Propagation of solitons in easy-axis ferromagnetic chains with extended inhomogeneities

We investigate the impact of extended inhomogeneities on the dynamics of nonlinear magnetic excitations (solitons) propagating in a single-ion anisotropic Heisenberg spin chain. The extended inhomogeneous domain consists of a set of neighboring spins with disruption of the exchange interaction and/or easy-axis anisotropy. To explore the dynamics of the magnetization, we derive the corresponding Schrödinger equation incorporating linear and nonlinear perturbative terms. While, in the case of a homogeneous chain with an easy-axis anisotropy, the ensuing equation possesses a bright soliton-like solution, an extended inhomogeneity in the spin coupling and/or the anisotropy leads to a physically rich behavior in the soliton dynamics. An inhomogeneous domain with enhanced exchange interaction induces a potential barrier that either transmits or reflects the incident soliton. On the other hand, a segment with reduced coupling brings about a potential well that for a given range of initial velocities and exchange interaction mismatch the scattering patterns exhibits periodic regions of transmissions and trapping as a function of the length of the inhomogeneous domain. The transmission is associated with an excitation and a subsequent resonant de-excitation of the soliton’s shape oscillations at the well boundaries. A thorough analysis shows that the oscillations emanate from the interference of the solitons with emitted spin waves. The interplay of the exchange interaction and single-ion anisotropy mismatch leads to unusual soliton dynamics promoting a complex potential profile in the inhomogeneous domain.