Influence of surface anisotropy on exchange resonance modes in spherical shells

Abstract

The dynamical properties of saturated spherical shells are investigated in the exchange-dominated regime when assuming that surface anisotropy is present at both the inner and outer boundaries. It is found that surface anisotropy plays an important role in determining the dependence of lower-order eigenvalues on shell thickness. The mode frequency can increase with decreasing shell thickness, or is driven rapidly towards the ferromagnetic resonance frequency depending on the choice of the surface anisotropy constant at each boundary. The presence of surface anisotropy significantly modifies the size dependence of the modes which can be suppressed or amplified based on the coupling between boundaries. When surface anisotropy is present only on the outer boundary, similar behaviour to the solid sphere is observed for lower-order eigenvalues up to a thickness of after which large deviations begin to occur, where and are the inner and outer radius, respectively. Moreover, surface anisotropy introduces a dependence of the zeroth mode on shell thickness, removing the degeneracy with the ferromagnetic resonance and leading to a pronounced size dependence of this mode for thin shells.