Understanding magnetoelastic couplings of Ising monolayers

The coupling between two-dimensional Ising magnetic textures and the atomistic lattice is investigated on paradigmatic CrSiTe₃ monolayers by a direct comparison of diagonalized lattice stiffness (force constant) tensors and by a novel calculation of magnetic exchange tensors from the density matrix, on four stable magnetic phases. Two distinct space groups describe magnetic phases producing isotropic (P\bar{3}1m) or anisotropic (C2/m) distortions. The coupling between magnetization and lattice is then quantified by the softening/hardening of the lattice stiffness tensor with magnetization texture, and by the dependency of the magnetic exchange on the atomistic structure.