Topological excitations in magnetic materials

Abstract

In this work we propose a new route to describe topological excitations in magnetic systems through a single real scalar field. We show here that spherically symmetric structures in two spatial dimensions, which map helical excitations in magnetic materials, admit this formulation and can be used to model skyrmion-like structures in magnetic materials.

Dirac field in the background of a planar defect

“…The work deals mainly with the fermionic bound energy spectrum besides the scattering phase shift in the presence of the background defect studied before in [22,25,26]. In this model we can see that there is no fermionic zero mode, although the background configuration is topologically nontrivial.…”

“…We show that in the model considered in this paper, there is no fermionic zero mode, although the background configuration produces a planar topological structure that can be used to simulate a skyrmion-like structure with unity skyrmion number, a subject explored before in Refs. [25,26].…”

Configurational entropy for skyrmion-like magnetic structures

“…Note that there is only one degree of freedom left, given by the angle Θ(r). We can, for convenience, rewrite this quantity as [31][32][33]…”

“…Here, we aim to introduce the concept of configurational entropy in the context of skyrmions. For this reason, we first review a model introduced in [32], which has analytical solutions, and then investigate a new model, which generalizes a model studied in [31]. In the two cases, we bring novelties related to the subject of this work, which concerns the conformational entropy of the topological structures they support.…”

“…This potential has degenerate minima atφ ± = ±1 and φ 0 = 0 for any value of n. Note that for n = 1 we retrieve the model studied in [31]. In particular, for our study we use the solution connectingφ 0 = 0 andφ + = 1, which is given by φ n,s (r) = r n/(1−s) (1 + r 2/(1−s) ) n/2 .…”