Stationary and moving self-localized modes in 2D square magnets with a hole

A theory of elementary excitations in Heisenberg spin systems using the path integral method with a SU(2) coherent state basis has been formulated. Applying the stationary phase approximation leads to nonlinear lattice equations in which the intrinsic nonlinearity in the systems has been incorporated to all orders. With subtle situations in crossover from antiferromagnetism to superconductivity by hole doping in high-T-c, superconductors in mind, we generalize in this paper the previous formal results to the case of 2D ferromagnets and antiferromagnets with a fixed magnetic hole, with particular attention paid to interplaying between the intrinsic nonlinearity and the structural disorder due to the existence of the hole. Analytical and numerical calculations yield two kinds of localized modes, one which is mobile under certain conditions, is intrinsic due to the nonlinearity, and the other extrinsic due to the fixed magnetic hole. (C) 1998 Elsevier Science B.V. All rights reserved.