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Motivated by recent experimental results on GdRu$_2$Si$_2$ [Khanh, N.D.,Nakajima, T., Yu, X. et al., \emph{Nat. Nanotechnol.} \textbf{15}, 444-449(2020)], where nanometric square skyrmion lattice was observed, we proposesimple analytical mean-field description of the high-temperature part of thephase diagram of centrosymmetric tetragonal frustrated antiferromagnets withdipolar interaction in the external magnetic field. In the reciprocal spacedipolar forces provide momentum dependent biaxial anisotropy. It is shown thatin tetragonal lattice in the large part of the Brillouin zone for mutuallyperpendicular modulation vectors in the $ab$ plane this anisotropy has mutuallyperpendicular easy axes and collinear middle axes, what leads to double-Qmodulated spin structure stabilization. The latter turns out to be a squareskyrmion lattice in the large part of its stability region with the topologicalcharge $\pm 1$ per magnetic unit cell, which is determined by the frustratedexchange coupling, and, thus, nanometer-sized. In the presence of additionalsingle-ion easy-axis anisotropy, easy and middle axes can be swapped, whichleads to different phase diagram. It is argued that the latter case is relevantto GdRu$_2$Si$_2$.

Thermodynamically stable skyrmion lattice in tetragonal frustrated antiferromagnet with dipolar interaction