Localized modes in two-dimensional square anisotropic ferromagnets with a hole

Abstract

By using the path-integral method with a $\mathrm{SU}(2)$ coherent-state basis, two-dimensional anisotropic Heisenberg ferromagnets bearing a fixed magnetic hole are investigated with particular attention paid to interplaying between the intrinsic nonlinearity and the extrinsic structural disorder due to hole doping. Detailed numerical calculations are made for s-like localized modes to determine their eigenfrequencies and profiles as a function of a nonlinearity parameter and various anisotropic exchange parameters. A localized magnetic vortex is found in the neighborhood of a hole. Analytical and numerical analyses on their time evolution show two kinds of localized modes separately; one is mobile under certain conditions and intrinsic due to the nonlinearity, and the other is immobile and extrinsic due to the fixed magnetic hole.