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Register a new userNa order and Co charge disproportionation in Na$_{x}$CoO$_{2}$
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We have synthesized and characterized different stable phases of sodium cobaltates Na$_{x}$CoO$_{2}$ with sodium content $0.65<x<0.80$. We demonstrate that $^{23}$Na NMR allows to determine the difference in the susceptibility of the phases and reveals the presence of Na order in each phase. $^{59}$Co NMR experiments give clear evidence that Co charge disproportionation is a dominant feature of Na cobaltates. Only a small fraction ($approx$ 25%) of cobalts are in a non-magnetic Co$^{3+}$ charge state whereas electrons delocalize on the other cobalts. The magnetic and charge properties of the different Co sites are highly correlated with each other as their magnetic shift $K_{ZZ}$ scales linearly with their quadrupolar frequency $nu_Q$. This reflects the fact that the hole content on the Co orbitals varies from site to site. The unusual charge differentiation found in this system calls for better theoretical understanding of the incidence of the Na atomic order on the electronic structures of these compounds.
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$^{59}$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.
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.
The strength and effect of Coulomb correlations in the (superconducting when hydrated) x~1/3 and ``enhanced x~2/3 regimes of Na(x)CoO2 are evaluated using the correlated band theory LDA+U method. Our results, neglecting quantum fluctuations, are: (1) allowing only ferromagnetic order, there is a critical U_c = 3 eV, above which charge disproportionation occurs for both x=1/3 and x=2/3, (2) allowing antiferromagnetic order at x=1/3, U_c drops to 1 eV for disproportionation, (3) disproportionation and gap opening occur simultaneously, (4) in a Co(3+)-Co(4+) ordered state, antiferromagnetic coupling is favored over ferromagnetic, while below U_c ferromagnetism is favored. Comparison of the calculated Fermi level density of states compared to reported linear specific heat coefficients indicates enhancement of the order of five for x~0.7, but negligible enhancement for x~0.3. This trend is consistent with strong magnetic behavior and local moments (Curie-Weiss susceptibility) for x>0.5 while there no magnetic behavior or local moments reported for x<0.5. We suggest that the phase diagram is characterized by a crossover from effective single-band character with U >> W for x>0.5 into a three-band regime for x<0.5, where U --> U_eff <= U/sqrt(3) ~ W and correlation effects are substantially reduced.
We have synthesized and characterized the four different stable phases of Na ordered Na$_{x}$CoO$_{2}$, for $0.65<xlesssim 0.75$. Above 100K they display similar Curie-Weiss spin susceptibilities as well as ferromagnetic $q=0$ spin fluctuations in the CoO$_{2}$ planes revealed respectively by $^{23}$Na NMR shift and spin lattice $T_{1}$ data. The Co disproportionate already above 300K into Co$^{3+}$ and $approx $Co$^{3.5+}$ in all phases, which allows us to understand that magnetism is favoured. Below 100K the paramagnetic properties become quite distinct, and a 3D magnetic order sets in only for $x=0.75$, so that charge order has a subtle incidence on the low $T$ energy scales and transverse magnetic couplings.
The strength and effect of Coulomb correlations in the (superconducting when hydrated) x~1/3 regime of Na(x)CoO(2) have been evaluated using the correlated band theory LDA+U method. Our results, neglecting quantum fluctuations, are: (1) there is a critical $U_{c}$ = 3 eV, above which charge ordering occurs at x=1/3, (2) in this charge-ordered state, antiferromagnetic coupling is favored over ferromagnetic, while below $U_{c}$, ferromagnetism is favored; and (3) carrier conduction behavior should be very asymmetric for dopings away from x=1/3. For x < 1/3, correlated hopping of parallel spin pairs is favored, suggesting a triplet superconducting phase.
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