Multiple charge-density waves inR5Ir4Si10(R=Ho,Er, Tm, and Lu)

Abstract

The charge-density-wave (CDW) transitions in compounds ${R}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ $(\mathrm{R}=\mathrm{r}\mathrm{a}\mathrm{r}\mathrm{e}\ensuremath{-}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}$ element) have been studied by x-ray-diffraction and electrical conductivity experiments for temperatures between 20 and 300 K. At ${T}_{\mathrm{CDW}}$ incommensurate CDW's $[\stackrel{\ensuremath{\rightarrow}}{q}=(\ifmmode\pm\else\textpm\fi{}0.25\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}){c}^{*}$ with $\ensuremath{\delta}\ensuremath{\approx}0.03]$ develop in compounds with R=Ho, Er, Tm, and $({\mathrm{Lu}}_{0.16}{\mathrm{Er}}_{0.84}),$ while commensurate CDW's $[\stackrel{\ensuremath{\rightarrow}}{q}=(n/7){c}^{*}]$ develop in compounds with $R=\mathrm{Lu}$ and $({\mathrm{Lu}}_{0.34}{\mathrm{Er}}_{0.66}).$ ${T}_{\mathrm{CDW}}$ varies between 83 K in R=Lu and 161.4 K in R=Ho. The compounds with an incommensurate CDW exhibit a second transition at ${T}_{\mathrm{lock}\ensuremath{-}\mathrm{in}}l{T}_{\mathrm{CDW}},$ with ${T}_{\mathrm{lock}\ensuremath{-}\mathrm{in}}$ between 55 K in R=Er and 111.5 K in R=Tm. In ${\mathrm{Ho}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and ${\mathrm{Er}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ this is a pure lock-in transition at which $\ensuremath{\delta}$ becomes zero. In ${\mathrm{Tm}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and $({\mathrm{Lu}}_{0.16}{\mathrm{Er}}_{0.84}{)}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}\ensuremath{\delta}$ also becomes zero, but below ${T}_{\mathrm{lock}\ensuremath{-}\mathrm{in}}$ additional satellite reflections have been discovered, at commensurate positions $(n/8){c}^{*}$ in ${\mathrm{Tm}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and at incommensurate positions $(n/8\ifmmode\pm\else\textpm\fi{}{\ensuremath{\delta}}_{2}){c}^{*}$ with ${\ensuremath{\delta}}_{2}\ensuremath{\approx}0.01$ in $({\mathrm{Lu}}_{0.16}{\mathrm{Er}}_{0.84}{)}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}.$ The development of this second CDW can be understood by a two-step mechanism similar to the mechanism for the development of the primary CDW in ${\mathrm{Er}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ [Galli et al., Phys. Rev. Lett. 85, 158 (2000)]. At ${T}_{\mathrm{lock}\ensuremath{-}\mathrm{in}}$ the primary CDW becomes commensurate, leading to a partly restoration of the Fermi surface, as evidenced by an anomalous decrease of the electrical resistivity for T below ${T}_{\mathrm{lock}\ensuremath{-}\mathrm{in}}$ in ${\mathrm{Ho}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and ${\mathrm{Er}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}.$ The modified Fermi surface then provides the favorable nesting conditions for the development of a second CDW in ${\mathrm{Tm}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and $({\mathrm{Lu}}_{0.16}{\mathrm{Er}}_{0.84}{)}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}.$ The electronic character of this transition is suggested by the anomalous increase of the resistivity for T below ${T}_{\mathrm{lock}\ensuremath{-}\mathrm{in}}.$