Phase shift, ellipticity, angle, and topological number in skyrmion lattices

We theoretically study skyrmion lattices realized in a Kondo lattice model on triangular lattice, focusing the phase, ellipticity, and angle of constituent multiple-$Q$ waves. Analyzing numerical data obtained previous [Ozawa R, Hayami S Motome Y 2017 Phys. Rev. Lett. 118 147205], we extract these parameters for two types with number $1$ $2$. show that topological transition between driven by an external magnetic field is accompanied significant modulations all three parameters.