научная статья по теме ROLE OF ELECTRONIC CORRELATIONS IN THE FERMI SURFACE FORMATION OF NAXCOO2 Физика

Текст научной статьи на тему «ROLE OF ELECTRONIC CORRELATIONS IN THE FERMI SURFACE FORMATION OF NAXCOO2»

Pis'ma v ZhETF, vol.93, iss.2, pp.83-87

© 2011 January 25

Role of electronic correlations in the Fermi surface formation

of Na^CoOz

A. Shorikov, M. M. Korshunov*'vl\ V. I. Anisimov Institute of Metal Physics Ural Division RAS, 620219 Yekaterinburg GSP-170, Russia *L.V. Kirensky Institute of Physics, Siberian Branch of R AS, 660036 Krasnoyarsk, Russia vMax-Planck-Institut fur Physik komplexer Systeme, D-01187 Dresden, Germany

Submitted 6 December 2010

Band structure of metallic sodium cobaltate Na,COi (»=0.33, 0.48, 0.61 0.72) has been investigated by local density approximation+Hubbard U (LDA+J7) method and within Gutzwiller approximation for the Co-i29 manifold. Correlation effects being taken into account results in suppression of the e'B hole pockets at the Fermi surface in agreement with recent angle-resolved photo-emission spectroscopy (ARPES) experiments. In the Gutzwiller approximation the bilayer splitting is significantly reduced due to the correlation effects. The formation of high spin (HS) state in Co d-shell was shown to be very improbable.

1. Introduction. Puzzling properties of sodium cobaltate Na^CC^ are the topic of many recent theoretical and experimental investigations [1]. This material holds much promise for thermoelectronics due to its large thermopower [2] together with the relatively low resistivity [3]. The discovery of superconductivity with Tc about 5K in Nao.33CoO2-l.3H2O [3] revived the interest in lamellar sodium cobaltates. Moreover, the charge and magnetic long range orders on the frustrated triangular lattice of cobaltate is of the fundamental interest. The band theory predict the complicated Fermi surface (FS) with one large hole pocket around the F = (0,0,0) point and six small pockets near the K = (0, ,0) points of the hexagonal Brillouin zone at least for x < 0.5 [4, 5]. However, intensive investigations by several ARPES groups reveal absence of six small pockets in both ~SnrC0>-i/n>0 and in its parent compound Na,.C02 [6-10].

The disagreement between ARPES spectra and ab-initio calculated band structure points to the importance of the electronic correlations in these oxides. Other evidences for the correlated behavior come from the data on an anomalous Hall effect and a drop of the thermopower in holistic magnetic field [11].

The six hole pockets are absent in the L(S)DA+U calculations [12, 13]. However, in this approach, the insulating gap is formed by a splitting of the local single-electron states due to spin-polarization, resulting in a spin polarized Fermi surface with an area twice as large as that observed through ARPES. Moreover, the long range ferromagnetic order has been set by hand because of limitation of LDA+f/. The predicted large local mag-

e-mail: korshunov0phys.ufl.edu, present address: Department of Physics, University of Florida, Gainesville, Florida 32611, USA

netic moments as well as the splitting of bands can be considered as artifacts of the L(S)DA+f/ method.

Although LDA+f/ method is usually applied to describe insulators [14], there are some achievement in investigation of metals and metallic compounds [15, 16]. To analyze the effect of electronic correlations on the Fermi surface formation in sodium cobaltate we employ non-magnetic LDA+f/ method. Then, we use a Gutzwiller approximation to display the effect of correlations on the bilayer splitting and compare it with LDA+f/ results.

Co d-level splits by crystal field of oxygen octahedron in lower i2s and higher e9 bands. The deficiency of Na in Na3!C02 introduces additional holes in the system. Cobalt, having d6 configuration and filled t29 shell in parent NaC02, is nonmagnetic. But in nonstoichio-metric compound part of Co ions become magnetic with local moment about 1/j.b- This value is provided by d5 configuration and one hole in i2s shell. However, the experiments revealed the magnetic susceptibility at room temperature that is much higher than it was expected for dilute magnetic impurity in non-magnetic solvent. Explanation of this anomaly was suggested in Ref. [17] as transition from low-spin (LS) state with six d-electrons on i2s shell to high-spin (HS) state with five d-electrons on i2s shell and one electron on eg. The possibility of such transition will be discussed below.

2. LDA+f/ results. Nao.eiCo02 crystallize in the hexagonal unit cell (PG^/mmc space group) with a = 2.83176(3) A and c = 10.8431(2) A at 12K Ref [18]. Displacement of Na atoms from their ideal sites 2d (1/3,2/3,3/4) on about 0.2A are observed in non-stoichiometric cobaltates for both room and low temperatures. This is probably due to the repulsion of a randomly distributed Na atoms, locally violating hexagonal

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A. Shorikov, M. M. Korshunov, V. I. Anisimov

symmetry [18]. In the present investigation Na atoms are shifted back to their 2d ideal sites. In order to avoid charge disproportionation which can arises from some Na distribution if the supercell is used in calculation, the change in the Na concentration has been considered in virtual crystal approximation (VCA) where each 2d site is occupied by virtual atoms with fractional number of valence electrons x and a core charge 10 — x instead of Na. Note, that all core states of virtual atom are left unchanged and corresponds to Na ones. We have chosen 4s, 4p, and 3d states of cobalt, 2s, 2p, and 3d states of oxygen, and 3s, 3p, and 3d states of Na as the valence states for TB-LMTO-ASA computation scheme [19]. The radii of atomic spheres where 1.99 a.u. for Co, 1.61 a.u. for oxygen, and 2.68 a.u. for Na. Two classes of empty spheres (pseudo-atoms without core states) were added to fill the unit cell volume.

Crystal field of oxygen octahedron splits Co d-band into doubly degenerate eg and triply degenerate t2g subbands (without taking spin into account). LDA calculations shows that those manifolds are separated by about 2 eV [4]. Here partially filled t2g subband crosses the Fermi level whereas eg subband due to strongly hybridization with nearest oxygen atoms is positioned well above the Fermi level. The procedure proposed in Ref. [20] allows one to calculate the Coulomb repulsion parameter U taking into account the screening of localized d-shell by itinerant s- and p-electrons. Resulting U is equal to 6.7 eV. However, the presence of the t2g-eg splitting give the reason to take into account an additional screening channel provided by the less localized eg electrons. The value of U = 2.67 eV for i2s orbitals was calculated using the "constrained LDA" method [21], where the screening by the eg electrons is also taken into account. This value was used in the present calculation for all doping concentrations x. Hund's exchange parameter J depends weakly on screening effects due to its "on-site" character. Its value was also calculated within the "constrained LDA" method and was found to be 1.07 eV.

First, we have verified the possibility of HS state formation on Co d-shell. For this purpose the unit cell of Nao.eiC02 with two Co atoms was considered. We have started from a saturated A-type antiferromagnetic configuration with five electrons on the t2g and one on the eg shells. Small U = 2.67 eV does not stabilize such magnetic configuration and LS state was obtained. Increasing U up to 5 eV however results in HS state with large local magnetic moment about 1.96 hb- Nevertheless, this HS state has the total energy about 1.75 eV higher then the energy of a LS state. This large difference in total energy of both considered spin states arises form the hexagonal structure of cobaltates where the angle of Co-O-Co bond is close to 90° in contrast to almost

180° in, e.g., RC0O3 (R—La, Ho). In the latter case the eg band has the width of about 3-5 eV and its bottom lies just above the Fermi level. The system wins energy of 2 J forming a HS state overcoming the gap energy which is less than 1 eV. Due to this fact the difference between the LS and intermediate spin states in RC0O3 is less then 250 meV [22]. The angle of Co-O-Co bond is close to 90° in cobaltates and it results in a weak overlap between eg orbitals and hence in a narrow eg band with larger gap between it and the t2g band. Our calculation confirms that formation of the HS state in Na^CoOa is rather improbable and cannot be stabilized by any distortion of crystal structure or clusterization proposed in Ref. [17]. Local magnetic moments on Co sites can arise only because of the doped holes due to Na atoms deficiency. Those holes order on Co atoms and form nonmagnetic Co3+ and magnetic Co4+ ions with d6 and d5 configurations, respectively. In the following, we consider only the LS state.

The ordering of holes on i2s shell and corresponding long-range magnetic and charge orders in Nao.sCoC^ arise probably due to specific arrangement of Na atoms. These arrangements were observed experimentally [23] for several doping concentrations including x = 0.5. Proper description of such order within the "unrestricted Hartree-Fock" gives strong spin and orbital polarization and local magnetic moment of about 1 ¡¿b on Co4+ sites as well as the insulating ground state with a sizable gap. To describe the non-ordered systems, the implementation of the "restricted Hartree-Fock" method is more suitable. In the latter, starting from the non-magnetic configuration of the d-shell with the equal number of spin-up and spin-down electrons, LDA+f/ method gives the non-magnetic solution without spin or orbital polarization. Note, that the gap does not open and Na^CoOi» remains metallic for all Na concentration.

Obtained band structure of Na^CoOi» for »=0.33, 0.48, 0.61, and 0.72 are shown in Fig.l. Dashed (black) lines correspond to LDA results whereas solid (red) lines are the bands obtained by LDA+f/ method. Cobalt d and oxygen p states are separated by a small gap of about —1.25 eV for x = 0.61 and x = 0.72. However, this gap disappears for lower doping concentration since th

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