Skyrmion crystals and their symmetries

We discuss the phase diagram of Skyrmion crystals as a function of both density and pressure. The use of symmetry properties of the various phases and of Fourier expansions tailored to fit these symmetries facilitates our discussion. A simple cubic arrangement of half-Skyrmions is, almost everywhere, the lowest-energy phase. At very high densities the simple cubic phase undergoes a transition to a body-centered-cubic crystal of half-Skyrmions. The transition to a crystal of Skyrmions at low densities, that was previously suggested, is not accessible thermodynamically. A first-order phase transition leading to a phase separation occurs before the previous transition can be reached.

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