Nonmonotonic evolution of the charge gap in ZnV${}_2$O${}_4$ under pressure

A${}^{2+}$V${}_2$O${}_4$ spinels provide a unique opportunity for studying the evolution of the charge gap of Mott insulators that approach the itinerant electron limit under the application of external pressure. Here we report high-pressure resistivity and optical measurements in ZnV${}_2$O${}_4$ that provide unambiguous evidence of an unusual nonmonotonic behavior of the charge gap, $\Delta$, as a function of pressure $P$. These unexpected results suggest that ZnV${}_2$O${}_4$ undergoes a crossover from a Mott insulator with a charge gap dominated by the on-site Coulomb repulsion $U$, to a second type of insulator in the high pressure regime. Our Monte Carlo simulations of the three-band Hubbard model relevant for ZnV${}_2$O${}_4$ reproduce the nonmonotonic behavior of $\Delta \left(P\right)$ and provide a partial understanding of this exotic phenomenon.

Figure 1

Room temperature absorbance spectra of ZnV${}_2$O${}_4$ in the midinfrared range for the low-pressure (a) and high-pressure (b) regime. The dashed gray line in (a) is the linear extrapolation used to determine the absorption edge (intersection of the linear extrapolation with the frequency axis marked by an open circle) at the lowest pressure (0.9 GPa).

Figure 2

Pressure dependence of the activation energy obtained from the fittings of the $R$ vs $T$ curves (open symbols), and from the position of the absorption edge (closed symbols).

Figure 3

Low-frequency part of Fig. 1 showing the highest-frequency phonon mode (phonon mode 4). The threefold splitting of this phonon mode with increasing pressure is indicated by the arrows, for the highest pressure (20.2 GPa).

Figure 4

Pressure dependence of the lattice volume $V\left(p\right)$ of ZnV${}_2$O${}_4$ at room temperature for pressures up to 20 GPa which shows an anomaly in $V\left(p\right)$ around 10–12 GPa. The inset shows the (440) Bragg reflection of ZnV${}_2$O${}_4$ and the (220) Bragg reflection of Au which is used as pressure calibrant. The splitting of the cubic (440) reflection of ZnV${}_2$O${}_4$ into tetragonal (400) and (224) reflections is clearly visible for pressures above 20 GPa.

Figure 5

(a) QMC results for the average charge densities in each $t_{2g}$ orbital as a function of chemical potential $\mu$ for different values of $t$, $J=0.8$ (eV), and $U=3.9$ (eV). The temperature was fixed at $T=0.05$ (eV) and we set $\Delta =1.0$ (eV) so that $xy$ orbital mainly is occupied by one electron and the other electron occupies the $yz$ or $zx$ orbitals. Charge gap as a function of $t/U$ extracted from the $\rho \left(\mu \right)$ curves is shown in panel (b). Error bars indicate uncertainty due to the finite temperature. (c) Néel temperature as a function of $t/U$ for $\mu =3.05$ eV.