Modes of natural vibration for magnetic domains

We analyze wall-vibration modes for the case of plane parallel stripe domains in a uniaxial film whose easy axis is normal to the film plane, using Landau-Lifshitz equations carried to the limit of vanishing wall thickness. We take into account long-range dipole interactions and wall-moment twist due to stray fields from magnetic charges on the film surfaces. The small-amplitude wall displacement q(k, z) depends on the position coordinate z normal to the film plane, and on a two dimensional wave vector k parallel to the film plane. Numerically computed natural frequencies v_n(k) depend on the number of nodes n(=0, 1, 2 …) in the dependence of q on z. Surface and bulk modes are distinguished by the z-dependence of computed eigenmodes q_n(k, z). The spectrum of computed natural frequencies compares favorably with available experimental data.