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Frustrated magnets can elude the paradigm of spontaneous symmetry breaking and instead exhibit emergent symmetries at low temperatures. However, the underlying mechanisms are often referred to as “accidental”, i.e. making a predictive connection between the microscopic couplings and symmetries of a frustrated magnet and its emergent symmetries often remains impossible and can only be resolved by a detailed study of its collective magnetism. Here we report the explicit construction of a family of spin models that, for a wide variety of lattice geometries with triangular motifs in one, two and three spatial dimensions, such as the kagome or hyperkagome lattices, exhibit an emergent, continuous U(1) symmetry. This is particularly notable also because the underlying Hamiltonian actually has very little symmetry — a bond-directional, off-diagonal exchange model inspired by the microscopics of spin-orbit entangled materials (the Gamma-prime model). We further discuss thermal order- by-disorder effects which lead to the formation of a Z6 symmetric phase of maximally non-coplanar states at low but finite temperatures and its implications for multi-stage thermal ordering depending on spatial dimensionality. We explore the thermodynamics for representative one-, two-, and three-dimensional lattice geometries tracking the emergent symmetries using Monte Carlo simulations. Finally, we comment on the fate of the model in the quantum spin-1/2 limit.

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Sagar Ramchandani, University of Cologne
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Contact: Aprem Joy