Magnetostatic modes in ferromagnetic nanowires

We present an approach to the theory of the magnetostatic modes of ferromagnetic nanowires of uniform cross section which allows one to address structures of arbitrary cross sectional shape, without resorting to the use of a basis set. The method applies to the case where the magnetization is parallel to the axis of the structure. Use of the extinction theorem leads us to two homogeneous integral equations, each in the form of a line integral around the periphery of the nanowire. These relate the magnetic scalar potential to its normal derivative on the boundary. An appropriate procedure allows one to extract dispersion relations for the magnetostatic modes from these equations, as a function of wave vector parallel to the axis of the wire. Two related statements allow one to generate the form of the magnetic potential or other quantities such as the components of transverse magnetization. We illustrate the method with results for nanowires of square, rectangular, and elliptical cross sections.