we demonstrated that the dispersion relations of spin waves in both the out-of-plane and in-plane directions are highly dependent on the temperature by employing a temperature-related phase-field method based on Ginzburg–Landau theory. By combining analytical and numerical results, we proposed a dispersion relation that reveals temperature-dependent spin wave stiffness, energy gap, and so on. We not only elucidate the temperature effect on spin waves from the perspectives of thermodynamics and micromagnetic dynamics but also provide the relevant equations. These findings should serve as a valuable theoretical guide for future investigations into magnetization dynamics and the development of spintronic devices.