General spin-order theory via gauge Landau-Lifshitz equation

The continuum limit of the tilted SU(2) spin model is shown to lead to a gauge Landau-Lifshitz equation which provides a unified description for various spin orders. For a definite gauge with zero field strength, we find a double periodic solution, where the conical spiral, in-plane spiral, helical, and ferromagnetic spin orders become special cases. For another gauge with nonzero field strength, we obtain the skyrmion-crystal solution. By simulating the influence of magnetic field and temperature for our model, we find a spontaneous formation of a skyrmion-fragment lattice similar to the spin texture found in experiment very recently; we also obtain a wider range of skyrmion-crystal phase in the parameter space in comparison to the conventional Dzyaloshinsky-Moriya model.