Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects

Magnetic solitons in quasi-one-dimensional anisotropic Heisenberg magnets are stable nonlinear excitations that can transport spin, energy, and information over long distances. This paper develops a practical theory for neutron (inelastic) scattering from such solitons and clarifies how quantum and thermal fluctuations control the observable spectrum. Starting from an easy-axis Heisenberg ferromagnet with nearest-neighbor exchange and uniaxial anisotropy, a single soliton is treated as a particle-like mode characterized by conserved quantities that may be interpreted as the number of magnons bound in the soliton and the soliton quasi-momentum. Exploiting the integrability of the model and the possibility of separating kinetic and potential energies in action-angle variables, the soliton contribution to the dynamic structure factor S(q, ω) and to the double-differential scattering cross section is derived. The derivation adapts the Kawasaki-type approach used in earlier soliton scattering studies, but is reformulated here in a simplified and transparent way that yields a general working formula without cumbersome intermediate steps. The resulting response naturally splits into quasi-elastic and inelastic parts. Soliton translation produces a pronounced quasi-elastic intensity and can generate central-peak behavior through the soliton’s response to external perturbations. Thermal averaging leads to explicit conditions under which the quasi-elastic component reduces to a Gaussian form; the analysis also delineates when this approximation fails, in particular for “massive” solitons with large bound-magnon number. At larger energy transfers, scattering into excited soliton states becomes possible, providing access to internal soliton modes and to dissipation mechanisms in real materials. The obtained expressions connect measurable line shapes and spectral weights to soliton width, effective mass, stability, and transport characteristics. Overall, the work provides a concrete basis for interpreting neutron-scattering signatures of solitonic states in quasi-one-dimensional magnets and for designing experiments that isolate their contribution, with relevance to nonlinear magnetic dynamics, spin-transport phenomena, and prospective quantum-technology applications.