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.
Skyrmion is a topologically stable spin texture and expected to be applied to the future computer memory. On the semiconductors such as FeGe and MnSi, the skyrmion configuration is stable in the sense that it is not strongly affected by a small variation of external stimuli such as temperature, magnetic field etc. In recent experiments, it was reported that the skymion shape is deformed from isotropic (or circular shape) to anisotropic (or elliptic shape) by an external mechanical stress. This shape deformation is caused by the so-called “strain-induced anisotropy (SIA)” of Dzyaloshinskii-Moriya interaction (DMI). In this presentation, we study the reason why this SIA appears in the DMI coefficient on the basis of Finsler geometry modeling technique by introducing a microscopic strain field τ, which is caused by or interacts with the applied external mechanical force.
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