23Na NMR study of sodium order in NaxCoO2 with 22K Neel temperature

We report a systematic study of the $c$ lattice parameter in the Na$_{x}$CoO$_{2}$ phases versus Na content $x>0.5$, in which sodium always displays ordered arrangements. This allows us to single out the first phase which exhibits an AF magnetic order at a Neel temperature $T_{N}=$22 K which is found to occur for $xapprox 0.77(1)$. Pure samples of this phase have been studied both as aligned powders and single crystals. They exhibit identical $^{23}$Na NMR spectra in which three sets of Na sites could be fully resolved, and are found to display $T$ dependencies of their NMR shifts which scale with each other. This allows us to establish that the $T$ variation of the shifts is due to the paramagnetism of the Co sites with formal charge state larger than 3$^{+}$. The existence of a sodium site with axial charge symmetry and the intensity ratio between the sets of $^{23}$Na lines permits us to reveal that the 2D structure of the Na order corresponds to 10 Na sites on top of a 13 Co sites unit cell, that is with $x=10/13approx 0.77$. This structure fits with that determined from local density calculations and involves triangles of 3 Na sites located on top of Co sites (so called Na1 sites). The associated ordering of the Na vacancies is quite distinct from that found for $x<0.75$.

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.