Soliton-like excitations in a deformable spin model

Abstract

Nonlinear excitations in a one-dimensional deformable, discrete, classical, ferromagneticchain are numerically investigated. In the continuum limit the equations of motion arereduced to a Klein–Gordon equation, with a Remoissenet–Peyrard substrate potential.From a numerical computation of the discrete system with a suitable choice of thedeformability parameters, the soliton solutions are shown to exist and move both witha monotonic oscillating (i.e. nanopteron) and a monotonic nonoscillating tail,and also with a non-oscillating tail but with a splitting propagating shape. Thestability of all these various soliton shapes is confirmed numerically in a range of thereduced magnetic fields greater than for a rigid magnetic chain i.e. . From a kink–antikink and a kink–kink colliding simulation, we found variouseffects, including a bound state of a kink and an antikink, as well as a movingkink profile with higher topological charge that appears to be the bound stateof two kinks. For some values of the deformability parameter, with a suitablechoice of the initial velocity, we observed that the presence of an internal modeleads to the combination of an attractive and a repulsive phenomenon, that ariseswhen the kink–kink collision is engaged. The fact that this collision happensonly in the centre of the magnetic chain with the presence of a minimal distancebetween the two kinks as long as the collision is produced is also a feature of thedeformability effect in the dynamics of a magnetic chain. From our results, it appearsthat the value of the shape parameter of the substrate potential or the modifiedZeeman energy is a factor of utmost importance when modelling magnetic chains.