Dipole exchange spin waves and microwave response of ferromagnetic spheres

We present a method that allows one to analyze the dipole exchange spin waves in ferromagnetic spheres, along with their interaction with spatially varying microwave magnetic fields. We present explicit calculations of the mode spectrum of such a sphere, along with the response functions which describe excitation of spin wave modes by spatially inhomogeneous fields. Our theory will prove useful for describing the dynamic response of very small ferromagnetic spheres, in the limit where exchange influences their response. Our formalism is arranged so the single sphere response function constructed here may be utilized in our recent description of the collective spin wave modes of arrays of ferromagnetic spheres.