Successive spatial symmetry breaking under high pressure in the spin-orbit-coupled metal $\mathbf{C}{\mathbf{d}}_{\mathbf{2}}\mathbf{R}{\mathbf{e}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$

The $5d$-transition-metal pyrochlore oxide $\mathrm{C}{\mathrm{d}}_2\mathrm{R}{\mathrm{e}}_2{\mathrm{O}}_7$, which was recently suggested to be a prototype of the spin-orbit-coupled metal [Phys. Rev. Lett. 115, 026401 (2015)], exhibits an inversion-symmetry-breaking (ISB) transition at 200 K and a subsequent superconductivity below 1 K at ambient pressure. We study the crystal structure at high pressures up to 5 GPa by means of synchrotron x-ray powder diffraction. A rich structural phase diagram is obtained, which contains at least seven phases, and is almost consistent with the electronic phase diagram determined by previous resistivity measurements. Interestingly, the ISB transition vanishes at $\sim 4\mathrm{GPa}$ where the enhancement of the upper critical field was observed in resistivity. Moreover, it is shown that the point groups at 8 K, probably kept in the superconducting phases, sequentially transform into piezoelectric, ferroelectric, and centrosymmetric structures on the application of pressure.

Figure 1

Temperature evolutions of representative x-ray diffraction profiles under pressures of 3 and 5 GPa: (a) and (b) for the forbidden 002 reflections, (c) and (d) for the 0016 reflection, and (e) and (f) for the 888 reflections, respectively. The indices are based on the cubic lattice structure of phase I.

Figure 2

Temperature dependence of the intensities of the forbidden 002 reflection $I$(002) and the broadening parameters $\mathrm{\Delta }H$ for the 0016 (red) and 888 (blue) reflections at (a) 1 GPa, (b) 3 GPa, (c) 4 GPa, and (d) 5 GPa. $I$(002) is normalized by the intensity of the fundamental 111 reflection. $\mathrm{\Delta }H$ is estimated by subtracting the FWHM at room temperature and 1 GPa from that at each point. The lines are fits to the equation ${(T_{\mathrm{c}}-T)}^{\beta }$ except for those at 5 GPa, which are drawn for eye guides.

Figure 3

(a) Temperature-pressure phase diagram of $\mathrm{C}{\mathrm{d}}_2\mathrm{R}{\mathrm{e}}_2{\mathrm{O}}_7$. Filled marks indicate the transition temperatures obtained in the present paper: transitions with ISB (red), monoclinic distortions (blue), and discontinuous changes in $\mathrm{\Delta }H$(0016) (green). Open marks refer to the anomalies in the previous resistivity measurements [29]. The pressure values of the resistivity data have been slightly corrected, taking into account the reduction in pressure at elevated temperatures (no in situ measurements of pressure were performed there). Thin and thick lines represent second-order and first-order transitions, respectively. Space groups are shown for each phase; those without inversion symmetry are underlined. (b) Relevant translationengleiche subgroups from the $Fd\text{−}3m$ prototype structure of the pyrochlore oxide. Space groups in the green, red, and blue frames have centrosymmetric, piezoelectric, and ferroelectric point groups, respectively. Those assigned to the multiple phases of $\mathrm{C}{\mathrm{d}}_2\mathrm{R}{\mathrm{e}}_2{\mathrm{O}}_7$ are marked by thick frames.