High-pressure insulating phase of ${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ with collapsed volume

We investigated the effect of pressure on the crystal structure and transport properties of the Magnéli phase η-${\mathrm{Mo}}_4{\mathrm{O}}_{11}$, which at ambient pressure undergoes two successive charge-density-wave (CDW) transitions at $T_{\mathrm{CDW}\text{−}1}\approx 105\mathrm{K}$ and $T_{\mathrm{CDW}\text{−}2}\approx 30\mathrm{K}$, respectively. We find that η-${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ exhibits a structural phase transition from the low-pressure monoclinic $P{2}_1/a$ phase to a high-pressure $P{2}_1$ phase at $P_c\approx 3.5\mathrm{GPa}$. Around $P_{\mathrm{c}}$, the lattice parameters experience a sudden change with a large volume collapse of $\mathrm{\Delta }V/V=-8.1\%$, while the room-temperature resistivity exhibits a sudden jump by two orders of magnitude, signaling a pressure-induced metal-to-insulator transition. For $P<P_c$, the high-pressure resistivity measurements revealed opposite pressure dependences of these two CDW transitions, i.e., $T_{\mathrm{CDW}\text{−}1}$ is enhanced gradually to ∼130 K while $T_{\mathrm{CDW}\text{−}2}$ is almost suppressed completely by the application of 2.6 GPa pressure. For $P\ge P_c$, the temperature dependence of resistivity changes to an insulating-like behavior, but the activation energy is reduced gradually upon further increasing pressure. We have rationalized the insulating ground state of the high-pressure phase in terms of the structural modifications and charge redistribution based on the refinement of single-crystal x-ray diffraction data at 8.9 GPa.

Figure 1

(a) The background-subtracted diffraction patterns of η-${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ at high pressures and room temperature. Typical Rietveld refinement results of ${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ under (b) 7.9, (c) 5.3, and (d) 0.5 GPa. The experimental data and fitted XRD profile were shown as black crosses and pink lines, respectively. The marks show the positions of the allowed Bragg reflections for $P{2}_1/a$ and $P{2}_1$ phases. The difference between the observed and the fitted XRD patterns was shown with a green line at the bottom of the diffraction peaks.

Figure 2

(a)–(e) Pressure dependences of the lattice parameters, volume per formula unit ($V$/f.u.), and the axial ratios ($c/a$ and $b/a$) for the η and ${\eta }^{\prime }$ phases. The open symbols represent the experimental results of the single-crystal sample at 8.92 GPa. The solid lines in (d) represent the fitting results to experimental data by using the Birch-Murnaghan equation of state. (f) The resistivity of ${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ under external pressure from ambient to 11 GPa at 295 K measured with a cubic anvil cell (CAC).

Figure 3

Temperature dependence of resistivity under various pressures up to 2.6 GPa for η-${\mathrm{Mo}}_4{\mathrm{O}}_{11}$. The arrow indicates the CDW transition temperatures. The inset shows the pressure dependence of the CDW transition temperatures $T_{\mathrm{CDW}\text{−}1}$ and $T_{\mathrm{CDW}\text{−}2}$ determined from the present work and taken from Ref. [14].

Figure 4

(a) Temperature dependence of the resistivity $\rho \left(T\right)$ under various pressures from 4.2 to 11.8 GPa measured with a palm cubic anvil cell (CAC). The inset shows the $d\rho /dT$ curves and the criterion used for determining the resistivity anomaly temperature $T_{\mathrm{u}}$. (b) A plot of logarithmic form of the normalized resistance vs $1000/T$ for resistivity data. The broken lines in (b) represent the linear fitting curves. (c) Variation with pressure of the activation energy $E_{\mathrm{g}}$ and $T_{\mathrm{u}}$.

Figure 5

Schematic crystal structure of (a) η-${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ with $P{2}_1/a$ and (b) ${\eta }^{\prime }-{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ with $P{2}_1$ space group at ambient pressure and 8.92 GPa, respectively. The different Mo cations have been indicated by different colored balls. The red balls are oxygen ions. (c) The top view along the $a$-axis of the Mo3 and Mo4 sublattice structure of η-${\mathrm{Mo}}_4{\mathrm{O}}_{11}$ at ambient. The Mo4 and O ions form the infinite -Mo4-O-Mo4- zigzag chains along the $b$-axis as indicated by the yellow dashed line. (d) The view along the normal to (5 0 −1) of the Mo3 and Mo4 sublattice structural characterization of ${\eta }^{\prime }-{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ at 8.92 GPa with $P{2}_1$ space group. Armchairlike -Mo4-O-Mo4- chains are marked by the dashed line. α and β are the O-Mo4-O bond angle and Mo4-O-Mo4 bond angle, respectively. $l_1$ and $l_2$ are the distances of nearest-neighbor and next-nearest-neighbor Mo4 cations, respectively.

Figure 6

(a) Crystal structure and (b) Brillouin zone of ${\eta }^{\prime }-{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. (c,d) The band structure of ${\eta }^{\prime }-{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ without the spin-orbit coupling (SOC) effect and with the SOC effect. (e,f) The band structure of ${\eta }^{\prime }-{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ considering different values of on-site Coulomb interactions energy $U$. (g) The density of states near the Fermi level with $U=7\mathrm{eV}$.