Magnetostatic-mode spectrum of rectangular ferromagnetic particles

Approximate methods for obtaining the magnetostatic mode spectrum of thin rectangular samples have been known for some time. However, our experimental results from lithographic arrays of submicron Permalloy particles show that these methods perform relatively poorly if the (in-plane) applied field is not large compared to 4π${\mathit{M}}_{\mathit{s}}$. We present an improved method for finding the spectrum that takes into account both the elliptical character of the mode precession and sample edge effects. We show that the case of an infinite magnetic strip can be reduced to a one-dimensional eigenvalue problem which we solve numerically, yielding insight into the more difficult rectangular case. Effects of the nonuniform demagnetization field on the spatial patterns and frequencies of the modes are also studied.