Multiple charge density wave transitions in the antiferromagnetsRNiC2(R=Gd,Tb)

Abstract

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 ${\mathbit{q}}_{1}=(0.5,\ensuremath{\eta},0)$ below ${T}_{1}$, at which the resistivity shows a sharp inflection, suggesting the charge density wave (CDW) formation. The value of $\ensuremath{\eta}$ decreases with decreasing temperature below ${T}_{1}$, and then a transition to a commensurate phase with ${\mathbit{q}}_{1\mathrm{C}}=(0.5,0.5,0)$ takes place. The diffuse scattering observed above ${T}_{1}$ indicates the presence of soft phonon modes associated with CDW instabilities at ${\mathbit{q}}_{1}$ and ${\mathbit{q}}_{2}=(0.5,0.5,0.5)$. The long-range order given by ${\mathbit{q}}_{2}$ is developed in addition to that given by ${\mathbit{q}}_{1\mathrm{C}}$ in ${\mathrm{TbNiC}}_{2}$, while the short-range correlation with ${\mathbit{q}}_{2}$ persists even at 6 K in ${\mathrm{GdNiC}}_{2}$. The amplitude of the ${\mathbit{q}}_{1\mathrm{C}}$ lattice modulation is anomalously reduced below an antiferromagnetic transition temperature ${T}_{\mathrm{N}}$ in ${\mathrm{GdNiC}}_{2}$. In contrast, the ${\mathbit{q}}_{2}$ 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 ${\mathbit{q}}_{1\mathrm{C}}$ and ${\mathbit{q}}_{2}$ in terms of frustration.