Helimagnetism in XY models: Domain walls, frustrations, fractional vortices, and phase transitions.

Abstract

We consider in this paper a model for two-dimensional XY helimagnets, which was proposed in Pimpinelli et al. [J. Phys. Condens. Matter 3, 4693 (1991)]. In this model the usual spin waves and vortices coexist with chirality degrees of freedom in such a way that the degeneracy space of the order parameter is O(2)\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$. In Pimpinelli et al. the low-temperature behavior of the model was addressed, and an infinite sequence of first-order phase transitions was shown to take place, due to the spin-wave coupling between domains with opposite chirality. Here we investigate the same model at higher temperatures, where vortices in the spin system and kinks on domain walls are thermally excited. The kinks in domain walls are associated with noninteger (fractional) vortices. This is presumably a common feature also in conventional helimagnets, where the ${\mathit{Z}}_{2}$ chirality is due to the twofold handedness of helices. We also discuss the applicability of this scenario to the helimagnetic compound ${\mathrm{BaCo}}_{2}$(${\mathrm{AsO}}_{4}$${)}_{2}$.