Vestigial Potts nematicity in a triangular lattice magnet

Motivated by recent experimental evidence for spontaneous rotational symmetry breaking in the hexagonal antiferromagnet Fe_1/3NbS₂, this talk discusses the general theory of nematic order in magnetic system with hexagonal symmetry, focusing in particular on the possibility of a vestigial nematic phase. In stark contrast to tetragonal systems, such as the iron-pnictides, nematic order in hexagonal systems is described by the 3-state Potts model. We develop the general theory of (single-q) magnetic order at degenerate symmetry-related wave vectors, and show that distinct magnetic phases can be elegantly captured by composite order parameters: bilinears of the primary magnetic order parameters which transform irreducibly under the symmetry group. Singling out the composite nematic order parameter, we extend the Landau-type mean field theory with magnetic fluctuations and show that a vestigial nematic phase, i.e., a non-magnetic phase with broken rotation symmetry, can exist. We discuss experimental signatures and interpret our results in light of the reported measurements on Fe_1/3NbS₂.