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Skyrmions in chiral magnetic materials are topologically stable andenergetically balanced spin configurations appearing under the presence offerromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI).Much of the current interest has focused on the effects of magneto-elasticcoupling on these interactions under mechanical stimuli, such as uniaxialstresses for future applications in spintronics devices. Recent studies suggestthat skyrmion shape deformations in thin films are attributed to an anisotropyin the coefficient of DMI, such that $D_{x}\!\not=\!D_{y}$, which makes theratio $\lambda/D$ anistropic, where the coefficient of FMI $\lambda$ isisotropic. It is also possible that $\lambda_{x}\!\not=\!\lambda_{y}$ while $D$is isotropic for $\lambda/D$ to be anisotropic. In this paper, we study thisproblem using a new modeling technique constructed based on Finsler geometry(FG). Two possible FG models are examined: In the first (second) model, the FGmodeling prescription is applied to the FMI (DMI) Hamiltonian. We find thatthese two different FG models' results are consistent with the reportedexperimental data for skyrmion deformation. We also study responses of helicalspin orders  under lattice deformations corresponding to uniaxial extension/compressionand find a clear difference between these two models in the stripe phase,elucidating which interaction of FMI and DMI is deformed to be anisotropic byuniaxial stresses.

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