Theory of Dipole-Exchange Spin Excitations in a Spherical Ferromagnetic Nanoshell, consideration of the Boundary Conditions

Abstract

The paper continues study of dipole-exchange spin excitations in a spherical ferromagnetic nanoshell started by the author in the previous paper. The proposed model considers the magnetic dipole-dipole interaction, the exchange interaction, the anisotropy effects and the damping effects. A new method of obtaining the values' spectrum of the wavenumbers for the investigated excitations – the method based on the application of general boundary conditions – is proposed. Consequently, the values' spectra of the wavenumbers and the frequencies of the investigated excitations are obtained in addition to the previously obtained dispersion law. Exploitation of the above-mentioned method essentially extends the area of application of the obtained results compared to the previous paper. The obtained dependence of the wavenumber on the angular mode number is shown to be weak and close to linear. On the other hand, the obtained dependence of the wavenumber on the radial mode number is shown to be essential. The obtained spectrum of wavenumbers' values is shown to transform to a quasi-one-dimensional form once specific conditions are satisfied; these conditions are found.