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Crystal-field symmetry and ordered phases in arrays of helical XY spin chains.

The effect of crystal-field symmetry and strength on the nature of ordered phases in three-dimensional systems consisting of arrays of helical XY spin chains is investigated. The phase diagrams of chiral chains in arrays with twofold symmetry always exhibit a Lifshitz point, where paramagnetic, ferromagnetic, and incommensurate phases meet. In contrast, the phase diagrams of chains in arrays in which the crystal field has higher symmetry than twofold have no Lifshitz point, whether the chains are chiral or not. In these arrays, the initial phase transition is always paramagnetic to incommensurate. The existence of a Lifshitz point in the phase diagram of nonchiral chains in arrays with twofold symmetry depends sensitively on the interchain coupling.