Spin Dynamics in the Carrier-Doped $S=\frac{1}{2}$ Triangular Lattice of ${\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{o}\mathrm{O}}_2·y{\mathrm{H}}_2\mathrm{O}$

We probed the local electronic properties of the mixed-valent ${\mathrm{C}\mathrm{o}}^{+4-x}$ triangular lattice in ${\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{o}\mathrm{O}}_2·y{\mathrm{H}}_2\mathrm{O}$ by ${}^{59}\mathrm{C}\mathrm{o}$ NMR. We observed two distinct types of Co sites for $x\ge \frac{1}{2}$, but the valence seems averaged out for $x\sim \frac{1}{3}$. Local spin fluctuations exhibit qualitatively the same trend down to $\sim 100\mathrm{K}$ regardless of the carrier concentration $x$, and hence the nature of the electronic ground state. A canonical Fermi-liquid behavior emerges below $\sim 100\mathrm{K}$ only for $x\sim \frac{1}{3}$.

Figure 1

(a) Schematics of the undoped ($x=0$) ${\mathrm{C}\mathrm{o}}^{4+}$ triangular lattice with $S=\frac{1}{2}$. When the nearest-neighbor exchange interaction $J$ tends to align two $S=\frac{1}{2}$ spins (#1 and #2) in an antiparallel configuration, frustration would result for spin #3. (b) For finite values of $x$ ($x=\frac{1}{3}$ in this panel), extra electrons could help local-singlet formation, and alter spin correlations dramatically.

Figure 2

${}^{59}\mathrm{C}\mathrm{o}$ NMR line shape with $H_{\mathrm{e}\mathrm{x}\mathrm{t}}=8\mathrm{T}$ applied along $a$ axis. (The line shapes for ${\mathrm{N}\mathrm{a}}_{0.72}{\mathrm{C}\mathrm{o}\mathrm{O}}_2$ and ${\mathrm{N}\mathrm{a}}_{0.3}{\mathrm{C}\mathrm{o}\mathrm{O}}_2·1.3{\mathrm{H}}_2\mathrm{O}$ were obtained with $H_{\mathrm{e}\mathrm{x}\mathrm{t}}$ applied within the $ab$ plane for aligned ceramics and single crystals, respectively. The line shapes for $x=0.75$ and 0.72 are corrected for $T_2$.) The arrows indicate the central transition ${\nu }_{-1/2,+1/2}$ at various Co sites. For $x=0.75$, 0.72, and 0.67, ${}^{23}\mathrm{N}\mathrm{a}$ NMR line was superposed above $\sim 88\mathrm{M}\mathrm{H}z$. Some of the furthest satellite transitions are not shown.

Figure 3

The ${}^{59}\mathrm{C}\mathrm{o}$ NMR Knight shifts ${}^{59}\mathrm{K}_a$ at $B$, $B’$, $D$, $F$, $G$, and $H$ sites. (Note that ${}^{59}\mathrm{K}_{\mathrm{o}\mathrm{r}\mathrm{b}}\sim 2–3\%$ is not subtracted.) Also plotted are ${}^{59}\mathrm{K}_c$ measured at $A$ and $A’$ sites scaled to match with $B$ and $B’$ sites (see the main text).

Figure 4

The temperature dependence of $\frac{1}{T_{1}T}$.