  The recent experimental confirmation of a transformation between meron and
skyrmion 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, and
monopoles, can be stabilized by combining simple physical ingredients, such as
lattice symmetry, frustration, and spin anisotropy. The current challenge is to
find the combinations of these ingredients that produce specific topological
spin textures. Here we report a simple mechanism for the stabilization of
meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets. In
particular, the meron/skyrmion crystals can form even in absence of magnetic
field. The application of magnetic field leads to a rich variety of topological
spin textures that survive in the long wavelength limit of the theory. When
conduction electrons are coupled to the spins, these topological spin textures
twist the electronic wave functions to induce Chern insulators and Weyl
semimetals for specific band filling fractions.
