Figure 1

The susceptibility $\chi$ (a) and in-plane resistivity $\rho$ (b) of single crystals of ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ with $x$ determined by ICP (c). In panel (a), $\chi$ is measured in an in-plane field $H=5\mathrm{T}$ ($\mathbf{H}\mathbf{\perp }\widehat{\mathbf{c}}$). In the crystal with $x=0.75$, $\chi$ fits the Curie-Weiss form $\chi =C/(T+\theta )$, with $\theta \sim 150\mathrm{K}$ and $C=0.224\mathrm{emu}\mathrm{K}/\mathrm{Oe}\mathrm{\text{mole}}$. For $x=0.5$, sharp transitions are observed at $T_{c1}$ and $T_{c2}$ (arrows). Panel (b) shows the $T$ dependence of $\rho$ at selected $x$. Insulating behavior is observed at $x=0.5$ (data displayed at lower scale), in contrast to metallic behavior in the rest. At low $T$, $\rho$ is $T$ linear for $x=0.71$ but varies as $T^2$ for $x=0.3$. In panel (c), the $c$-axis lattice parameter measured by XRD is plotted against the Na content $x$ fixed by ICP in powder samples.Reuse & Permissions

Figure 2

The phase diagram of nonhydrated ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ (a), room temperature electron diffraction pattern of a crystal with $x=\frac{1}{2}$ (b), and the Na superstructure lattice (c). In panel (a), the charge-ordered insulating state at $\frac{1}{2}$ is sandwiched between the paramagnetic metal at 0.3 and the Curie-Weiss metallic state at 0.65–0.75. The superconducting state is obtained on intercalation with ${\mathrm{H}}_2\mathrm{O}$ [6, 7]. In panel (b), the diffraction pattern is taken along $[001]$ with 200 kV electrons in a Phillips CM200 electron microscope (sample nominally at 300 K). Bragg spots of the hexagonal lattice are encircled. The spots located at $n_1{\mathbf{b}}_1^{\prime }+n_2{\mathbf{b}}_2^{\prime }$ correspond to the supercell with lattice vectors ${\mathbf{a}}_1^{\prime }$ and ${\mathbf{a}}_2^{\prime }$, drawn in panel (c) (the superlattice spots are caused primarily by the ordering of Na ions).Reuse & Permissions

Figure 3

The thermopower $S$ and the Hall coefficient $R_H$ in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ for $x=\frac{1}{2}$ (a), and plots of the in-plane thermal conductivity $\kappa$ (b), and $R_H$ (c) for several values of $x$. In panel (a), both $|S|$ and $|R_H|$ begin to increase steeply just below $T_{c2}$ (88 K) and attain maxima at 40 and 30 K, respectively (note $-S$ and $-R_H$ are plotted). Below the peak values, they fall towards zero as $T\to 0$, consistent with a particle-hole symmetric state. In panel (b), $\kappa$ at $x=\frac{1}{2}$ rises to a very large peak value comparable to that of quartz, whereas it remains small at all other $x$. Panel (c) shows that the curve of $R_H$ vs $T$ at $x=0.50$ is qualitatively different from all other $x$ values. In the metallic samples, $R_H$ increases with $T$, consistent with strongly interacting carriers hopping on a triangular lattice.Reuse & Permissions