Zero-field square skyrmion crystal by spin–orbit and spin–charge couplings in noncentrosymmetric magnets

We investigate the possibility of a square skyrmion crystal at a zero magnetic field by focusing on the mutual interplay among the charge, spin, and orbital degrees of freedom in electrons. By taking into account the effect of the spin–orbital coupling as the Dzyaloshinskii–Moriya interaction and that of the spin–charge coupling as the biquadratic interaction in an effective spin model and performing the simulated annealing, we find that the square skyrmion crystal is robustly stabilized from zero to finite magnetic fields on a two-dimensional noncentrosymmetric square lattice. We also show that the zero-field square skyrmion crystal changes into a topologically trivial double-$Q$ state by increasing the magnetic field. The present results provide another route to realize the zero-field square skyrmion crystal based on noncentrosymmetric itinerant magnets