X-ray scattering and electrical resistivity measurements were performed on ${\mathrm{GdNiC}}_2$ and ${\mathrm{TbNiC}}_2$. We found a set of satellite peaks characterized by ${\mathit{q}}_1=(0.5,\eta ,0)$ below $T_1$, at which the resistivity shows a sharp inflection, suggesting the charge density wave (CDW) formation. The value of $\eta$ decreases with decreasing temperature below $T_1$, and then a transition to a commensurate phase with ${\mathit{q}}_{1\mathrm{C}}=(0.5,0.5,0)$ takes place. The diffuse scattering observed above $T_1$ indicates the presence of soft phonon modes associated with CDW instabilities at ${\mathit{q}}_1$ and ${\mathit{q}}_2=(0.5,0.5,0.5)$. The long-range order given by ${\mathit{q}}_2$ is developed in addition to that given by ${\mathit{q}}_{1\mathrm{C}}$ in ${\mathrm{TbNiC}}_2$, while the short-range correlation with ${\mathit{q}}_2$ persists even at 6 K in ${\mathrm{GdNiC}}_2$. The amplitude of the ${\mathit{q}}_{1\mathrm{C}}$ lattice modulation is anomalously reduced below an antiferromagnetic transition temperature $T_{\mathrm{N}}$ in ${\mathrm{GdNiC}}_2$. In contrast, the ${\mathit{q}}_2$ order vanishes below $T_{\mathrm{N}}$ in ${\mathrm{TbNiC}}_2$. We demonstrate that $R{\mathrm{NiC}}_2$ ($R$ = rare earth) compounds exhibit similarities with respect to their CDW phenomena, and discuss the effects of magnetic transitions on CDWs. We offer a possible displacement pattern of the modulated structure characterized by ${\mathit{q}}_{1\mathrm{C}}$ and ${\mathit{q}}_2$ in terms of frustration.

• Received 26 January 2016
• Revised 8 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.165108