Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

Speight, J.M.; Winyard, Thomas

doi:10.1103/physrevb.101.134420

Cited by 10 publications

(4 citation statements)

References 17 publications

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“…Example solutions of solvable rank one models and their properties are discussed in [10] and also [16]. We note that a similar reformulation in terms of a flat gauge field was recently applied to a rather different ferromagnetic model in [17].…”

Section: Examplesmentioning

confidence: 88%

Gauged sigma models and magnetic Skyrmions

Schroers

2019

SciPost Phys.

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We give a succinct summary of the recently discovered solvable models of magnetic skyrmions in two dimensions, and of their general solutions. The models contain the standard Heisenberg term, the most general translation invariant Dzyaloshinskii-Moriya (DM) interaction term and, for each DM term, a particular combination of anisotropy and Zeeman potentials. We argue that simple mathematical features of the explicit solutions help understand general qualitative properties of magnetic skyrmion configurations in more generic models.

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Section: Examplesmentioning

confidence: 88%

Gauged sigma models and magnetic Skyrmions

Schroers

2019

SciPost Phys.

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“…We then evolve the system in eq. 1, using a gradient decent method, in particular an arrested Newton flow algorithm (described in detail in [32]), solving for the motion of a particle in C under the potential F dis , φ = −gradF dis (φ), (A1)…”

Section: Discussionmentioning

confidence: 99%

“…24 according to our chosen orthonormal basis {x 1 , x2 , x3 }. We then solved the resulting 1-dimensional boundary problem (where H purely fixes the boundary conditions), using a Newton flow algorithm [32] which we describe briefly in appendix A.…”

Section: A Meissner State Solutionsmentioning

confidence: 99%

Symmetries, length scales, magnetic response, and skyrmion chains in nematic superconductors

2023

Self Cite

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Nematic systems are two component superconductors that break rotational symmetry, but exhibit a mixed symmetry that couples spatial rotations and phase difference rotations. We show that a consequence of this induced spatial anisotropy is mixed normal modes, that is the linear response to a small perturbation of the system about its ground state, generally couples magnetic and condensate degrees of freedom. We will study the effect of mode mixing on the magnetic response of a nematic system as the strength of applied field is increased. In general we show that the coupled modes generate magnetic field perpendicular to the applied field, causing the magnetic response to spontaneously twist direction. We will study this for the Meissner effect with weak fields and also for stronger applied fields, which produce a mixture of Skyrmions and composite vortices, forming orientation dependent bound states. We will also calculate the anisotropies of the resulting first and second critical fields Hc 1 and Hc 2 . The Skyrmion lattices for Hc 1 ≤ H ≤ Hc 2 in nematic superconductors are shown to be structurally complicated, in contrast to the triangular or square vortex lattices in conventional superconductors. For low fields the magnetic response of the system involves a loosely bound collection of parallel Skyrmion chains. As the external field is increased the chains attract one another, causing a transition where the unit cell becomes triangular for high applied fields. This unique Skyrmion lattice and the magnetic twisting are clear indicators that could be used experimentally to identify materials that exhibit nematic superconductivity. To obtain these results we develop and present a novel method to find the unit cell of a vortex lattice that can be applied to other kinds of superconducting systems.

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“…The baby Skyrme energy is then discretised using a 4th order central finite-difference scheme. This yields a discrete approximation E dis [ϕ] to the static energy functional E[ϕ], which we can regard as a function E dis : C → R, where the discretised configuration space is the manifold C = (S 2 ) N1 N2 ⊂ R 3 N1 N2 [26,27].…”

Section: A Initial Configurationsmentioning

confidence: 99%

Baby Skyrmion crystals

Leask

2021

Preprint

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This paper describes a model for baby Skyrme crystal chunks with arbitrary potential by considering energy contributions from the bulk and surface of a crystal chunk. We focus on two potentials which yield distinct Skyrme lattices: the standard potential V = m 2 (1 − ϕ 3 ) and the easy plane potential V = 1 2 m 2 (ϕ 1 ) 2 . In both models, the static energy functional is minimized over all 2dimensional period lattices, yielding the minimal energy crystal structure(s). For the standard potential, the Skyrmions form a hexagonal crystal structure, whereas, for the easy plane potential, the minimal energy crystal structure is a square lattice of half-charge lumps. We find that square crystal chunks are the global minima in the easy plane model for charges B > 6 with 2B a perfect square (m 2 = 1). In contrast, we observe that hexagonal crystal chunks in the standard model become the global minima for surprisingly large charges, B > 954 (m 2 = 0.1).

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Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

Cited by 10 publications

References 17 publications

Gauged sigma models and magnetic Skyrmions

Gauged sigma models and magnetic Skyrmions

Symmetries, length scales, magnetic response, and skyrmion chains in nematic superconductors

Baby Skyrmion crystals

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