Three-dimensional chiral skyrmions with attractive interparticle interactions

Abstract

We introduce a new class of isolated three-dimensional skyrmion that can occur within the cone phase of chiral magnetic materials. These novel solitonic states consist of an axisymmetric core separated from the host phase by an asymmetric shell. These skyrmions attract one another. We derive regular solutions for isolated skyrmions arising in the cone phase of cubic helimagnets and investigate their bound states.PACS numbers: 75.30. Kz, 12.39.Dc, The Dzyaloshinskii-Moriya (DM) interaction in noncentrosymmetric magnets is a result of their crystallographic handedness 1 and is responsible for the formation of long-range modulations with a fixed sense of the magnetization rotation 1,2 and the stabilization of two-dimensional axisymmetric localized structures called skyrmions 3,4 . Long-range homochiral modulations (helices) were found in the noncentrosymmetric cubic ferromagnet MnSi several decades ago and since then, other cubic ferromagnets with B20 structures have been investigated intensively 5-7 as have other chiral magnetic materials 8,9 . Isolated chiral skyrmions have been discovered recently in PdFe/Ir(111) nanolayers with induced DM interactions and strong easy-axis anisotropy 10-12 .Chiral skyrmions are two-dimensional topological solitons with an axisymmetric structure localized in nanoscale cylindrical regions. They exist as ensembles of weakly repulsive particles in the saturated phase of noncentrosymmetric magnets 4,13,14 in which all the atomic spins are parallel to an applied magnetic field. In cubic helimagnets, below a certain critical field, H D , the saturated phase transforms into the chiral helical state with the propagation direction along the applied field called the cone phase 2 . Unlike the saturated phase, the boundary values imposed by the longitudinal modulations of the cone phase violate a rotational symmetry of the system, and are thus incompatible with the axisymmetric arrangement of skyrmions investigated in Refs. 4, 10, 11, and 13. Then, the question arises: "are there any localized states compatible with the encompassing cone phase?"In our report we address this compatibility problem and derive regular solutions for asymmetric skyrmions embedded into the cone phase. We demonstrate that unlike the repulsive axisymmetric skyrmions existing in the saturated states, chiral solitons in the cone phase have an attractive interskyrmion potential and form biskyrmion and multiskyrmion states.We consider the standard model for magnetic states in (color online). Magnetic structure of an isolated skyrmion in the cone phase: calculated contour plots of mz(x, y) in three layers with ∆ψc = 2π/3. Details of the magnetization distribution are given in Fig. 2. cubic non-centrosymmetric ferromagnets 1,2 ,where m = (sin θ cos ψ; sin θ sin ψ; cos θ) is the unity vector along the magnetization M, A is the exchange stiffness constant, D is the Dzyaloshinskii-Moriya (DM) coupling energy, and H is the applied magnetic field.Chiral modulations along the applied field with the period L D = 4πA/|D| correspon...

Direct observation of attractive skyrmions and skyrmion clusters in the cubic helimagnet Cu2OSeO3

“…The frontal parts of skyrmion cores in the wall have a similar structure as those in nonaxisymmetric skyrmions and play the role of nuclei for individual nonaxisymmetric skyrmions. The attractive interaction between such skyrmions [13] explains the formation of skyrmion clusters observed in our experiments.…”

“…[3,4,12] and experimentally investigated in nanolayers of chiral ferromagnets [5,6] were embedded in the magnetically saturated phase in which all the atomic spins are parallel. Recently, fundamentally different solitonic states embedded in the cone phase of chiral ferromagnets have been investigated mathematically [13]. Unlike the axisymmetric skyrmions, these three-dimensional chiral * j.c.loudon@gmail.com † leonov@hiroshima-u.ac.jp solitons are inhomogeneous along their axes and asymmetric in the basal planes as shown in Figs.…”

“…Unlike the axisymmetric skyrmions, these three-dimensional chiral * j.c.loudon@gmail.com † leonov@hiroshima-u.ac.jp solitons are inhomogeneous along their axes and asymmetric in the basal planes as shown in Figs. 1(a)-1(c) [13]. Whereas skyrmions embedded in the saturated phase repel one another, these skyrmions are mutually attractive and so tend to produce clusters of skyrmions [13,14].…”

“…1(a)-1(c) [13]. Whereas skyrmions embedded in the saturated phase repel one another, these skyrmions are mutually attractive and so tend to produce clusters of skyrmions [13,14].…”

“…Nonaxisymmetric skyrmions have been investigated theoretically in bulk [13] and confined chiral helimagnets [14], but no experimental observations of these states have been reported to date. Here we show that attractive skyrmions can occur in the cone phase of the cubic helimagnet Cu 2 OSeO 3 by presenting transmission electron micrographs of skyrmion clusters and provide a theoretical description of these results.…”