On the Ordering of Na+ Ions in NaxCoO2

Abstract

Abstract. The influence of electrostatic interactions on the ordering of sodium ions in Na x CoO 2 is studied theoretically through Monte-Carlo simulations. For large x small di-or tri-vacancy clusters are stable with respect to isolated Na vacancies. At commensurate fillings these small clusters order in triangular superstructures. These results agree with recent electron diffraction data at x = 1/2 and 3/4. We have performed neutron Laüe diffraction experiments at higher x, which confirm the predictions of this simple model. The consequences on the properties of the electronic charges in the Co layers are discussed.In the past decade, Na x CoO 2 has emerged as a system of fundamental interest because of its high thermoelectric power, unusual magnetic properties and possibility, when hydrated, to superconduct [1]. The density x of intercalated sodium atoms tunes directly the density of states of quasi-particles in the metallic CoO 2 sheets. For simple fractional fıllings, electron diffraction (ED) experiments [2,3] provide evidence for the ordering of Na + ions at room temperature. This non-trivial order is generally believed to be the consequence of intricate interactions between Na + ions, mobile electrons, and phonons. We show here that the dominant process driving this ordering is simply the Coulomb potential between Na + ions. Sodium ions can occupy sites between oxygen atoms, which form two interpenetrating triangular lattices denoted Na 1 and Na 2 . Cobalt ions lie above and below Na 1 sites, resulting in an extra energy cost ∆ = ∆ c + ∆ sr relative to an Na 2 site (∆ c in the long-range Coulomb part and ∆ sr a short range repulsion between Na and Co ions shells). Na ions are bigger than the distance between nearest Na 1 and Na 2 sites, forbidding simultaneous occupancy of nearest-neighboring sites and that makes Coulomb energy minimization highly nontrivial. Our model Hamiltonian includes: (i) a long-range Coulomb potential, e/(4πεε 0 r) (the dielectric constant, taken as isotropic, is fıxed at ε = 6 to account quantitatively for the variations of the chemical potential, in terms of x, measured in cell devices [4]); (ii) Na-Na ionshell repulsion V=0.04eV for neighbors on the same sublattice; and (iii) on-site energy ∆ sr = 0.01eV. A system of two sheets of Na ions, each containing a maximum number of 1176 ions, intercalated between two CoO 2 layers (with periodic boundary conditions in 3 dimensions) is simulated at fınite temperature and fıxed chemical potential µ through a Grand-Canonical Monte-Carlo method. The hexagonal cell parameters a=2.84Å and c=10.87Å are fıxed to those measured in the x = 0.75 phase, and elastic deformations are neglected. We maintain neutrality at each step by varying the charges in the Co layers assuming a uniform spreading.The organization of Na ions is driven by the spontaneous formation of multivacancy clusters, as illustrated in Figure 1. At large distance d, the repulsion energy between two vacancies decreases as 1/d. However neighboring vacancies can reduce their energy...

Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice

“…It seems likely that the charge ordering of the electrons in the CoO 2 layers observed at x = 0.5 is induced by Na ordering. 8 Recently, experimental studies by Zandbergen et al 83 and Roger et al 84 , first principles calculations by Zhang et al 85 and classical electrostatic calculations by Zhang et al and Roger et al have shown that as x is varied not only is the doping of the CoO 2 planes varied, but so is the Na ordering. However, there remains debate over the exact nature of the Na order at specific values of x.…”

“…However, there remains debate over the exact nature of the Na order at specific values of x. 83,84,85 There is additional evidence from NMR experiments of the presence of inequivalently charged Co ions with Co 3+ (S=0) and Co 4+ (S=1/2) induced by the charged Na layer of ions. 79 This effect implies that a large fraction of the electrons in the Co planes behave as S = 1/2 localized moments.…”

“…85. Note that Roger et al84 proposed different ordering patterns for x = 0.71 and 0.75, which involved 'vacancy clustering'.…”

Synthesis of sodium cobaltate NaxCoO2 single crystals with controlled Na ordering

“…The mobility of the sodium ions and their electrostatic repulsion leads to the appearance of distinct phases. These phases are characterized by their sodium content and despite discrepancies in previous studies, well defined Na orderings have been clearly established for some phases [6][7][8][9][10][11]. These Na orderings were successfully achieved by systematic synthesis in the polycrystalline form based on careful selections of the stoichiometry and synthesis temperature [8,12].…”