Elastic moduli and Poisson's ratio of 2-dimensional magnetic skyrmion lattice

By analyzing the magnetic energy, we investigated the deformation of magnetic chiral structures and derived estimates of the skyrmion lattice (SkL) elastic moduli and SkL Poisson's ratio. We verified that the SkL system is close to an elastically isotropic system in which skyrmions display a particle behavior with only nearest-neighbor interactions. We found that with the applied external field, the SkL shear modulus decreases and SkL Poisson's ratio increases. We also obtained an estimate for the critical energy required for the crystal axis reorientation of the SkL, which like the SkL shear modulus also decreases with the external field. These trends indicate that the SkL becomes soft and less solid as the external field increases until the chiral structures disappear at the critical field.