Magnons in a square bar

We present a theoretical investigation of magnon excitations within a simple cubic, ferromagnetic crystal bar of square cross section formed by the intersection of 100] surfaces. The eigenfrequency spectrum for spin waves in the bulk, and localized at the surfaces and edges of the bar is obtained and examined in the presence of dipolar, and nearest and next nearest neighbor exchange spin-spin interactions, for values of the one-dimensional wavevector extending form the origin to the boundary of the one-dimensional Brillouin zone for the bar. The modes obtained are wavelike in the direction parallel to the bar axis. The localization of the modes is determined from an examination of their eigenvectors.