Square skyrmion, meron and vortex crystals in centrosymmetric tetragonal magnets

The vast majority of the magnetic skyrmion crystals that have been reported in the literature form hexagonal superstructures (triple-Q ordering) and they are induced by a finite magnetic field. Here, we present a new guiding principle for finding square skyrmion, meron and vortex crystals (double-Q ordering) in centrosymmetric tetragonal magnets even in the absence of magnetic field. The phase diagram of the microscopic theory remains qualitatively the same in the continuum limit, allowing us to extract the universal mechanism for the stabilization of these exotic phases.
When conduction electrons are coupled to the meron crystals, the net skyrmion number induces a finite topological Hall effect. Moreover, 3D extensions of the meron crystals produce Weyls points in the electronic band structure.