The crucial importance of the $t_{2g}$--$e_g$ hybridization in transition metal oxides

Abstract

We studied the influence of the trigonal distortion of the regular octahedron along the (111) direction, found in the $\mathrm{Co}{\mathrm{O}}_2$ layers. Under such a distortion the $t_{2g}$ orbitals split into one $a_{1g}$ and two degenerated $e_g^{\prime }$ orbitals. We focused on the relative order of these orbitals. Using quantum chemical calculations of embedded clusters at different levels of theory, we analyzed the influence of the different effects not taken into account in the crystalline field theory; that is metal-ligand hybridization, long-range crystalline field, screening effects and orbital relaxation. We found that none of them are responsible for the relative order of the $t_{2g}$ orbitals. In fact, the trigonal distortion allows a mixing of the $t_{2g}$ and $e_g$ orbitals of the metallic atom. This hybridization is at the origin of the $a_{1g}$--$e_g^{\prime }$ relative order and of the incorrect prediction of the crystalline field theory.

References in corpus (7)

• Fermi surface and quasiparticle dynamics of Na(x)CoO2 {x=0.7} investigated by Angle-Resolved Photoemission Spectroscopy
• Fermi surface evolution and Luttinger theorem in Na${}_x$CoO${}_2$: a systematic photoemission study
• ARPES on Na${}_{0.6}$CoO${}_2$: Fermi surface, extended flat dispersion, and unusual band splitting
• Nesting, spin-fluctuations, and odd-gap superconductivity in NaxCoO2 yH2O
• An ab-initio evaluation of the local effective interactions in the superconducting compound $Na\_0.35CoO\_2-1.3H\_2O$
• Electronic States in Two-Dimensional Triangular Cobalt Oxides: Role of Electronic Correlation
• Comparison of the Electronic Structures of Two Non-cuprate Layered Transition Metal Oxide Superconductors

Cited by in corpus (26)

• Topological insulators and metal-insulator transition in the pyrochlore iridates
• Competing Exotic Topological Insulator Phases in Transition Metal Oxides on the Pyrochlore Lattice with Distortion
• The Paired Electron Crystal: order from frustration in the quarter-filled band
• Topological states in pyrochlore iridates: long-range anisotropy strongly competing with spin-orbit interaction
• Stacking-dependent ferroicity of reversed bilayer: altermagnetism or ferroelectricity
• Impact of spin-orbit coupling on the magnetism of Sr3MIrO6 (M = Ni, Co)
• Topological Insulators and Quantum Spin Liquids
• Electronic structure of the $\mathrm{C}{\mathrm{a}}_3\mathrm{C}{\mathrm{o}}_4{\mathrm{O}}_9$ compound from ab initio local interactions
• Fragile Symmetry-Protected Half Metallicity in Two-Dimensional van der Waals Magnets: A Case Study of Monolayer FeCl2
• Orbitally relieved magnetic frustration in NaVO2
• Theoretical analysis of oxygen vacancies in layered sodium cobaltate Na_xCoO_{2-δ}
• Effective Hamiltonian for transition-metal compounds. Application to Na_xCoO_2
• Experimental study of the incoherent spectral weight in the photoemission spectra of the misfit cobaltate [Bi2Ba2O4][CoO2]2
• Crystal growth engineering and origin of the weak ferromagnetism in antiferromagnetic matrix of orthochromates from $t$-$e$ orbital hybridization
• Dynamical mean field theory of an effective three-band model for Na${}_x$CoO${}_2$
• The origin of a${}_{1g}$ and e${}_g$' orderings in Na${}_x$CoO${}_2$
• s-wave Superconductivity due to Suhl-Kondo Mechanism in Na${}_x$CoO${}_2\cdot y$H${}_2$O: Effect of Coulomb Interaction and Trigonal Distortion
• Effect of covalency and interactions on the trigonal splitting in NaxCoO2
• Lattice distortion in the spin-orbital entangled state in RVO3 perovskites
• Trimer Formation and Metal-Insulator Transition in Orbital Degenerate Systems on a Triangular Lattice
• Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in Na0.82CoO2
• Evidence of exchange-striction and charge disproportionation in the magneto-electric material Ni3TeO6
• Revisiting the crystal electric field of P2-NaxCoO2 for the intermediate spin state of Co3+
• Orbital order in NaTiO${}_2$ : A first principles study
• Modulated, three-directional, and polar structural instability in layered $d^1$ NaTiO${}_2$
• Weak electronic correlations in the cobalt oxychalcogenide superconductor Na2CoSe2O