Comparative study of low-temperature x-ray diffraction experiments on $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($R=\mathrm{Nd}$, Eu, and Pr)

The cubic symmetry of pyrochlore iridium oxides $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($R=\mathrm{Nd}$, Eu, and Pr) has been investigated by high resolution x-ray diffraction experiments down to 4 K, in order to clarify the relationship between the metal-insulator transition (MIT) and the small structural phase transition suggested by Raman scattering experiments in these compounds. We have found that a small negative thermal expansion of the order of ${10}^{-3}$ Å appears only in ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ below the MIT, $T_{\mathrm{MIT}}=34$ K, ascribable to the magnetovolume effect of the long-range order of Ir moments. However, any breaking of the cubic symmetry of three iridates has not been observed as appearance of superlattice reflections nor splittings of cubic reflections below $T_{\mathrm{MIT}}$. These results imply that lowering of the cubic symmetry plays a minor role for the change in the electronic state of these compounds, while a magnetic order of Ir moments plays a major role for the MIT.

Figure 1

X-ray diffraction patterns of (a) ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, (b) ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, and (c) ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ measured at room temperature (RT). Observed and refined data are shown by crosses and solid curves, respectively. The difference between the data and the model is plotted by the dashed curves in the lower part. Vertical bars represent positions of the Bragg reflections. Si powder was mixed as a reference for the Rietveld analysis in order to estimate the lattice constant of the samples precisely.

Figure 2

Temperature dependence of $\rho$ of polycrystalline samples of $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($R=\mathrm{Nd}$, Eu, and Pr). Inset shows $\rho$ of ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ around $T_{\mathrm{MIT}}=120$ K. The dashed line in the inset is a guide to the eyes for the slope above $T_{\mathrm{MIT}}$.

Figure 3

Temperature dependences of (a)–(c) $C_P/T$ and (d)–(f) $M/H$ for powder samples of ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7,{\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, and ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, respectively. The samples used in this study show qualitatively the same behaviors of previous reports [8, 10, 46]. For ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, there exist quantitative differences in the upturn of $C_P/T$ at low temperatures, which may be attributable to the small difference of the off-stoichiometry of samples. A similar behavior has been observed in the systematic change of $x$ for the zirconium analogs of ${\mathrm{Pr}}_{2+x}{\mathrm{Zr}}_{2-x}{\mathrm{O}}_{7+y} \left(-0.02\le x\le 0.02\right)$ [47]. Figures (d)–(f) include results of both zero-field-cooling (ZFC) and field-cooling (FC) measurements of $M/H$. Insets of (d) and (e) show comparisons between $\rho$ (for a log scale) and $\Delta M/H$ for ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, respectively. Here $\Delta M/H$ is a difference of the susceptibility between the ZFC measurement $\left(M_{\mathrm{ZFC}}/H\right)$ and the FC measurement $\left(M_{\mathrm{FC}}/H\right)$: $\Delta M/H=M_{\mathrm{FC}}/H-M_{\mathrm{ZFC}}/H$.

Figure 4

$2\theta \text{−}\theta$ scans around the (444) reflections for (a) ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and for (b) ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ at temperatures above and blow $T_{\mathrm{MIT}}$. Insets show enlargements around the peak positions.

Figure 5

$2\theta \text{−}\theta$ scans around the (800) reflections for (a) ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and for (b) ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ at temperatures above and blow $T_{\mathrm{MIT}}$. Insets show enlargements around the peak positions.

Figure 6

(a) Temperature dependence of the lattice constant $a\left(T\right)$ of $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($R=\mathrm{Nd}$, Eu, and Pr), which were estimated from the peak position of the (444) reflections. The data was normalized by the data at $T=80$ K: $\Delta a\left(T\right)/a\left(80\mathrm{K}\right)=a\left(T\right)/a\left(80\mathrm{K}\right)-1$. The dashed line for ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ below $T_{\mathrm{MIT}}$ indicates the linear fit result corresponding to the estimation of $\alpha =-1.5\left(1\right)\times {10}^{-6} \mathrm{K}{}^{-1}$. (b) $\Delta a\left(T\right)/a\left(80\mathrm{K}\right)$ of ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ around $T_{\mathrm{MIT}}=34$ K. The vertical axis is the same as that of (a). In this plot, $a\left(T\right)$ is examined from peak positions at the (800), (444), and (440) peaks. The dashed line is extrapolated from the data of ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ in (a). (c) Temperature dependence of the full width at half maximum (FWHM) of the (444) peak of three compounds. The definition of the symbols is the same as that in (a).