Neutron scattering study of novel magnetic order in Na0.5CoO2

Unveiled magnetic transition in Na battery material: μ+SR study of P2-Na0.5VO2

Muon-spin spectroscopy has clarified that the magnetic transition occurs not at 13 K but at 2 K in P2-Na_0.5VO₂.

A possibility of high spin hole states in doped CoO2 layered systems

We introduce and investigate an effective five-band model for t2g and eg electrons to describe doped cobalt oxides with Co(3+) and Co(4+) ions in two-dimensional CoO2 triangular lattice layers, as in Na1-xCoO2. The effective Hamiltonian includes anisotropic kinetic energy (due to both direct Co-Co and indirect Co-O-Co hoppings), on-site Coulomb interactions parameterized by intraorbital Hubbard repulsion U and full Hund's exchange tensor, crystal field terms and Jahn-Teller static distortions. We study it using correlated wave functions on 6 × 6 clusters with periodic boundary conditions. The computations indicate a low S = 0 spin to high S = 2 spin abrupt transition in the undoped systems when increasing strength of the crystal field, while intermediate S = 1 spins are not found. Surprisingly, for the investigated realistic Hamiltonian parameters describing low-spin states in CoO2 planes, doping generates high S = 5/2 spins at Co(4+) ions that are pairwise bound into singlets, seen here as pairs of up and down spins. It is found that such singlet pairs self-organize at higher doping into lines of magnetic ions with coexisting antiferromagnetic and ferromagnetic bonds between them, forming stripe-like structures. The ground states are insulating within the investigated range of doping because computed HOMO-LUMO gaps are never small enough.

Electrochemical investigation of the P2–NaxCoO2 phase diagram

Sodium layered oxides NaxCoO2 form one of the most fascinating low-dimensional and strongly correlated systems; in particular P2–NaxCoO2 exhibits various single-phase domains with different Na+/vacancy patterns depending on the sodium concentration. Here we used sodium batteries to clearly depict the P2–NaxCoO2 phase diagram for x≥0.50. By coupling the electrochemical process with an in situ X-ray diffraction experiment, we identified the succession of single-phase or two-phase domains appearing on sodium intercalation with a rather good accuracy compared with previous studies. We reported new single-phase domains and we underlined the thermal instability of some ordered phases from an electrochemical study at various temperatures. As each phase is characterized by the position of its Fermi level versus the Na+/Na couple, we showed that the synthesis of each material, even in large amounts, can be carried out electrochemically. The physical properties of the as-prepared Na1/2CoO2 and Na2/3CoO2 ordered phases were characterized and compared. Electrochemical processes are confirmed to be an accurate route to precisely investigate in a continuous way such a complex system and provide a new way to synthesize materials with a very narrow existence range.

An ab initio evaluation of the local effective interactions in the NaxCoO2 family

We used quantum chemical ab initio methods to determine the effective parameters of Hubbard and t-J models for the Na(x)CoO(2) compounds (x = 0 and 0.5). As for the superconducting compound we found the a(1g) cobalt orbitals above the e'(g) ones by a few hundreds of meV due to the e'(g)-e(g) hybridization of the cobalt 3d orbitals. The correlation strength was found to increase with the sodium content x, whereas the in-plane AFM coupling decreases. The less correlated system was found to be the pure CoO(2), however it is still strongly correlated and very close to the Mott transition. Indeed we found U/t ∼ 15, which is the critical value for the Mott transition in a triangular lattice. Finally, we found the magnetic exchanges in the CoO(2) layers to be strongly dependent on the weak local structural distortions.

Charge and spin orderings in triangular t-J-V model with quarter filling: application to Na(0.5)CoO(2)

We investigated the ground state (GS) properties of the single-orbital t-J-V model in a quarter-filling two-dimensional triangular lattice with the slave-boson mean-field approach. We found that the charge ordering (CO) and spin ordering arising from the spin exchange interaction J competes with that from the inter-site Coulomb interaction V. For comparatively large J, the stable GS is insulating with striped CO and antiferromagnetic ordering, avoiding the homogeneous frustrated phase. Accompanying the insulating CO phase, a small insulating gap is opened. Within a reasonable J and V parameter region, our results are consistent with the recent neutron scattering experiments in Na(0.5)CoO(2), which possibly elucidate its CO, magnetic and other GS properties.

Pressure-induced structural phase transitions on Na(0.5)CoO(2): a first principles study

First principles calculations have been carried out to study the pressure effects on the structural, electronic and magnetic properties of Na(0.5)CoO(2). An unexpected Na ion structural transformation has been predicted from our calculations. The main factor for such a transformation has been attributed to the increasing Coulomb repulsion between the Na1 and Co ions with the increase of pressure. The experimentally observed insulator-metal transition has been found to be induced by this structural transformation. Furthermore, due to the strong coupling between Na ordering and Co magnetic ordering, a magnetic phase transition follows after the structural transformation.

Magnetotransport properties in K(0.50)CoO(2) single crystals

We have measured susceptibility and angle-dependent magnetoresistance (AMR) on K(0.50)CoO(2) single crystals. A possible magnetic structure similar to that of Na(0.5)CoO(2), a G-type anti-ferromagnetic (AF) structure (both in-plane and inter-plane are AF), is proposed. At ∼20 K, a loop is observed between zero-field-cooled (ZFC) and field-cooled (FC) susceptibility. The absolute value of magnetoresistance (MR) at 20 K is much larger than other cases with H applied within the ab plane. This could arise from the magnetic field being applied in the ab plane, leading to spin-flop of the small magnetic moment of Co(3.5-δ) sites at 20 K to form in-plane ferromagnetic ordering, as observed in Na(0.52)CoO(2).

Phase diagram of NaxCoO2 studied by Gutzwiller density-functional theory

The ground state of NaxCoO2 (0.0<x<1.0) is studied by the local density approximation plus the Gutzwiller approach, where charge transfer and orbital fluctuations are all self-consistently treated ab initio. In contrast to previous studies, which are parameter-dependent, we characterized the phase diagram as (1) Stoner magnetic metal for x>0.6 due to a_{1g} van Hove singularity near the band top, (2) correlated nonmagnetic metal without e_{g};{'} pockets for 0.3<x<0.6, and (3) e_{g};{'} pockets appear for x<0.3, and additional magnetic instability is revealed. Experimental quasiparticle properties are well explained, and the a_{1g}-e_{g};{'} anticrossing is attributed to spin-orbital coupling.

59Co NMR evidence for charge ordering below T_(CO) approximately 51 K in Na0.5CoO2

The CoO2 layers in NaxCoO2 may be viewed as a spin S=1/2 triangular-lattice doped with charge carriers. The underlying physics of the cobaltates is very similar to that of the high T_(c) cuprates. We will present unequivocal 59Co NMR evidence that below T_(CO) approximately 51 K, the insulating ground state of the itinerant antiferromagnet Na0.5CoO2 (T_(N) approximately 86 K) is induced by charge ordering.

Charge and spin order on the triangular lattice: NaxCoO2 at x=0.5

The nature of electronic states due to strong correlation and geometric frustration on the triangular lattice is investigated in connection to the unconventional insulating state of NaxCoO2 at x=0.5. We study an extended Hubbard model using a spatially unrestricted Gutzwiller approximation. We find a new class of charge and spin ordered states at x=1/3 and x=0.5 where antiferromagnetic (AFM) frustration is alleviated via weak charge inhomogeneity. At x=0.5, we show that the square root of 3a x 2a off-plane Na dopant order induces weak square root of 3a x 1a charge order in the Co layer. The symmetry breaking enables successive square root of 3a x 1a AFM and 2a x 2a charge- or spin-ordering transitions at low temperatures. The Fermi surface is truncated by the 2a x 2a hexagonal zone boundary into small electron and hole pockets. We study the phase structure and compare to recent experiments.

Shubnikov-de Haas effect in the metallic state of Na0.3CoO2

Shubnikov-de Haas oscillations for two well-defined frequencies, corresponding, respectively, to areas of 0.8 and 1.36% of the first Brillouin zone, were observed in single crystals of Na(0.3)CoO2. The existence of Na superstructures in Na0.3CoO2, coupled with this observation, suggests the possibility that the periods are due to the reconstruction of the large Fermi surface around the Gamma point. An alternative interpretation in terms of the long sought-after epsilon'(g) pockets is also considered but found to be incompatible with existing specific heat data.

On the Origin of the Metallic and Anisotropic Magnetic Properties of NaxCoO2 (x ≈ 0.75)

Nonstoichiometric Na(x)CoO2 (0.5 < x < 1) consists of CoO2 layers made up of edge-sharing CoO6 octahedra and exhibits strongly anisotropic magnetic susceptibilities as well as metallic properties. A modified Curie-Weiss law was proposed for systems containing anisotropic magnetic ions to analyze the magnetic susceptibilities of Na(x)CoO2 (x approximately 0.75), and implications of this analysis were explored. Our study shows that the low-spin Co4+ (S = 1/2) ions of Na(x)CoO2 generated by the Na vacancies cause the anisotropic magnetic properties of Na(x)CoO2 and suggests that the six nearest-neighbor Co3+ ions of each Co4+ ion adopt the intermediate-spin electron configuration, thereby behaving magnetically like low-spin Co4+ ions. The Weiss temperature of Na(x)CoO2 is more negative along the direction of the lower g factor (i.e., theta|| < theta(perpendicular) < 0 and g|| < g(perpendicular)). The occurrence of intermediate-spin Co3+ ions surrounding each Co4+ ion accounts for the apparently puzzling magnetic properties of Na(x)CoO2 (x approximately 0.75), i.e., the large negative Weiss temperature, the three-dimensional antiferromagnetic ordering below approximately 22 K, and the metallic properties. The picture of the magnetic structure derived from neutron scattering studies below approximately 22 K is in apparent conflict with that deduced from magnetic susceptibility measurements between approximately 50 and 300 K. These conflicting pictures are resolved by noting that the spin exchange between Co3+ ions is more strongly antiferromagnetic than that between Co4+ and Co3+ ions.

In-plane ferromagnetism in charge-ordering Na0.55CoO2

The magnetic and transport properties are systematically studied on the single crystal Na(0.55)CoO2 with the resistivity divergence below 50 K. A weak ferromagnetic ordering is observed in susceptibility below 20 K with the magnetic field parallel to the Co-O plane, while no such ferromagnetic ordering is observed with the field perpendicular to the Co-O plane. It gives evidence for the existence of in-plane ferromagnetism below 20 K. The observed magnetoresistance of 30% at the field of 6 T at low temperatures indicates an unexpectedly strong spin-charge coupling in the triangle lattice NaxCoO2 system.

Charge and spin ordering in insulating Na0.5CoO2: effects of correlation and symmetry

Ab initio band theory including correlations due to intra-atomic repulsion is applied to study charge disproportionation and charge and spin ordering in insulating Na0.5CoO2. Various ordering patterns (zigzag and two striped) for four-Co supercells are analyzed before focusing on the observed "out-of-phase stripe" pattern of antiferromagnetic Co4+ spins along charge-ordered stripes. This pattern relieves frustration and shows distinct analogies with the cuprate layers: a bipartite lattice of antialigned spins, with axes at 90degrees angles. Substantial distinctions with cuprates are also discussed, including the tiny gap of a new variant of "charge-transfer" type within the Co 3d system.