On solitary waves in classical anisotropic Heisenberg chains with generalized boundary conditions

TL;DR

This paper studies solitary wave solutions in classical anisotropic Heisenberg chains with generalized boundary conditions, revealing two stable solution branches and their similarities to dark solitons, with numerical analysis of their stability.

Contribution

It introduces generalized boundary conditions for classical Heisenberg chains and identifies two stable branches of solitary wave solutions with properties akin to dark solitons.

Findings

Two branches of one-soliton solutions identified

Solutions are similar to dark solitons of the Nonlinear Schrödinger equation

Solitary waves are highly, but not absolutely stable under interactions

Abstract

We examine solitary waves in classical Heisenberg chains with an uniaxial anisotropy and a parallel magnetic field in a continuum approach. The boundary conditions commonly used are generalized to nonlinear spin wave states, which themselves turn out to be stable only for an anisotropy of the easy-plane type. In this case we obtain two different branches of one-soliton solutions which can be mapped onto each other by a formal time inversion. Moreover, they show some remarkable similarity to dark solitons of the Nonlinear Schr\"odinger equation. Numerical simulations for the discrete Heisenberg chain show that these solitary waves are highly, but not absolutely stable under interaction with linear excitations and as well under scattering with each other. The possible significance of these solitary waves in a phenomenological theory of one-dimensional magnets is briefly addressed.