Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices

Abstract

Typically, the chiral magnetic Skyrmion is a single-state excitation. Here we propose a system, where multiplet of Skyrmion states appears and one of these states can be the ground one. We show that the presence of a localized curvilinear defect drastically changes the magnetic properties of a thin perpendicularly magnetized ferromagnetic film. For a large enough defect amplitude a discrete set of equilibrium magnetization states appears forming a ladder of energy levels. Each equilibrium state has either a zero or a unit topological charge; i.e., topologically trivial and Skyrmion multiplets generally appear. Transitions between the levels with the same topological charge are allowed and can be utilized to encode and switch a bit of information. There is a wide range of geometrical and material parameters, where the Skyrmion level has the lowest energy. Thus, periodically arranged curvilinear defects can result in a Skyrmion lattice as the ground state.

Spin eigenexcitations of an antiferromagnetic skyrmion

“…For the derivation of the effective potential energy of the domain wall E eff we need to calculate the defined in (2b) energy density W = W ex + W an + W dmi for the case of Ansatz (18) formulated in the curvilinear coordinates (u, v). While the anisotropy contribution is trivial W an = sin 2 Θ the calculation of the exchange W ex = (∇Θ) 2 + Ω 2 sin 2 Θ and DMI W dmi = −2 sin 2 Θ (e n · ∇Θ) terms requires the technique previously developed for the curvilinear systems [46,47]. Here ∇ = e t |R | −1 (1 − κv) −1 ∂ u + e n ∂ v is the surface gradient and Ω = −κ(1−κv) −1 e t is the vector of spin-connection [48,49].…”

Chiral Skyrmion and Skyrmionium States Engineered by the Gradient of Curvature

“…Other possible solutions represent a Néel skyrmion. While smallradius skyrmions can appear for an arbitrary geometryinduced DMI with a radius governed by the DMI coefficient [14,15], in the present case we obtain three magnetization textures with different winding numbers Q, Fig. 1(c).…”

“…Finite dimensions of nanostructures can lead to the confinement of a skyrmion [24] and skyrmion formation under an external influence [26]. Considering curvilinear effects, an alternative way to stabilize skyrmions is to utilize a curvature-induced DMI of interfacial type in samples with geometrically defined axis of anisotropy [12][13][14][15].…”

“…Primarily, activities are dedicated to flat magnetic thin films with perpendicular magnetic anisotropy. Recently, it was shown that local curvature can lead to the emergent exchange-driven Dzyaloshinskii-Moriya interaction (DMI) [12,13] enabling the route to realize skyrmions [14] and field-free skyrmion lattices even as a ground state [15].…”

Experimental and Theoretical Study of Curvature Effects in Parabolic Nanostripes

“…In the emergent field of magnetism in curved geometries there are two exchange‐induced curvilinear interactions, namely Dzyaloshinskii–Moriya and anisortopy interactions . This leads to a number of remarkable theoretical discoveries including magnetochiral effects, topologically induced magnetization patterns, stabilization of individual skyrmions and skyrmion lattices on curvilinear defects, mesoscopic Dzyaloshinskii–Moriya interaction (DMI), coupling between chiralities in spin and physical spaces in the case of Möbius ring to name just a few. The experimental validation of these exciting predictions is still pending.…”