Pressure-tuned insulator to metal transition in ${\mathbf{Eu}}_{\mathbf{2}}{\mathbf{Ir}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$

We have studied the effect of pressure on the pyrochlore iridate ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, which, at ambient pressure, has a thermally driven insulator to metal transition at $T_{\mathrm{MI}}\sim 120\mathrm{K}$. As a function of pressure, the insulating gap closes, apparently continuously near $P\sim 6\mathrm{GPa}$. However, rather than $T_{\mathrm{MI}}$ going to zero as expected, the insulating ground state crosses over to a metallic state with a negative temperature coefficient of resistivity, suggesting that these ground states have a novel character. The high-temperature state also crosses over near 6 GPa from an incoherent to a conventional metal, implying that there is a connection between the high- and the low-temperature states.

Figure 1

Resistivity as a function of temperature from $P=2.06$ to 12.15 GPa. The left-hand panel contains all of our results, showing that the resistivity is strongly suppressed by increasing pressure. The right-hand panel focuses on the intermediate-pressure data. Red arrows indicate the metal-insulator transition (see Fig. 2 and the text); blue arrows indicate the minimum in $\rho \left(T\right)$.

Figure 2

Locating the metal-insulator transition $T_{\mathrm{MI}}$. The color coding is the same as in Fig. 1. The transition does not have a strong signature in $\rho \left(T\right)$, however, panel (a) shows that there is a marked change in slope of $\ln \left(\rho \right)$ vs $T$ near 100 K at all pressures, while panel (b) shows that the onset of this behavior can be found, for all pressures below 7.88 GPa, in a sharp downturn in $\partial \rho /\partial T$. As a guide to the eye, we have shown plausible extrapolations of the high-temperature slope and the slope immediately below 100 K. At each pressure, we have placed $T_{\mathrm{MI}}$ at the midpoint between the onset of the downturn and the temperature at which these extrapolations meet; whereas, the error bars (see Fig. 4) extend to these two temperatures. The inset of (b) zooms in on $\partial \rho /\partial T$ near 100 K for 3.49 GPa. In (a), some curves are offset vertically for clarity.

Figure 3

Location of $T^{*}$ and $T_{\min }$. The main panel in (a) shows $\rho \left(T\right)$ from 6.06 to 10.01 GPa, whereas, the inset shows an expanded view around $T^{*}$ and $T_{\min }$. The curves are offset vertically to give a better view of the data. The main panel in (b) shows $\rho \left(T\right)$ from 7.88 to 12.15 GPa. The inset is an expanded view of the two highest-pressure curves with $RRR<1$.

Figure 4

The phase diagram for ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ constructed from our resistivity data. At low pressures, $P<6\mathrm{GPa}$, the finite-temperature MIT is indicated by red squares; the value at 0 GPa is taken from Ref. 8. At high pressures, $P>6\mathrm{GPa}$, the transition between conventional and negative $\partial \rho /\partial T$ metallic states, is indicated by blue circles. The $T^{*}$ crossover is shown by orange triangles. All the lines are guides to the eye. The quantum critical point (QCP) separating the insulating and the negative $\partial \rho /\partial T$ metal lies on the $P$ axis near $P_c=6.06\pm 0.60\mathrm{GPa}$. Both $T_{\mathrm{MI}}$ and $T_{\min }$ depend weakly on $T$.

Figure 5

(a) $\ln \left[\rho \right(T\left)\right]$ vs $1/T$ at selected pressures between 100 and 30 K. The gap $\Delta \left(P\right)$ is extracted by fitting a single exponential to the resistivity data at each pressure in the temperature range of $60\mathrm{K}\le T<T_{\mathrm{MI}}$ (dashed lines). These curves have been shifted vertically to allow easier comparison of the slopes. (b) The maximum value of the gap $\Delta \left(P\right)$, extracted as shown in (a), is continuously suppressed by pressure.

Figure 6

(a) The conductivity $\sigma \left(T\right)$ below 20 K. The data were extrapolated to 0 K to get the residual conductivity values plotted in (b). The residual conductivity plotted as a function of pressure, indicates that the pressure-induced insulator to metal quantum phase transition is continuous.

Figure 7

(a) Semilogarithmic plot of resistivity from room temperature to 200 mK at $P=10.01\mathrm{GPa}$. (b) Magnetoresistance as a function of magnetic field at $P=10.01\mathrm{GPa}$. Data were taken in a temperature range from 100 mK to 8 K. MR is suppressed by increasing temperature. The inset shows a quadratic fit (black dashed line, $M\propto H^2$) to the low-field data at $T=200\mathrm{mK}$. At high fields, MR tends toward saturation.