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The recent experimental confirmation of a transformation between meron andskyrmion topological spin textures in the chiral magnet Co$_8$Zn$_9$Mn$_3$[S.-Z. Lin et al., Phys. Rev. B 91, 224407 (2015); X. Z. Yu et al., Nature 564,95 (2018)] confirms that the skyrmion crystals discovered in 2009 [S.M\"{u}hlbauer et al., Science 323, 915 (2009)] are just the tip of the iceberg.Crystals of topological textures, including skyrmions, merons, vortices, andmonopoles, can be stabilized by combining simple physical ingredients, such aslattice symmetry, frustration, and spin anisotropy. The current challenge is tofind the combinations of these ingredients that produce specific topologicalspin textures. Here we report a simple mechanism for the stabilization ofmeron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets. Inparticular, the meron/skyrmion crystals can form even in absence of magneticfield. The application of magnetic field leads to a rich variety of topologicalspin textures that survive in the long wavelength limit of the theory. Whenconduction electrons are coupled to the spins, these topological spin texturestwist the electronic wave functions to induce Chern insulators and Weylsemimetals for specific band filling fractions.

Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets