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Frustrated ground states of a generalized XY model and their mapping to non-magnetic structural analogues

Ground state phases of a generalized XY model with magnetic and generalized nematic couplings on a non-bipartite triangular lattice are investigated in the exchange interactions parameter space. We demonstrate that the model displays a number of ordered and quasi-ordered phases as a result of geometrical frustration and/or competition between the magnetic and generalized nematic interactions. The nature and the extent of the respective phases depend on the parameter $q$, characterizing the higher-order harmonics term in the Hamiltonian. Motivated by the recent discovery of the experimental realization of the model with $q=2$ in the seemingly unrelated field of the systems chemistry [A.B. Cairns et al., Nature Chemistry 8, 442 (2016)], the model for $q>2$ is discussed in the context of the prediction of structural phases of a class of bimetalic cyanides based on a mapping between the two systems.