Evolution of Co charge disproportionation with Na order in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$

${}^{59}\mathrm{Co}$ NMR experiments have been performed on single crystals of the layered cobaltate ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ with $x=0.77$, which is an antiferromagnet with Néel temperature $T_N=22$ K. In this metallic phase, six Co sites are resolved in the NMR spectra, with distinct quadrupole frequencies ${\nu }_Q$, magnetic shifts $K_{ZZ}$ and nuclear spin lattice relaxation rates $1/T_1$. Contrary to the $x=1/2$ or $x=2/3$ phases, the 3D stacking of the Na planes is not perfect for $x=0.77$ but this does not influence markedly the electronic properties. We evidence that the magnetic and charge properties of the Co sites are highly correlated with each other as $K_{ZZ}$ and ${(1/T_1)}^{1/2}$ scale linearly with ${\nu }_Q$. The data analysis allows us to separate the contribution ${\nu }_Q^{\mathrm{latt}}$ of the ionic charges to ${\nu }_Q$ from that ${\nu }_Q^{\mathrm{el}}$ due to the hole orbitals on the Co sites. We could extend coherently this analysis to all the known phases in the Na cobaltate phase diagram. The variation with $x$ of ${\nu }_Q^{\mathrm{latt}}$ is found to fit rather well numerical computations done in a point charge model. The second term ${\nu }_Q^{\mathrm{el}}$ allowed us to deduce the hole concentration on the cobalts. These detailed experimental results should stimulate theoretical calculations of the electronic structure involving both the Co orbital configurations and DMFT approaches to take into account the electronic correlations.

Figure 1

Experimental ${}^{59}\mathrm{Co}$ NMR spectrum (top thick black line) of the SC1 sample measured in the fixed magnetic field $B_0\parallel c$. The simulations of the spectra for six distinct Co sites NMR signals are shown by color lines. The parameters used in the simulations are presented in Table 1. The sum of the simulated cobalt spectra with the weight coefficients from Table 1 is shown by a red dotted line.

Figure 2

${}^{59}\mathrm{Co}$ NMR spectra of SC1 sample measured at long-time interval $\tau =100$ $\mu \mathrm{s}$ between rf pulses in the two directions of the applied magnetic field. The simulation of the spectra of Co1 are shown by the red dotted lines. See text for details.

Figure 3

(a) $K_{ZZ}$, (b) ${(1/T_1)}^{1/2}$ (closed symbols) and the corresponding pure spin contribution ${(1/T_{1\mathrm{spin}})}^{1/2}$ (open symbols), see the text, (c) ${(1/T_2)}^{1/2}$ vs ${\nu }_Q$ for cobalt sites in $x=0.77$ phase (red squares) and $x=2/3$ phase (blue circles). All experimental points were obtained at $T=80$ K. Linear fits are shown as eye guides.

Figure 4

(a) The lattice contribution to the quadrupole frequency variation ${\nu }_{Q0}^{\mathrm{latt}}$ (black open diamonds and black line) computed for a uniform distribution of Na and Co sites. It results from the contributions ${\nu }_{QA}$ and ${\nu }_{QB}$ (green open up and down triangles, correspondingly). The actual possible incidence of Na order on ${\nu }_Q^{\mathrm{latt}}$ is illustrated by the horizontal magenta ticks. Including the Co charge disproportionation slightly reduces this differentiation (orange ticks) and only slightly modifies the average magnitude of the computed ${\nu }_Q^{\mathrm{latt}}$ values with respect to the uniform case. (b) Comparison of the experimental ${\nu }_Q$ data (red full circles) with point charge calculations. The ${\nu }_0\left(x\right)$ values deduced from the analyses of Fig. 3 (blue closed squares and dashed line) parallels the variation of the computed data. See text for details.

Figure 5

${}^{59}\mathrm{Co}$ NMR spectra taken with the applied magnetic field $H\parallel c$ in different samples and experimental conditions: (a) single-crystal SC1 measured at $\mathrm{T}=40$ K in the fixed magnetic field $B_0=7$ T. Spectra measured at short time interval $\tau =6\mu \text{s}$ between rf pulses (black line) and long $\tau =100\mu \text{s}$ (red line) are shown. (b) Powder sample measured at $T=30$ K, $\tau =10\mu \mathrm{s}$ and in sweep field mode with ${\nu }_0=66.3$ MHz. (c) Single-crystal SC4 measured at $T=80$ K in the sweep field mode with ${\nu }_0=136$ MHz. Spectra measured at $\tau =5\mu \mathrm{s}$ (black line) and $\tau =100\mu \mathrm{s}$ (red line) are shown.

Figure 6

${}^{59}\mathrm{Co}$ NMR spectra measured in $H\perp c$ orientation: (a) single-crystal SC1 measured at $T=40$ K in the fixed magnetic field $B_0=7$ T. Spectra measured at short time interval $\tau =6\mu \mathrm{s}$ between rf pulses (black line) and long $\tau =100\mu \mathrm{s}$ (red line) are shown. (b) Single-crystal SC4 measured at $T=80$ K in the sweep field mode and ${\nu }_0=136$ MHz. Spectra measured at $\tau =5\mu \mathrm{s}$ (black line), $\tau =50\mu \mathrm{s}$ (green line), and $\tau =120\mu \mathrm{s}$ (red line) are shown.

Figure 7

Comparison of the part of $H\parallel c$ ${}^{59}\mathrm{Co}$ NMR spectra of the SC1 (bottom) and SC4 (top) samples measured at $T=80$ K. In the inset of upper panel we show the same group of satellite lines measured at different time interval $\tau$ between rf pulses which proves that the observed substructure is not associated with experimental noise but come from effects due to differences in the stacking of the Na layers.

Figure 8

Spin-lattice relaxation curves measured on different cobalt sites in SC1 sample in the same experimental conditions as spectrum in Fig. 1. The fits of the data with the magnetization relaxation functions from Ref. [8] with parameters from Table 1 are also shown.

Figure 9

${(1/T_1)}^{1/2}$ vs ${\nu }_Q$ for different cobalt sites in $x=2/3$ (open blue circles) and $x=0.71$ (green full squares) phases measured in NQR experiments at $T=4.2$ K. Linear fits are shown by solid lines with corresponding color.