Analytical theory of the dipole-exchange oscillations in long ferromagnetic nanowires of elliptical cross-section in a transverse external magnetic field

The analytical theory of the dipole-exchange spin-wave excitations of ferromagnetic cylinders of elliptical cross section with the bias magnetic field perpendicular to the axis of the cylinder is presented. Explicit analytical expressions for the frequency spectrum and the magnetization spatial distribution are derived. Their evolution as a function of cross-section's aspect ratios has been investigated. The developed formalism allows successful interpretation of experimental Brillouin Light Scattering spectra obtained previously for Ni nano-wires both qualitatively and quantitatively. It also provides a tool for comprehensive analysis of phenomena, in which spatial distribution and polarization of high-frequency magnetization play crucial role. - Highlights: • The analytical theory of the spin-wave modes of elliptical cylinder sample is given. • Explicit expressions for the frequency spectrum are derived. • Spatial distribution and polarization of rf magnetization have been found. • Experimental spectrum of Ni nano-wires was quantitatively explained