Nature of Possible Magnetic Phases in Frustrated Hyperkagome Iridate

Abstract

Based on Kitaev-Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions, we studied nature of possible magnetic phases in frustrated hyperkagome iridate, Na${}_4$Ir${}_3$O${}_8$ (Na-438). Using Monte-Carlo simulation, we showed that the phase diagram is mostly covered by two competing magnetic ordered phases; Z${}_2$ symmetry breaking (SB) phase and Z${}_6$ SB phase, latter of which is stabilized by the classical order by disorder. These two phases are separated 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 3D XY universality class, below which U(1) to Z${}_6$ crossover phenomena appears; the Z${}_6$ spin anisotropy becomes irrelevant in a length scale shorter than a crossover length ${\Lambda }_{\ast }$ while becomes relevant otherwise. A possible phenomenology of polycrystalline Na-438 is discussed based on this crossover phenomena.

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• Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$
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