Charge density wave and lock-in transitions of CuV2S4

The three-dimensional charge density wave (CDW) compound ${\mathrm{CuV}}₂{\mathrm{S}}₄$ is known to undergo phase transitions at $\ensuremath{\sim}91$ and $\ensuremath{\sim}50\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Employing single-crystal x-ray diffraction on an annealed crystal, we confirm the formation of an incommensurate CDW at ${T}_{\text{CDW}}\ensuremath{\approx}91\phantom{\rule{4pt}{0ex}}\mathrm{K}$, and we establish the nature of the transition at ${T}_{\text{lock-in}}\ensuremath{\approx}50\phantom{\rule{4pt}{0ex}}\mathrm{K}$ as a lock-in transition toward a threefold superstructure. As-grown crystals develop the same incommensurate CDW as the annealed crystal does, but they fail to go through the lock-in transition. Instead, the length of the modulation wave vector continues to decrease down to low temperatures in as-grown crystals. These findings are corroborated by distinct temperature dependencies of the electrical resistivity, magnetic susceptibility, and specific heat measured on as-grown and annealed crystals. A superspace model for the crystal structure of the incommensurate CDW suggests that the formation of extended vanadium clusters is at the origin of the CDW. In the lock-in phase, short and long V-V distances persist, but clusters now percolate the entire crystal. The lowering toward orthorhombic symmetry appears to be responsible for the precise pattern of short and long V-V distances. However, the orthorhombic lattice distortion is nearly zero for the annealed crystal, while it is visible for the as-grown material, again suggesting the role of lattice defects in the latter.