Frustration-induced skyrmion crystals in centrosymmetric magnets.

Recent theoretical and experimental studies on the frustration-induced skyrmion crystal (SkX) in centrosymmetric magnets are reviewed, with some emphasis on their symmetry and topological aspects. Special importance of frustration and chirality is highlighted. Theories cover the studies based on both the spin models and the electronic models. In the former, the frustrated Heisenberg models on the triangular or the square lattices interacting either via the long-range RKKY interaction or via the competing short-range exchange interactions are treated, where frustration is borne by the oscillating nature of the long-range RKKY interaction or by the competition between the shorter-range exchange interactions. Special attention is paid to the role played by the magnetic anisotropy including the dipolar interaction. The electronic models discussed are mainly the Kondo lattice model on the triangular lattice, which reduces to the RKKY Heisenberg in the weak-coupling limit. Experiments on centrosymmetric SkX-hosting magnets cover the hexagonal magnets Gd$_2$PdSi$_3$ (triangular) and Gd$_3$Ru$_4$Al$_{12}$ (breathing kagome), and the tetragonal magnets GdRu$_2$Si$_2$ and EuAl$_4$. Various experimental data, including magnetization or susceptibility, specific heat, Hall resistivity, resonant magnetic $x$-ray scattering, neutron scattering, Lorentz transmission electron miscroscopy, etc are reviewed and discussed in conjunction with the theoretical results. The nature of a variety of phases surrounding the SkX phase in the phase diagram, many of which are of multiple-$q$ character, is also examined. Finally, some discussion is given about the physical origin of the centrosymmetric SkX formation, its unique features in comparison with the non-centrosymmetric SkX induced by the antisymmetric Dzaloshinskii-Moriya interaction, together with some open and challenging problems for the future.