Nematicity in charge and orbital ordered structure: a new description of phase transitions in La$_{0.33}$Ca$_{0.67}$MnO$_{3}$

Doped manganites have a well-known unidirectional superlattice modulation at low temperatures, although the origin of the modulation is still under debate. The phase transition of the modulation in this compound has been characterized by the superlattice reflections and the transition temperature was determined when the modulation becomes long-range. Here we report a new description of the phase transition in La$_{0.33}$Ca$_{0.67}$MnO$_{3}$ from the aspect of symmetry by measuring anisotropy based on transmission electron microscopy results. Instead of one phase transition, we found that the electronic structures undergo smectic, nematic and isotropic behaviors upon warming. Comparing to previous characterizations of the phase transition in La$_{0.33}$Ca$_{0.67}$MnO$_{3}$, this symmetry measurement enables a better unification between electronic structure and other properties such as the crystal lattice variation. Moreover, we directly observed the creation of dislocation pairs in the smectic phase, which is consistent with the dislocation-proliferation mechanism predicted by the nematicity theory in correlated systems. The defect observations also suggest the charge and orbital ordering nature of the modulation in La$_{0.33}$Ca$_{0.67}$MnO$_{3}$.