TOPOLOGICAL EXCITATIONS IN LOW DIMENSIONAL MAGNETS

We review excitations in low dimensional magnetic systems with emphasis on nonlinear, in particular soliton exciations. First, we discuss soliton band formation in Ising-type systems, making contact with recent neutron scattering experiments. Furthermore we demonstrate how chirality emerges as a new degree of freedom of a soliton. The xy-model is discussed with emphasis on the soliton character of the elementary excitations and the emergence of incommensurate modes in external fields. We discuss spin-1 chains and their representation as a chain of rotors or as a nonlinear σ-model. We then go on to derive classical soliton solutions in magnetic chains and soliton bound states, so called breathers. Semiclassical quantization of solitons in an easy-plane situation is discussed and how the band structure closely resembles that of solitons in Ising systems with transverse exchange. The quantization of breathers remarkably leads to the same bound state energies as the spin-½ xyz-model. The interplay between orbital motion and quantum spin phases is not restricted to one-dimensional systems. We show that in two-dimensional doped antiferromagnets, such phases lead to a quasiparticle dispersion that is in agreement with the observed doping dependence in high T_c compounds without having to invoke next nearest neighbor hopping.