Thermodynamically stable skyrmion lattice in a tetragonal frustrated antiferromagnet with dipolar interaction

Motivated by recent experimental results for GdRu₂Si₂ [Khanh et al., Nat. Nanotechnol. 15, 444 (2020)], in which a nanometric square skyrmion lattice was observed, we propose a simple analytical mean-field description of the high-temperature part of the phase diagram of centrosymmetric tetragonal frustrated antiferromagnets with dipolar interaction in the external magnetic field. Dipolar forces provide momentum-dependent biaxial anisotropy in reciprocal space. It is shown that in a tetragonal lattice, in the large part of the Brillouin zone, for mutually perpendicular modulation vectors in the $ab$ plane this anisotropy has mutually perpendicular easy axes and collinear middle axes, which leads to double-Q modulated spin structure stabilization. In the large part of its stability region, the latter turns out to be a square skyrmion lattice with a topological charge of ±1 per magnetic unit cell, which is determined by the frustrated exchange coupling and thus nanometer sized. Easy and middle axes can be swapped in the presence of additional single-ion easy-axis anisotropy. This results in the different phase diagram. It is argued that the latter case is relevant to GdRu₂Si₂.