Phase separation at the dimer-superconductor transition in ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$

The detailed evolution of the local atomic structure across the ($x$, $T$) phase diagram of transition metal dichalcogenide superconductor ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ ($0\le x\le 0.3$, $10\mathrm{K}\le T\le 300\mathrm{K}$) is obtained from high-quality x-ray diffraction data using the atomic pair distribution function (PDF) method. The observed hysteretic thermal structural phase transition from a trigonal ($P\overline{3}m1$) to a triclinic ($P\overline{1}$) dimer phase for low Rh content emphasizes the intimate connection between the lattice and electronic properties. For superconducting samples away from the dimer/superconductor phase boundary, structural transition is absent and the local structure remains trigonal down to 10 K. In the narrow range of compositions close to the boundary, PDF analysis reveals structural phase separation, suggestive of weak first-order character of the Rh-doping induced dimer-superconductor quantum phase transition. Samples from this narrow range show weak anomalies in electronic transport and magnetization, hallmarks of the dimer phase, as well as superconductivity albeit with incomplete diamagnetic screening. The results suggest that the dimer and superconducting orders exist in the mutually exclusive spatial regions.

Figure 1

Details of ${\mathrm{IrTe}}_2$ structures. (a) Undistorted high-temperature trigonal model ($P\overline{3}m1$). (b) Distorted low-temperature triclinic model ($P\overline{1}$) featuring Ir dimers. (c) Sketch of local ${\mathrm{IrTe}}_6$ octahedral environments expected in the absence/presence of Ir dimers (top/bottom). Dimerization results in dramatic distortions of associated interatomic distances relative to the high-temperature structure: Ir-Ir and Te-Te dimer distances reduce by 0.83 and 0.5 Å, respectively, while the lateral Te-Te distance elongates by 0.29 Å [35], as indicated by block arrows.

Figure 2

Comparisons of magnetic susceptibility and total scattering data for selected ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ compositions: (a) dc susceptibility for $x=0.12$ and 0.2 samples at H = 10 Oe in zero-field-cooling (solid symbols) and field-cooling (open symbols) modes at low-temperature. (b) Reduced total scattering functions, $F\left(Q\right)$, and (c) xPDFs, $G\left(r\right)$, for $x=0$ sample at 300 (red) and 10 K (blue).

Figure 3

Comparison of azimuthally integrated 2D diffraction patterns of ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ for 300 (solid red line) and 10 K (solid blue line) over a narrow range of momentum transfer $Q$ for (a) $x=0$, (b) 0.03, (c) 0.06, (d) 0.12, (e) 0.2, and (f) 0.3. All patterns are normalized by the intensity of (001) reflection ($P\overline{3}m1$ indexing).

Figure 4

Comparison of experimental xPDFs of ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ for $0\le x\le 0.3$ over 10-Å range at (a) 300 and (b) 10 K. The data for the end members are shown as colored profiles, and for the intermediates as gray profiles. $\mathrm{\Delta }G\left(r\right)$ in both panels represents the difference between $x=0$ (light red/blue) and 0.3 (dark red/blue) xPDFs, shown as a solid green line and offset for clarity. At 300 K, all xPDF profiles look very similar. At 10 K, xPDF profiles apparently cluster into two groups, those resembling $x=0$ (light blue), and those that are similar to $x=0.3$ (dark blue). Arrows in (a) mark lattice repeat distance peaks in the trigonal phase.

Figure 5

Comparison of experimental xPDFs of ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ over 10-Å range at 10 K for $x=0$ (solid light blue line), 0.1 (solid dark green line), 0.12 (solid light green line), and 0.3 (solid dark blue line). See text for details.

Figure 6

Structural refinements of $P\overline{3}m1$ model (solid red line) to ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ xPDF data at 300 K (open blue symbols) over 10-Å range. The difference between the data and the model is shown as a solid green line underneath and is offset for clarity. (a) $x=0$ (${\mathrm{r}}_W=3.9\%$), (b) $x=0.03$ (${\mathrm{r}}_W=3.8\%$), (c) $x=0.06$ (${\mathrm{r}}_W=4.1\%$), (d) $x=0.12$ (${\mathrm{r}}_W=4.2\%$), (e) $x=0.2$ (${\mathrm{r}}_W=4.1\%$), and (f) $x=0.3$ (${\mathrm{r}}_W=4.1\%$). Refinement of $x=0.1$ data (not shown) results in a fit with residual of ${\mathrm{r}}_W=3.9\%$.

Figure 7

Detection of structural transition in ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ by $P\overline{3}m1$ modeling of xPDF data. Rh content is indicated in the panels. (a) Fit residual, $r_W\left(T\right)$, normalized to 300 K value. (b) Isotropic atomic displacement parameter of Ir, $U\left(T\right)$, normalized to the 300-K value. (c) Fit residual, $r_W\left(T\right)$, for data collected on cooling (blue) and warming (red) for samples with selected Rh content. Hysteresis loops for 10% and 12% Rh samples are scaled for clarity, as indicated. Loops have been offset for clarity. Quantities shown in (a) and (b) are based on data acquired on warming using cryostat equipment; these shown in (c) are based on data collected on thermal cycling utilizing cryostream equipment. The shaded area in (c) denotes lack of data in the collection mode used.

Figure 8

Structural refinements of $P\overline{3}m1$ model (solid red line) to ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ xPDF data at 10 K (open blue symbols) over 10-Å range. Difference between the data and the model is shown as solid green line underneath (offset for clarity). (a) $x=0$ (${\mathrm{r}}_W=14.8\%$), (b) $x=0.03$ (${\mathrm{r}}_W=13.5\%$), (c) $x=0.06$ (${\mathrm{r}}_W=12.9\%$), (d) $x=0.1$ (${\mathrm{r}}_W=7.7\%$), (e) $x=0.12$ (${\mathrm{r}}_W=5.7\%$), and (f) $x=0.2$ (${\mathrm{r}}_W=3.9\%$). Refinement to $x=0.3$ data (not shown) gives a similar quality fit to that for $x=0.2$.

Figure 9

Structural refinements at 10 K. Fits of $P\overline{1}$ model to the data of (a) $x=0$ (${\mathrm{r}}_W=2.0\%$), (b) $x=0.03$ (${\mathrm{r}}_W=2.1\%$), (c) $x=0.06$ (${\mathrm{r}}_W=2.3\%$), (d) $x=0.1$ (${\mathrm{r}}_W=6.3\%$), and (e) $x=0.12$ (${\mathrm{r}}_W=7.3\%$). (f) $P\overline{3}m1+P\overline{1}$ two-phase model refinement to $x=0.12$ data (${\mathrm{r}}_W=2.7\%$). See text for details.

Figure 10

(a) ($x,T$) phase diagram of ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$. Solid blue and red circles represent magnetic phase transition temperature obtained from susceptibility measurements on cooling and warming, while the solid green circles denote superconducting transition temperature, after reference [31]. Solid blue and red squares mark the structural transition temperature in ${\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{Te}}_2$ from this study. Solid green squares denote superconducting transitions observed in samples used here. The values of superconducting $T_c$ are multiplied by a factor of 10 for clarity. (b) $P\overline{1}$ phase fraction obtained from local structure refinements (solid gray symbols). The same phase fraction deduced from susceptibility measurements reported by Kudo et al. [31] (solid magenta circles). All lines are guides to the eye. Horizontal dashed line in (b) marks the estimated PDF sensitivity threshold to the presence of the local dimer phase [55].