Crystal electric field ofP2-NaxCoO2for the intermediate spin state of Co

G. J. Shu

¹

,

F. C. Chou

²

Abstract

The magnetic moment per Co 4+ of P2(γ)-type NaxCoO2 in Curie-Weiss metal regime is revisited and examined under a newly proposed modification of the octahedral crystal electric field (CEF). The proposed model explains the origin of the existence of the intermediate state S=1 for Co 3+ through an exciton-like elementary excitation of the narrow gap between the split eg and t2g groups. The CoO2 layer is proposed to be constructed from the tilted edge-sharing square-planar CoO2 chains with inter-chain coupling. The square-planar CEF of CoO2 requires covalent bond formation between Co and the four in-plane neighboring oxygens, while the oxygens sitting in the neighboring chains can be viewed as apical oxygens of low effective charge for a CoO6 pseudo-octahedron. The reason why angle-resolved photoemission spectroscopy (ARPES) failed to observe the local-density approximation (LDA) predicted e ′ g hole pockets at kz=0 and the reversed order of the t2g splittings between LDA and CEF calculations can also be resolved using the proposed model. PACS numbers: 71.70.Ch; 71.70.Ej; 75.30.Cr; 71.28.+d e 3d 6 e g Co 3+ t 2g a 1g e g ' Co O h LDA FIG. 1. (color online) The crystal structure of NaxCoO2 is presented with the CoO2 and Na layers in the space group P 63/mmc. The conventional electronic configuration of Co 3+ (3d 6 ) in an octahedral crystal field splits into eg − t2g groups, and the additional splitting of t2g (e ′ g − a1g) is due to trigonal distortion. In contrary to the spectrum of lower a1g predicted from the CEF calculation, the a1g is higher based on LDA calculations. 1,2 Layered P2-type (or γ-type) Na x CoO 2 is an important class of material for both fundamental and applied aspects, e.g., it is a good candidate thermoelectric material with a high thermoelectric figure-of-merit (ZT) at high temperature; 3 has a great similarity to the important battery cathode electrode material Li x CoO 2 ; 4 , has superconductivity, as observed in Na 1/3 CoO 2 after hydration; 5 and has an intriguing Curie-Weiss metal behavior as a strongly correlated electron material. 6 The crystal structure of Na x CoO 2 can be viewed as a Na layer sandwiched between CoO 2 triangular lattice layers as illustrated in Fig. 1. A 2D triangular lattice of CoO 2 formed by the closely packed CoO 6 octahedra is commonly observed in many cobalt oxide compounds in contrast to the high T c cuprate materials, which contain a 2D square lattice of CuO 2 . The CoO 2 layer has been the basic building block of many layered cobalt oxide compounds, including Na x CoO 2 , Pb 2 Sr 2 Co 2 O y , and Co 3 Co 4 O 9 , of various types of staging and the unavoidable incommensurability is due to layer mismatch. 7 The physical properties of materials with a hole-doped CoO 2 layer have often been interpreted from the mixed valence of Co 3+ and Co 4+ . However, the early d-orbital energy levels for Co under the octahedral crystal field assumption (see Fig. 1) cannot be used to reasonably interpret the Curie-Weiss metal behavior, especially concerning the puzzling quest...

Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins inNa0.82CoO2

“…3, it is intriguing to note that an activation behavior with a gap of ∼2.6 meV is implied. It is clear that α is not only temperature-dependent, as noted previously, [17] but displays field-dependence when the same temperature range is chosen in the paramagnetic regime.…”

“…1(c)), the temperaturedependent Curie constant (C = N µ 2 ef f /3k B ) for N a 0.82 CoO 2 has been revealed from the Curie-Weiss law (χ = χ • + C T −Θ ) analysis by using the homogeneous susceptibility χ(T)=M/T data from different temperature sections above ∼5 T N . [17] The Curie constants were found to be persistently higher than the value expected from the spin-only S=1/2 of Co 4+ . In particular, the Curie constant could be interpreted to arise from three contributions, including the localized spins of…”

“…1. [17] It was proposed and verified that the small gap of b 2g -a 1g ∼17 meV at H=1 Tesla could be subjected to easy thermal activation above ∼100 K, and the fraction of the thermally activated excited intermediate spin (IS) state of S=1 (b 1 2g a 1 1g ) versus the ground state (LS) of S=0 (b 2 2g a 0 1g ) for Co 3+ spins was shown to follow the Boltzmann distribution statistically. In this study, we explore the field dependence of the IS state of Co 3+ and use it to interpret the intriguing spin dynamics of N a 0.82 CoO 2 , including how and why the narrow b 2g -a 1g gap size is tuned sensitively by the magnetic field, and why FM-like behavior is observed at low field but an A-type antiferromagnetic (AF) ordering is confirmed at high field.…”

“…The thermally activated IS state of Co 3+ for a system with a narrow b 2g -a 1g gap of ∼17 meV (at H=1 Tesla) appears convincingly responsible for the intriguing magnetic properties. [17] Measurement results obtained by the same data analysis method previously applied to N a x CoO 2 , [17] including the DC homogeneous susceptibilities (χ=M/H) measured under various fields and a zero-field measurement using AC susceptibility measurement with H AC =5 Oe/10 Hz, are shown in Fig. 2.…”

Sodium layer chiral distribution and spin structure of Na2Ni2TeO6 with a Ni honeycomb lattice

“…X-ray diffraction studies have shown that the crystal structure of Na 2 Ni 2 TeO 6 can be indexed with a space group P 6 3 /mcm satisfactorily, and a 3D antiferromagnetic (AFM) spin ordering of T N ∼27 K has been proposed; however, the impact of Na ion diffusion on the crystal and spin structure has never been explored in detail, in contrast to its sister compound Na x CoO 2 which has been studied extensively and shown rich physical insights. [3][4][5][6][7][8][9]12,14 It is highly desirable to investigate the 2D structure of the Na-layer that reflects the potential field generated by the (Te/Ni)-O honeycomb sublattice and its relationship to the magnetic structure of Ni spins. In particular, due to the diffusive nature of intercalated Na ions, a unique dynamic magneto-phonon coupling of the system could be revealed through the detailed analysis of the Na ion distribution and crystal structure change as a function of temperature.…”