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

A theory of localized modes in two-dimensional square anisotropic ferromagnets with a hole is extended to the antiferromagnetic case. Here a path-integral method based on the SU(2) coherent state representation is employed. Detailed numerical calculations are made for s-like modes, and their eigenfrequency is determined as a function of nonlinearity parameter and various anisotropic exchange interactions and uniaxial anisotropies. Particular attention is paid to interplaying between the intrinsic nonlinearity and extrinsic hole doping. It turns out that the former stabilizes the magnetic localized mode generated by the latter (or vice versa), and it takes a vortex shape in the neighborhood of a doped hole. In contrast to the ferromagnetic case, the mobile nonlinear self-localized mode is unlikely to exist.