Solitary excitations in one-dimensional magnets

The present status of theoretical and experimental investigations of solitary excitations in one-dimensional magnetic systems is reviewed. A survey of exact solutions to the nonlinear equations of motion for pertinent classical chain systems (sine-Gordon chain and ferromagnetic Heisenberg chains with various anisotropies) is given. Particular emphasis is devoted to the role of solitons in the thermodynamics of such systems. Models corresponding to real quasi-one-dimensional magnets are broadly discussed to demonstrate the properties of their solitary excitations. The experimental significance of such nonlinear excitations in the static and dynamic quantities of such systems is discussed in detail. The models and model substances are the easy-plane ferromagnet (model substances CsNiF3 and (C6H11NH3)CuBr3), the easy-plane antiferromagnet (CH3)4NMnCl3) and the S = ½ Ising chain with transverse interactions (CsCoCl3). The quantum aspects of solitary excitations are treated in some theoretical detail. Finally, open questions and possible future investigations are discussed.