Patterning of sodium ions and the control of electrons in sodium cobaltate

Abstract

NaxCoO2 has emerged as a material of exceptional scientific interest due to the potential for thermoelectric applications, and because the strong interplay between the magnetic and superconducting properties has led to close comparisons with the physics of the high-Tc cuprates. The density, x, of the sodium in the intercalation layers can be altered electrochemically, directly changing the number of conduction electrons on triangular Co layers. Recent electron diffraction measurements reveal a kaleidoscope of Na+ ion patterns as a function of concentration. Here we use single-crystal neutron diffraction supported by numerical simulations to determine the long-range three-dimensional superstructures of these ions. We show that the sodium ordering and its associated distortion field are governed by pure electrostatics, and the organizational principle is the stabilization of charge droplets that order long range at some simple fractional fillings. Our results provide a good starting point to understand the electronic properties in terms of a Hubbard Hamiltonian taking into account the electrostatic potential from the Na superstructures. The resulting depth of potential wells in the Co layer is greater than the single-particle hopping kinetic energy. As a consequence, holes occupy preferentially the lowest potential regions and, therefore, the Na+ ion patterning plays a decisive role in the transport and magnetic properties.

12 pages, 4 figures, new version published in Nature

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• Searching for Stable Na-ordered Phases in Single Crystal Samples of gamma-NaxCoO2
• Sodium vacancy ordering and the co-existence of localized spins and itinerant charges in NaxCoO2
• Electronic texture of the thermoelectric oxide Na0.75CoO2
• Spin correlations and cobalt charge states: A new phase diagram of sodium cobaltates
• NQR and X-ray investigation of the structure of Na${}_{2/3}$CoO${}_2$ compound
• Na ordering imprints a metallic kagome lattice onto the Co planes of Na2/3CoO2
• Frustration-induced nanometre-scale inhomogeneity in a triangular antiferromagnet
• Direct link between low temperature magnetism and high temperature sodium order in NaxCoO2
• Na atomic order, Co charge disproportionation and magnetism in Na${}_x$CoO${}_2$ for large Na contents
• Magnetic and Electronic Properties of Li${}_x$CoO${}_2$ Single Crystals
• Discontinuous Lifshitz Transition Achieved by Band-Filling Control in NaxCoO2
• Melting of the Na layers in solid Na0.8CoO2
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• Competition between charge and spin order in the $t-U-V$ extended Hubbard model on the triangular lattice
• Impact of lithium composition on the thermoelectric properties of the layered cobalt oxide system LixCoO2
• ^{59}Co NMR evidence for charge ordering below T_{CO}\sim 51 K in Na_{0.5}CoO_2
• 59Co NMR evidence for charge and orbital order in the kagome like structure of Na2/3CoO2
• The origin of strong correlations and superconductivity in Na${}_x$CoO${}_2$
• Electronic phase diagram of LixCoO2 revisited with potentiostatically de-intercalated single crystals
• Crystal-to-stripe reordering of sodium ions in NaxCoO2 (x>=0.75)
• Strong correlations enhanced by charge-ordering in highly doped cobaltates
• Theoretical analysis of oxygen vacancies in layered sodium cobaltate Na_xCoO_{2-δ}
• Magnetic inhomogeneity on a triangular lattice: the magnetic-exchange versus the elastic energy and the role of disorder
• Sodium Trimer Ordering on NaxCoO2 Surface
• Na order and Co charge disproportionation in Na${}_x$CoO${}_2$
• 23Na NMR study of sodium order in NaxCoO2 with 22K Neel temperature
• Rearrangement of Sodium ordering and its effect on physical properties in $N{a}_{x}Co{O}_2$ system
• Restoration of long range order of Na ions in $N{a}_{x}Co{O}_2$ at high temperatures by sodium site doping
• Spin polaron theory for the photoemission spectra of layered cobaltates
• Oxygen non-stoichiometry and the origin of Na ion ordering in P2-NaxCoO2
• Interplay between Magnetism and Na concentration in $N{a}_{x}Co{O}_2$
• The electronic structure of the Na${}_x$CoO${}_2$ surface
• Spin fluctuations, magnetic long-range order and Fermi surface gapping in NaxCoO2
• Considerable non-local electronic correlations in strongly doped Na${}_x$CoO${}_2$
• Interplay of frustration, magnetism, charge ordering, and covalency in a model of Na0.5CoO2
• Novel electronic states realized by the interplay between Li diffusion and Co${}^{3+}$$/$Co${}^{4+}$ charge ordering in Li${}_{\mathrm{x}}$CoO${}_2$
• Na-ion dynamics in Quasi-1D compound NaV2O4
• Metal-nonmetal transition in LixCoO2 thin film and thermopower enhancement at high Li concentration
• The Duel of Magnetic Interactions & Structural Instabilities: Itinerant Frustration in the Triangular Lattice Compound LiCrSe${}_2$
• Emergent charge ordering in near half doped Na${}_{0.46}$CoO${}_2$
• Ionic Hubbard model on a triangular lattice for Na_0.5CoO_2, Rb_0.5CoO_2 and K_0.5CoO_2: Mean-field slave boson theory
• Synthesis of sodium cobaltate Na${}_x$CoO${}_2$ single crystals with controlled Na ordering
• Origin of the electron disproportionation in the metallic sodium cobaltates
• Theory of carrier concentration-dependent electronic behavior in layered cobaltates
• New electronic orderings observed in cobaltates under the influence of misfit periodicities
• Electronic and magnetic properties of the ionic Hubbard model on the striped triangular lattice at 3/4 filling
• Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in Na0.82CoO2
• Evidence for Oxygen Holes due to d-p Rehybridization in Thermoelectric Sr_{1-x}Rh_{2}O_{4}
• Mott and Wigner-Mott transitions in doped correlated electron systems: effects of superlattice potential and inter-site correlation
• Na Site Doping a Pathway for Enhanced Thermoelectric Performance in $N{a}_{1-x}Co{O}_2$; The Case of Gd and Yb Dopants
• Interplay between magnetism and sodium vacancy ordering in NaxCoO2
• Enhanced low energy fluctuations and increasing out-of-plane coherence in vacancy ordered NaxCoO2
• Divacancy superstructures in thermoelectric calcium-doped sodium cobaltate
• Superconductivity from buckled-honeycomb-vacancy ordering
• Transition from a phase-segregated state to single-phase incommensurate sodium ordering in Na_xCoO_2 with x \approx 0.53
• Sodium ion ordering of Na0.77CoO2 under competing multi-vacancy cluster, superlattice and domain formation
• Ab-initio studying of spin states of sodium cobaltate Na${}_{2/3}$CoO${}_2$
• Orbital inversion and emergent lattice dynamics in infinite layer CaCoO${}_2$
• Spin-chain correlations in the frustrated triangular lattice material CuMnO${}_2$
• Temperature-driven sodium-ion dynamical-to-static crossover in the zig-zag ordered phase of Na${}_{0.5}$CoO${}_2$