Impact of surface anisotropy on the spin-wave dynamics in thin ferromagnetic film

TL;DR

This study investigates how surface anisotropy affects spin-wave behavior in thin ferromagnetic films, revealing increased mode interaction and nonreciprocity, with implications for nonreciprocal device design.

Contribution

The paper extends an analytical model to include perpendicular surface anisotropy and compares it with numerical simulations, demonstrating accurate predictions of spin-wave dynamics.

Findings

Surface anisotropy increases avoided crossing size.

Asymmetrical surface anisotropy induces nonreciprocity.

Mode crossing can be achieved under specific conditions.

Abstract

The spin-wave dynamics in the thin CoFeB film in Damon-Eshbach geometry are studied in three cases of boundary conditions -- free boundary conditions, symmetrical surface anisotropy, and one-sided surface anisotropy. The analytical model created by Wolfram and De Wames was extended to include perpendicular surface anisotropy in boundary conditions. Its comparison with numerical simulations demonstrate perfect agreement between the approaches. The analysis of the dispersion relation indicates that the presence of surface anisotropy increases the avoided crossing size between Damon-Eshbach mode and perpendicular standing modes. Additionally, asymmetrical one-sided surface anisotropy induces nonreciprocity in the dispersion relation. In-depth analysis of the avoided crossing size is conducted for systems with different boundary conditions, different thicknesses, surface anisotropy constant values, and external magnetic fields. It shows the significant role of the strength of surface localization of Damon-Eshbach mode and the symmetry of perpendicular standing modes in the avoided crossing broadening. Interestingly, for specific set of parameters the interaction between the particular modes can be suppressed, resulting in a mode crossing. Such a crossing, which occurs only on one side of the dispersion relation in a one-sided surface anisotropy system, can be utilized in nonreciprocal devices.