Skyrmions on 2D elastic surfaces with fixed boundary frame

Abstract

We report simulation results of skyrmions on fluctuating 2D lattices, where the vertices r i (∈ R 3 ) are treated as a dynamical variable and, hence, there is no crystalline structure. On the fluctuating surfaces, an external magnetic field perpendicular to the surface, Dzyaloshinskii-Moriya and ferromagnetic interactions are assumed in addition to the Helfrich-Polyakov Hamiltonian for membranes. The surface (or frame) tension τ is calculated under both isotropic and uniaxial strain conditions, and this calculation clarifies a nontrivial dependence of τ on the skyrmion, stripe, and ferromagnetic phases. We find that the variation of τ with respect to the applied magnetic field in the skyrmion phase is accompanied by a variation of the total number of skyrmions. Moreover, we find that this total number variation is qualitatively consistent with a recent experimental result for the creation/annihilation of skyrmions of 3D crystalline material under uniaxial stress conditions. It is also found that the stripe phase is significantly influenced by uniaxial strains, while the skyrmion phase remains unchanged. These results allow us to conclude that the skyrmion phase is stable even on fluctuating surfaces.

Anisotropy of exchange and Dzyaloshinskii-Moriya interactions effects on the stabilization of Néel-type skyrmions

“…Strong interfacial spin-orbit coupling in thin film systems such as Pt/Co/MgO [17] heterostructure, CoFeB/Pt [15] and Pt/Co/Ta [18], excites a large interfacial DM interaction. Some works show that a slight anisotropy in the DMI may lead to skyrmion structure deformed [19][20][21]. Monte Carlo and Firstprinciples simulations show that the anisotropies of the short-range exchange interaction may stabilize the skyrmion phase in magnetic frustration system under stress [22][23][24].…”

Skyrmion Crystals and Phase Transitions in Magneto-Ferroelectric Superlattices: Dzyaloshinskii–Moriya Interaction in a Frustrated J1 − J2 Model

“…Another way to check the stability of the skyrmion crystal is to numerically count the topological charges around each skyrmion [81]. If there is a phase transition, the charge number, which plays the role of an order parameter, evolves with T and goes to zero at the phase transition.…”