Spectrum of elementary excitations of a single domain wall in garnet films with in-plane magnetization

Epitaxial garnet films with in-plane magnetization are studied by microwave technique. Resonances related to different branches of domain wall excitations are observed : a low-frequency Goldstone branch of translational wall vibrations in the MHz band and a high-frequency Gilinskii branch in the GHz band. A strong coupling between neighbouring domain walls is observed, if their distance becomes comparable to the wall thichkness. In this case each resonance is split into two coupled rasonant modes, their frequencies being larger at smaller wall distances. Spin wave excitations of a single wall are analyzed by numerical solution of Landau-Lifshitz and magnetostatic equations for the case of a bulk orthorhombic ferromagnetic material. Unidirectional Gilinskii branch and asymmetric Goldstone branch are shown to exist in the spectrum of the wall excitations for the case of the propagation direction perpendicular to the magnetization in domains. Unexpected wall excitation spectra are predicted at some values of the anisotropy parameters when the wall becomes unstable. Such spectrum shows a gap in the wave number and a loop in the dispersion of the Goldstone branch