Magnetic Skyrmions at Critical Coupling

Abstract

We introduce a family of models for magnetic skyrmions in the plane for which infinitely many solutions can be given explicitly. The energy defining the models is bounded below by a linear combination of degree and total vortex strength, and the configurations attaining the bound satisfy a first order Bogomol'nyi equation. We give explicit solutions which depend on an arbitrary holomorphic function. The simplest solutions are the basic Bloch and Néel skyrmions, but we also exhibit distorted and rotated single skyrmions as well as line defects, and configurations consisting of skyrmions and anti-skyrmions. arXiv:1812.07268v2 [cond-mat.str-el]

Gauged sigma models and magnetic Skyrmions

“…1), or the deformation of a skyrmion to an anti-skyrmion via a line defect, as shown in the top row of Fig. 1 and discussed in some detail in [9].…”

“…This produces the standard DM term κ(n, ∇ × n) and the potential V A = κ 2 2 (1 − n 3 ) 2 . Expanding the square, the potential is seen to be a particular linear combination of an easy-plane anisotropy potential with a Zeeman potential, see [9]. This model with κ = 1 is the one whose solutions are shown in Fig.…”

“…We refer the reader to [10] for details. Furthermore, the study of solutions of arbitrary degree in [9] shows that the modified energy is well-defined for some solution for which the unmodified energy integral (3) is not.…”

Topological energy bounds for frustrated magnets

“…In models that support two-dimensional skyrmions, one often finds linear energy bounds of the form E ≥ CN , where E and N are the energy and degree of a skyrmion, and C is a positive constant. Bounds of this type have been derived for the O(3) sigma model [9], the baby Skyrme model [10], and chiral magnetic skyrmions stabilised by the DM interaction [11] (see also [12] for recent developments). Linear bounds support a particle-like interpretation of skyrmions, with the mass (energy) roughly proportional to the number of particles (degree).…”

Report on scipost_201905_00004v1

“…In the recent paper [1], it was shown that a model for static magnetic skrymions with a particular choice of coupling constants, called critical in [1], can be solved explicitly by viewing it as a gauged non-linear sigma model with a fixed su(2) connection. The purpose of this paper is to define and solve the relevant gauged non-linear sigma model in general geometric terms, and to discuss other applications.…”