Giant Electron-Electron Scattering in the Fermi-Liquid State of ${\mathrm{N}\mathrm{a}}_{0.7}\mathrm{C}\mathrm{o}{\mathrm{O}}_2$

The in-plane resistivity $\rho$ and thermal conductivity $\kappa$ of single crystal ${\mathrm{N}\mathrm{a}}_{0.7}{\mathrm{C}\mathrm{o}\mathrm{O}}_2$ were measured down to 40 mK. Verification of the Wiedemann-Franz law, $\kappa /T=L_0/\rho$ as $T\to 0$, and observation of a $T^2$ dependence of $\rho$ at low temperature establish the existence of a well-defined Fermi-liquid state. The measured value of coefficient $A$ reveals enormous electron-electron scattering, characterized by the largest Kadowaki-Woods ratio $A/{\gamma }^2$ encountered in any material. The rapid suppression of $A$ with magnetic field suggests a possible proximity to a magnetic quantum critical point. We also speculate on the possible role of magnetic frustration and proximity to a Mott insulator.

Figure 1

Temperature dependence of the in-plane thermal conductivity, plotted as $\kappa \left(T\right)/T$, and the in-plane electrical conductivity, plotted as $L_0/\rho \left(T\right)$, for sample A at two values of a magnetic field applied parallel to the current: (a) $H=0$, and (b) 10.5 T. $L_0=({\pi }^2/3)(k_B/e{)}^2$. The quantitative convergence of the two conductivities shows that the Wiedemann-Franz law is satisfied. Note that the roughly linear increase in $\kappa \left(T\right)/T$ is due to phonon conduction.

Figure 2

Temperature dependence of the electrical resistivity at low temperature, plotted as $\rho \left(T\right)-{\rho }_{\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t}}$ vs $T^2$, for sample A at several magnetic fields: $H=0$, 5.3, 10.5, and 16 T. ${\rho }_{\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t}}$ is a constant arbitrary offset chosen for clarity of display. The solid lines are linear fits to the data in a range below a temperature $T_0$ indicated by arrows. The slope of these lines is the inelastic electron-electron scattering coefficient $A$, plotted vs field in Fig. 3. Inset: The zero-field data at the lowest temperatures. Measurements on a second sample (B) show the $T^2$ behavior down to 50 mK.

Figure 3

Field dependence of the $T^2$ coefficient $A$ (in $\Delta \rho =A{T}^2$), and the upper limit of the $T^2$ range, $T_0$ (arrows in Fig. 2), for sample A. Lines are guides for the eye.

Figure 4

Kadowaki-Woods plot of coefficient $A$ (in $\Delta \rho =A{T}^2$) vs $\gamma$, the residual linear term in the specific heat ($\gamma =C/T$ as $T\to 0$), for a number of metals. The three lines are lines of constant Kadowaki-Woods ratio $r_{\mathrm{K}\mathrm{W}}=A/{\gamma }^2$, for values of 0.5, 5, and $50a_0$, as indicated. The first line at $0.5a_0$ is characteristic of heavy-fermion materials and also accounts for the quasi-2D Fermi-liquid ${\mathrm{S}\mathrm{r}}_2{\mathrm{R}\mathrm{u}\mathrm{O}}_4$; the second line at $5a_0$ corresponds to the highest values observed until now (typically in systems with magnetic frustration or close to a Mott insulator); the third line at $50a_0$ shows the order-of-magnitude larger value found in ${\mathrm{N}\mathrm{a}}_{0.7}{\mathrm{C}\mathrm{o}\mathrm{O}}_2$. (The data used in this plot are referenced in the text.) The data for ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ are for a sample doped with 5% Ge, for which the QCP is pushed to very low fields (see text).