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Recently, a number of experiments indicate the possible presence of spinliquid phases in quantum magnets with spin-1/2 and spin-1 moments sitting ontriangular-lattice-based structures in Ba3CuSb2O9 and Ba3NiSb2O9 respectively.In relation to these experiments, several theoretical proposals have been madefor spin liquid phases and spin-liquid-like behaviours on the stackedtriangular lattice. While the crystal structures of these materials arecurrently under debate, it is nonetheless interesting to understand possiblespin liquid phases on such frustrated lattices. In this work, we applySchwinger boson mean-field theory and projective symmetry group (PSG) analysisto investigate spin liquid phases on the fully three-dimensional 6H-Bstructure, in contrast to previous works that considered two-dimensionalsystems. We find that a nematic Z2 spin liquid phase, where thelattice-rotational symmetry is spontaneously broken, is the most promising spinliquid phase that is consistent with spiral magnetic ordering in the classicallimit. We discuss the implications of our results to future theoretical andexperimental works.

Three-dimensional nematic spin liquid in the stacked triangular lattice 6H-B structure