Nearly fully opened charge density wave gap in the quasi-two-dimensional conductor $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$: A comparative study with $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$

Molybdenum bronze $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ with a monoclinic structure has received continued interest due to a variety of magnetotransport properties in its charge density wave (CDW) state, while the orthorhombic phase $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ has been less reported. We successfully grew high-quality $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ single crystals via a chemical vapor transport method. Specific heat, magnetic susceptibility, and various electric transport properties in DC and pulsed fields were carefully measured. Our main findings include (1) $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ belongs to a quasi-two-dimensional (Q2D) system and undergoes a transition at $T_{\mathrm{CDW}}=\sim 96\mathrm{K}$ due to a CDW instability. Unlike the robust transition in $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$, the CDW modulation in $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ is rather broad and flexible, which results in negligible anomaly in specific heat. (2) $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ shows a clear nonlinear current-voltage relation below $T_{\mathrm{CDW}}$ due to a sliding motion of the CDW electrons. This indicates that the CDW gap in $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ is nearly fully opened, and the residual small number of electrons contribute to the CDW transport, different from the situation in $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. (3) The interlayer magnetoresistivity exhibits magnetic transition at ∼5 T and quantum oscillations at $B>15\mathrm{T}$ in applied magnetic fields up to 60 T. These field-induced oscillations featured with two main frequencies ($f_{\alpha }=30\mathrm{T}$ and $f_{\beta }=131\mathrm{T}$) are reminiscent of a Fermi surface reconstruction by magnetic breakdown in a strong field in $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. In this paper, we reveal that $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ is distinct from traditional quasi-one-dimensional or Q2D CDW compounds and provide an opportunity to study the CDW electrons and nonlinear transport properties in such a Q2D system.

Figure 1

(a) Crystal structure of $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. The blue dotted lines mark a unit cell of $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. (b) Collected single crystals, which display a clear surface. The inset of (b) shows the crystallographic directions of the sample. (c) X-ray diffraction (XRD) pattern of $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ for the $\left(00l\right)$ plane. The inset of (c) exhibits a typical energy dispersive spectroscopy (EDS) spectrum.

Figure 2

Temperature-dependent ${\rho }_b$ and ${\rho }_c$ of $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ under 0 T (black lines) and 9 T (red lines), respectively. Black arrow represents the charge density wave (CDW) transition at $T_{\mathrm{CDW}} \sim 96\mathrm{K}$. The inset shows the temperature-dependent ${\rho }_b$ of $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. Black arrows denote the two CDW transitions at $T_{\mathrm{CDW}1}=105\mathrm{K}$ and $T_{\mathrm{CDW}2}=30\mathrm{K}$.

Figure 3

Temperature-dependent susceptibility measured at $B=1\mathrm{T}$ with the $B//c$ axis and with the $B//ab$ plane for (a) $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ and (b) $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. The arrows denote the charge density wave (CDW) transition temperatures at 96 K and 105 K, respectively.

Figure 4

Temperature-dependent specific heat $C_p$ at zero field for $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ and $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$, respectively. The inset shows $C_p/T$ of $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ for clarity.

Figure 5

$I-V$ curves of ${\rho }_b$ at various temperatures for (a) $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ and (b) $\eta \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$. The red arrow in (a) denotes the threshold current for $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$.

Figure 6

Magnetic field-dependent (a) ${\rho }_b$ and (b) ${\rho }_c$ of $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ at different temperatures. The inset of (a) shows the Hall resistance at $T=2\mathrm{K}$.

Figure 7

(a) Magnetic field-dependent ${\rho }_c$ of $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ from 1.6 to 70 K in fields up to 60 T. The inset shows the magnetic field-dependent ${\rho }_b$ measured at 4.2 K. (b) The second derivative curves of ${\rho }_c$ as a function of $B$. The curves have been shifted vertically for clarity.

Figure 8

(a) The fast Fourier transform (FFT) spectra of the high-field oscillations in the temperature range of $1.6<T<20\mathrm{K}$. (b) The Lifshitz-Kosevich fitting for $f_{\alpha }$ and $f_{\beta }$. (c) The approximate Fermi surface (FS) sizes for $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ in zero field. (d) The calculated FS sizes for $\gamma \text{−}{\mathrm{Mo}}_4{\mathrm{O}}_{11}$ in the high-field state.