Towards an effective theory of skyrmion crystals

Abstract

We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, $D$, and the field, $B$, the skyrmions do not interact and the exact multiskyrmion solution is a sum of individual projections. In certain range of $B,D\ne 0$, skyrmions become stable and form a hexagonal lattice. The shape of one skyrmion on the plane is fully determined by $D$ and $B$. We describe multiskyrmion configurations by simple sums of individual skyrmion projections, of the same shape and adjusted scale. This procedure reveals pairwise and triple interactions between skyrmions, and the energy of proposed hexagonal structure is found in a good agreement with previous studies. It allows an effective theory of skyrmion structures in terms of variables, referring to individual skyrmions, i.e., their position, size and phase, elliptic distortions etc.

arXiv comment5 pages, 4 figures

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Cited by in corpus (12)

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• Skyrmion interactions and lattices in chiral magnets: analytical results
• Instantons in Chiral Magnets
• Triple helix vs. skyrmion lattice in two-dimensional non-centrosymmetric magnets
• Dynamical susceptibility of Skyrmion crystal
• Magnon topological transition in skyrmion crystal
• Goldstone mode of Skyrmion Crystal
• Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets
• Topological transition in spectrum of skyrmion crystal with uniaxial anisotropy
• Magnon band structure of skyrmion crystals and stereographic projection approach
• Magnon edge states of skyrmion crystal in non-uniform magnetic field
• Topological transition and emergent elasticity of dislocation in skyrmion lattice: Beyond Kittel's magnetic-polar analogy