Evolution of Co charge disproportionation with Na order in Na$_{x}$CoO$_{2}$

$^{59}$Co NMR experiments have been performed on single crystals of the layered cobaltate Na$_{x}$CoO$_{2}$ with x=0.77 which is an antiferromagnet with Neel temperature $T_{N}=22$~K. In this metallic phase six Co sites are resolved in the NMR spectra, with distinct quadrupole frequencies $ u _{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 $ u _{Q}$. The data analysis allows us to separate the contribution $ u_{Q}^{latt}$ of the ionic charges to $ u _{Q}$ from that $ u _{Q}^{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 $ u _{Q}^{latt}$ is found to fit rather well numerical computations done in a point charge model. The second term $ u _{Q}^{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.

NQR and X-ray investigation of the structure of Na$_{2/3}$CoO$_{2}$ compound

We have synthesized various samples of the $x=2/3$ phase of sodium cobaltate Na$_{x}$CoO$_{2}$ and performed X-ray powder diffractions spectra to compare the diffraction with the structure proposed previously from NMR/NQR experiments [H. Alloul emph{et al.}, EPL textbf{85}, 47006 (2009)]. Rietveld analysis of the data are found in perfect agreement with those, and confirm the concentration x=2/3 obtained in the synthesis procedure. They even give indications on the atomic displacements of Na inside the unit cell. The detailed NQR data allow us to identify the NQR transitions and electric field gradient (EFG) parameters for 4 cobalt sites and 3 Na sites. The spin-lattice and spin-spin relaxation rates are found much smaller for the non-magnetic Co$^{3+}$ sites than for the magnetic sites on which the holes are delocalized. The atomic ordering of the Na layers is therefore at the source of this ordered distribution of cobalt charges. The method used here to resolve the Na ordering and the subsequent Co charge order can be used valuably for other concentrations of Na.

Na ordering imprints a metallic kagome lattice onto the Co planes of Na2/3CoO2

We report $^{23}$Na and $^{59}$Co nuclear magnetic (NMR) and quadrupolar resonance (NQR) studies for the $x=2/3$ phase of the lamellar oxide Na$_{x}$CoO$_{2}$, which allowed us to establish reliably the atomic order of the Na layers and their stacking between the CoO$_{2}$ slabs. We evidence that the Na$^{+}$ order stabilizes filled non magnetic Co$^{3+}$ ions on 25% of the cobalt sites arranged in a triangular sublattice. The transferred holes are delocalized on the 75% complementary cobalt sites which unexpectedly display a planar cobalt kagom{e} structure. These experimental results resolve a puzzling issue by precluding localized moments pictures for the magnetic properties. They establish that the quasi ferromagnetic properties result from a narrow band connecting a frustrated arrangement of atomic orbitals, and open the route to unravel through similar studies the electronic properties of the diverse ordered phases of sodium cobaltates.

Na atomic order, Co charge disproportionation and magnetism in Na$_{x}$CoO$_{2}$ for large Na contents

We have synthesized and characterized four different stable phases of Na ordered Na$_{x}$CoO$_{2}$, for $0.65<x<0.8$. Above 100 K they display similar Curie-Weiss susceptibilities as well as ferromagnetic $q=0$ spin fluctuations in the CoO$_{2}$ planes revealed by $^{23}$Na NMR data. In all phases from $^{59}$Co NMR data we display evidences that the Co disproportionate already above 300 K into non magnetic Co$^{3+}$ and magnetic $approx $Co$^{3.5+}$ sites on which holes delocalize. This allows us to understand that metallic magnetism is favored for these large Na contents. Below 100 K the phases differentiate, and a magnetic order sets in only for $xgtrsim 0.75$ at $T_{N}=$22 K. We suggest that the charge order also governs the low $T$ energy scales and transverse couplings.