DIPOLE-EXCHANGE SPIN WAVES IN FERROMAGNETIC NANOSTRUCTURES WITH SPHERICAL GEOMETRIES

Dipole-exchange spin waves (SWs) are studied in ferromagnetic nanostructures with spherical geometries such as spheres, part spheres, and spherical shells, both individually and in finite-sized arrays. A microscopic theory is used based on a spin Hamiltonian, which incorporates the short-range exchange and long-range magnetic dipole-dipole interactions, as well as an external magnetic field applied in any direction. Our theory is advantageous for describing the dynamical properties of inhomogeneously magnetized samples, and the use of phenomenological boundary conditions is avoided. Numerical results are deduced for the frequencies of the discrete SW modes and their dependence on the radius, spacing between particles, applied field, etc. Applications are made to Permalloy Fe19Ni81 and alloy Co80Ni20 nanoparticles with their sizes varying from 10 to 100 nm. Through a Green function theory, the spatial distributions and spectral intensities of the SWs are also deduced. The mode-mixing (hybridization) effects on the SW branches are found to be important, depending on the particle sizes and geometries.