  Skyrmions in chiral magnetic materials 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 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 $D_{x}\!\not=\!D_{y}$, which makes the
ratio $\lambda/D$ anistropic, where the coefficient of FMI $\lambda$ is
isotropic. 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 this
problem using a new modeling technique constructed based on Finsler geometry
(FG). 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 helical
spin orders
  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.
