Mathematical modeling of skyrmion shape deformation under uni-axial stresses

Koibuchi, Hiroshi; Hog, Sahbi El; Egorov, V. I.; Kato, Fumitake; Diep, H. T.

doi:10.1088/1742-6596/1391/1/012013

Cited by 2 publications

(3 citation statements)

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“…where FMI and DMI energies S FM and S DM are given in two different combinations denoted by model 1 and model 2 [39] (see Appendix A)…”

Section: B the Hamiltonian And A New Variable For Mechanical Strainsmentioning

confidence: 99%

“…In this paper, using Finsler geometry (FG) modeling, which is a mathematical framework for describing anisotropic phenomena [36][37][38], we study two possible models for the deformation of skyrmions and magnetic stripes [39]. In one of the models, the FMI coefficient is deformed to be λ x = λ y , while DMI is isotropic, and in the other model, the DMI coefficient is deformed to be D x = D y while FMI is isotropic.…”

Section: Introductionmentioning

confidence: 99%

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Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

et al. 2021

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Skyrmions are topologically stable and energetically balanced spin configurations appearing under the presence of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI).Much of the current interest has focused on the effects of magneto-elastic coupling (MEC) on these interactions under mechanical stimuli, such as uniaxial stresses for future applications in spintronics devices. Recent studies suggest that skyrmion shape deformations in thin films are attributed to an anisotropy in the coefficient of DMI, such that D x = D y . This anisotropy is naturally understood as an effect of MEC, however, the relationship between MEC and anisotropy in DMI remains to be clarified. In this paper, we study this problem using a new modeling technique constructed based on Finsler geometry (FG). In the FG model, an MEC is implemented purely geometrically, and the implemented MEC dynamically deforms the coefficients of FMI and DMI to be direction-dependent. This modeling technique is in sharp contrast to the standard model of MEC, in which anisotropic constants are explicitly assumed as an input parameter. Two possible FG models are examined: In the first (second) model, the FG modeling prescription is applied to the FMI (DMI) Hamiltonian. We find that these two different FG models' results are consistent with the reported experimental data for skyrmion deformation. We also study responses of spins under lattice deformations corresponding to uniaxial extension/compression and find a clear difference between these two models in the stripe phase, elucidating which interaction of FMI and DMI is deformed to be anisotropic by uniaxial stresses.

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“…where FMI and DMI energies S FM and S DM are given in two different combinations denoted by model 1 and model 2 [39] (see Appendix A)…”

Section: B the Hamiltonian And A New Variable For Mechanical Strainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

et al. 2021

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“…The skyrmion can also be deformed by altering the material parameters of the system. Koibuchi et al 28 calculated the skyrmion deformation due to mechanical stresses that modulate the DMI, while Hu et al 29 have seen that elliptical skyrmions can be induced when there is an anisotropic strain. Mehmood et al 30 showed that the skyrmion shape can be manipulated by changing the perpendicular magnetic anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Elliptical skyrmions: theory and nucleation by a magnetic tip in an antiskyrmion-hosting material

Capic

2022

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Motivated by experimental findings in [ 1 ] and [ 2 ], we find an elliptical skyrmion can be nucleated in a material with a Dzyaloshinskii-Moriya interaction (DMI) that supports antiskyrmions. The DMI favors the elongation of the skyrmion along a given direction so that it is characterized by two size parameters. We derive analytical properties of the elliptical skyrmion using the Belavin-Polyakov (BP) pure exchange model. We show that the DMI which typically favors isotropic skyrmions or antiskyrmions, respectively, can also support elliptical antiskyrmions or skyrmions, respectively. Using the real material parameters extracted from 1 and including all relevant interactions, numerical computations indicate that the elliptical skyrmion can be nucleated from the stripe or labyrinth domain state by a magnetic force microscope tip in a thin film with a DMI favoring antiskyrmions that consists of at least a few atomic layers.

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Mathematical modeling of skyrmion shape deformation under uni-axial stresses

Cited by 2 publications

References 6 publications

Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

Elliptical skyrmions: theory and nucleation by a magnetic tip in an antiskyrmion-hosting material

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