Effects of second neighbor interactions on skyrmion lattices in chiral magnets.

In this paper we investigate the influences of the second neighbor interactions on a skyrmion lattice in two-dimensional chiral magnets. Such a system contains the exchange and the Dzyaloshinskii-Moriya for the spin interactions and therefore, we analyse three situations: firstly, the second neighbor interaction is present only in the exchange coupling; secondly, it is present only in the Dzyaloshinskii-Moriya coupling. Finally, the second neighbor interactions are present in both exchange and Dzyaloshinskii-Moriya couplings. We show that such effects cause important modifications to the helical and skyrmion phases when an external magnetic field is applied.