Three-state Nematicity in the Triangular Lattice Antiferromagnet Fe1/3NbS2

Nematic order is the breaking of rotational symmetry in the presence oftranslational invariance. While originally defined in the context of liquidcrystals, the concept of nematic order has arisen in crystalline matter withdiscrete rotational symmetry, most prominently in the tetragonal Fe-basedsuperconductors where the parent state is four-fold symmetric. In this case thenematic director takes on only two directions, and the order parameter in such"Ising-nematic" systems is a simple scalar. Here, using a novelspatially-resolved optical polarimetry technique, we show that a qualitativelydistinct nematic state arises in the triangular lattice antiferromagnetFe_1/3NbS_2. The crucial difference is that the nematic order on thetriangular lattice is a Z_3, or three-state Potts-nematic order parameter. Asa consequence, the anisotropy axes of response functions such as theresistivity tensor can be continuously re-oriented by external perturbations.This discovery provides insight into realizing devices that exploit analogieswith nematic liquid crystals.