Nature of the possible magnetic phases in a frustrated hyperkagome iridate

Based on the Kitaev-Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions, we studied the nature of possible magnetic phases in the frustrated hyperkagome iridate, Na4Ir3O8 (Na-438). Using Monte Carlo simulation, we showed that the phase diagram is mostly covered by two competing magnetic ordered phases, the Z(2) symmetry breaking (SB) phase and the Z(6) SB phase, latter of which is stabilized by the classical order by disorder. These two phases are intervened by a first-order phase-transition line with Z(8)-like symmetry. The critical nature at the Z(6) SB ordering temperature is characterized by the three-dimensional XY universality class, below which U(1) to Z(6) crossover phenomenon appears: the Z(6) spin anisotropy becomes irrelevant in a length scale shorter than a crossover length A,, while it becomes relevant otherwise. A possible phenomenology of polycrystalline Na-438 is discussed based on this crossover phenomenon.SCI(E)ARTICLErshindou@pku.edu.cn99