Two-dimensional dispersion of magnetostatic volume spin waves

TL;DR

This paper derives explicit analytical and semi-analytical expressions for the dispersion relations of volume spin waves in magnetic films, accounting for various regimes and anisotropies, aiding experimental interpretation and control.

Contribution

It provides the first explicit perturbative and semi-analytical formulas for the dispersion of volume magnetostatic spin waves in finite-thickness films with in-plane magnetization.

Findings

Derived perturbative expressions for mode profiles and frequencies.

Presented a semi-analytical formula for the lowest-frequency mode dispersion.

Results facilitate interpretation and control of spin wave propagation in experiments.

Abstract

The dipolar (magnetostatic) interaction dominates the behavior of spin waves in magnetic films in the long-wavelength regime. In an in-plane magnetized film, volume modes exist with a negative group velocity (backward volume magnetostatic spin waves), in addition to the forward surface-localized mode (Damon-Eshbach). Inside the film of finite thickness $L$, the volume modes have a nontrivial spatial dependence, and their two-dimensional dispersion relations $\omega(\mathbf{k})$ can be calculated only numerically. We present explicit perturbative expressions for the profiles and frequencies of the volume modes, taking into account an in-plane applied field and uniaxial anisotropy, for the regimes $\lVert \mathbf{k}L \rVert \gg 1$ and $\lVert \mathbf{k}L \rVert \ll 1$, which together provide a good indication of the behavior of the modes for arbitrary wavevector $\mathbf{k}$. Moreover, we derive a very accurate semianalytical expression for the dispersion relation $\omega(\mathbf{k})$ of the lowest-frequency mode that is straightforward to evaluate using standard numerical routines. Our results are useful to quickly interpret and control the excitation and propagation of spin waves in (opto-)magnetic experiments.