Unified Spin Order Theory via Gauge Landau-Lifshitz Equation

The continuum limit of the tilted SU(2) spin model is shown to give rise to the gauge Landau-Lifshitz equation which provides a unified description for various spin orders. For a definite gauge, we find a double periodic solution, where the conical spiral, in-plane spiral, helical, and ferromagnetic spin orders become special cases, respectively. For another gauge, we obtain the skyrmion-crystal solution. By simulating the influence of magnetic field and temperature for our covariant model, we find a spontaneous formation of skyrmion-fragment lattice and obtain a wider range of skyrmion-crystal phase in comparison to the conventional Dzyaloshinsky-Moriya model.