Electronic Thesis and Dissertation Repository


Doctor of Philosophy




Dr. Michael G. Cottam


The fabrication of magnetic nanowires and nanotubes, along with experimental studies, have motivated a theory of spin waves (SW) in ferromagnetic and antiferromagnetic cylindrical systems. The calculations are applied to situations where the external magnetic field is parallel to the cylindrical axis and the structures have a large length-to-diameter aspect ratio. A macroscopic theory is developed for the bulk and surface SW for various regimes of wavevectors.

First, a theory is given for magnetostatic modes, where the dipole-dipole interactions dominate in the SW dynamics. The magnetostatic form of Maxwell's equations and electromagnetic boundary conditions are used to derive the SW dispersion relations in nanotubes. A transfer matrix formalism is subsequently used to generalize these calculations to cylindrical multilayers. Next, the theory in magnetic cylindrical tubes is extended to the magnetic polaritons that arise at smaller wavevectors from the coupling between electromagnetic waves and the dipolar SW excitations. This involves solving for the dynamical response using the full form of Maxwell's equations with retardation effects. Another extension is to the dipole-exchange SW in magnetic nanotubes. This is applicable at larger wavevectors, where the dipole-dipole and exchange interactions are both important in the magnetization dynamics. A formalism is also developed for the linear response functions (Green's functions) in magnetic nanotubes, taking the wavevector regime of the magnetostatic modes. This enables us to calculate the spectral intensities of the modes. Numerical applications are presented for ferromagnets, such as Ni, Permalloy, and EuS, and for antiferromagnets, such as GdAlO3 and MnF2.