Solitary Nonlinear Excitations in Spin Systems: Theory

Abstract

We give a survey of the phenomena related to the existence and propagation of soliton-like excitations in quasi one-dimensional magnets. We introduce solitons as domain walls, mediating between equivalent ground states. Static soliton and antisoliton solutions are given. A particular model is discussed, which is equivalent to the Sine-Gordon chain and exhibits three types of solutions: solitons/breathers/phonons. The relevance of these models for real materials is discussed with particular emphasis on the different effects of ferro-, respectively antiferromagnetic ordering. The statistical mechanics of domain walls are investigated using the equivalence to the Sine-Gordon chain. Treating the kinks as classical noninteracting particles, the soliton density at finite temperatures and their contribution to the dynamic structure factor in easy-plane ferromagnetic and antiferromagnetic spin chains are calculated. The stability of the soliton solution is analysed. The parameter dependence and influence of the out-of-plane fluctuations in the continuum and the discrete model is given. Finally, the driven Sine-Gordon chain with damping is considered and some results for the interplay between chaos and spatial ordering are described.

Notes taken by: G. Ristow, N. Elstner and J. Behre