Shape correction, shape mode control, and stability of solitons in the discrete easy-plane ferromagnet

Abstract

The authors present a new one-parameter ansatz modifying the continuum soliton shape which allows control of the amplitude of the bound shape mode oscillation moving with the soliton along the discrete easy-plane ferromagnetic chain. The shape mode is usually excited, when as in previous simulations the start configuration of the single soliton is known only approximately. They are now able to choose the shape correction parameter in their ansatz such that the excitation of the shape mode is suppressed completely. Thus, well defined discrete solitons can be generated, an important precondition for studying soliton-soliton collisions. They analyse the frequency of the shape mode of the static in-plane soliton as a function of the magnetic field using an approximation related to their shape correction ansatz, from which they conjecture the range of existence of stable solitons and the corresponding shape modes coincide. They also obtain the generalised symmetry of the shape mode eigenfunction for moving solitons. Next they describe two series of static solitary solutions which contain large angles (greater than pi /2) between adjacent spins. Some members of these series are pairwise connected by a continuous crossover. Finally they introduce an approximation which yields qualitatively new results for the high-field limit of existence of stable moving solitons, extending the previously known range, and also discuss the relation of the static soliton branching point to linear stability analysis results.