Effective Hamiltonian for transition-metal compounds. Application to Na_xCoO_2

Abstract

We describe a simple scheme to construct a low-energy effective Hamiltonian H_eff for highly correlated systems containing non-metals like O, P or As (O in what follows) and a transition-metal (M) as the active part in the electronic structure, eliminating the O degrees of freedom from a starting Hamiltonian that contains all M d orbitals and all non-metal p orbitals. We calculate all interaction terms between d electrons originating from Coulomb repulsion, as a function of three parameters (F_0, F_2 and F_4) and write them in a basis of orbitals appropriate for cubic, tetragonal, tetrahedral or hexagonal symmetry around M. The approach is based on solving exactly (numerically if necessary) a MO_n cluster containing the transition-metal atom and its n nearest O atoms (for example a CoO_6 cluster in the case of the cobaltates, or a CuO_n cluster in the case of the cuprates, in which n depends on the number of apical O atoms), and mapping them into many-body states of the same symmetry containing d holes only. We illustrate the procedure for the case of Na_xCoO_2. The resulting H_eff, including a trigonal distortion D, has been studied recently and its electronic structure agrees well with angle-resolved photoemission spectra [A. Bourgeois, A. A. Aligia, and M. J. Rozenberg, Phys. Rev. Lett. 102, 066402 (2009)]. Although H_eff contains only 3d t_2g holes, the highly correlated states that they represent contain an important amount not only of O 2p holes but also of 3d e_g holes. When more holes are added, a significant redistribution of charge takes place. As a consequence of these facts, the resulting values of the effective interactions between t_2g states are smaller than previously assumed, rendering more important the effect of D in obtaining only one sheet around the center of the Brillouin zone for the Fermi surface (without additional pockets).

11 pages, 1 figure, accepted for publication in Phys.Rev. B

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Cited by in corpus (11)

• Quantum Transport Through a Stretched Spin--1 Molecule
• Non-Fermi liquid behavior in transport through Co doped Au chains
• Non-Fermi liquid behaviour in non-equilibrium transport through Co doped Au chains connected to four-fold symmetric leads
• Considerable non-local electronic correlations in strongly doped Na${}_x$CoO${}_2$
• Dynamical magnetic anisotropy and quantum phase transitions in a vibrating spin-1 molecular junction
• Effect of covalency and interactions on the trigonal splitting in NaxCoO2
• Spin and orbital ordering in bilayer Sr${}_3$Cr${}_2$O${}_7$
• Kondo physics in a Ni impurity embedded in O-doped Au chains
• Kondo behavior and conductance through $3d$ impurities in gold chains doped with oxygen
• Unusual Kondo physics in a Co impurity atom embedded in noble-metal chains
• Magnetic and orbital instabilities in a lattice of SU(4) organometallic Kondo complexes