Conduction anisotropy and Hall effect in the organic conductor $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$: Evidence for Luttinger liquid behavior and charge ordering

We present the high-temperature $(70\mathrm{K}<T<300\mathrm{K})$ resistivity anisotropy and Hall effect measurements of the quasi-one-dimensional (1D) organic conductor $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$. The temperature variations of the resistivity are pronouncedly different for the three different directions, with metalliclike at high temperatures for the $\mathbf{a}$ axis only. Above $220\mathrm{K}$ the Hall coefficient $R_H$ is constant, positive, and strongly enhanced over the expected value; and the corresponding carrier concentration is almost 100 times lower than calculated for one hole/unit cell. Our results give evidence for the existence of a high-temperature regime above $200\mathrm{K}$ where the 1D Luttinger liquid features appear in the transport properties. Our measurements also give strong evidence of charge ordering in $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$. At the charge-ordering transition $T_{\mathrm{CO}}\approx 100\mathrm{K}$, $R_H\left(T\right)$ abruptly changes its behavior, switches sign, and rapidly increases with further temperature decrease.

Figure 1

Temperature dependence of the dc resistivity $\rho$ vs $1∕T$, for $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ in the temperature range $70\mathrm{K}<T<300\mathrm{K}$, measured along the three crystal directions ${\rho }_{\mathbf{a}}$ $(\mathbf{j}\parallel \mathbf{a})$, ${\rho }_{{\mathbf{b}}^{\prime }}$ $(\mathbf{j}\parallel {\mathbf{b}}^{\prime })$, and ${\rho }_{{\mathbf{c}}^{\star }}$ $(\mathbf{j}\parallel {\mathbf{c}}^{\star })$. Inset: Activation energy ${\Delta }_{\mathbf{a}}$ vs temperature calculated for the $\mathbf{a}$ axis assuming ${\Delta }_{\mathbf{a}}=k_{B}T\ln ({\rho }_{\mathbf{a}}∕{\rho }_{\min })$, see text.

Figure 2

Temperature dependencies of the resistivity along the $\mathbf{a}$, ${\mathbf{b}}^{\prime }$, and ${\mathbf{c}}^{\star }$ axes for $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ in the high-temperature region $(T>230\mathrm{K})$.

Figure 3

Magnetic field dependence of the Hall resistivity of $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ for several fixed temperatures. Also shown is the sample geometry ($\mathbf{j}\parallel \mathbf{a}$, $\mathbf{B}\parallel {\mathbf{c}}^{\star }$) and the arrangement of contacts.

Figure 4

Temperature dependence of the Hall coefficient $R_H$ of $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ for $70\mathrm{K}<T<300\mathrm{K}$. For each temperature the Hall coefficient values were determined as the average of the several measurements taken during the cooling and heating cycles. Inset: $R_H\left(T\right)$ around $T_{\mathrm{CO}}$.

Figure 5

Temperature dependencies of the constant-volume resistivities ${\rho }_{\mathbf{a}}^{\left(V\right)}$ and ${\rho }_{{\mathbf{b}}^{\prime }}^{\left(V\right)}$ (see text for the details of the conversion procedure).

Figure 6

Temperature dependencies of the Hall coefficient $R_H$ for $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ (circles) and $(\mathrm{TMTSF}{)}_2{\mathrm{ReO}}_4$ (squares). Above $200\mathrm{K}$ $R_H$ of $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ has an almost constant value $0.38{\mathrm{cm}}^3{\mathrm{C}}^{-1}$ (dotted line). The dashed line represents the value $R_{H0}=3.31\times {10}^{-3}{\mathrm{cm}}^3{\mathrm{C}}^{-1}$ obtained for $(\mathrm{TMTTF}{)}_2{\mathrm{AsF}}_6$ and the carrier concentration of one hole/unit cell $(n=1.4\times {10}^{21}{\mathrm{cm}}^{-3})$.