Ju l 2 00 8 Coulomb-Enhanced Spin-Orbit Splitting : The Missing Piece in the Sr 2 RhO 4 Puzzle

Abstract

The outstanding discrepancy between the measured and calculated (local-density approximation) Fermi surfaces in the well-characterized, paramagnetic Fermi liquid Sr2RhO4 is resolved by including the spin-orbit coupling and Coulomb repulsion. This results in an effective spin-orbit coupling constant enhanced 2.15 times over the bare value. A simple formalism allows discussion of other systems. For Sr2RhO4, the experimental specific-heat and mass enhancements are found to be 2.2. Since the discoveries of high-temperature supercon-ductivity and colossal magnetoresistance in Mott insula-tors made metallic by hole-doping, transition-metal oxides have remained at the forefront of research. Their many lattice and electronic (orbital, charge, and spin) degrees of freedom are coupled by effective interactions (electron-phonon, hopping, t, Coulomb repulsion, U, and Hunds-rule coupling, J), and when some of these are of similar magnitude, competing phases may exist in the region of controllable compositions, fields, and temperatures. The interactions tend to remove low-energy degrees of freedom, e.g. to reduce the metallicity. This rarely happens by merely shifting spectral weight from a quasiparticle band into incoherent Hubbard bands, as in the U/t-driven metal-insulator transition for the single-band Hubbard model, but is usually assisted by lattice distortions which break the degeneracy of low-energy orbitals and split the corresponding quasiparti-cle –or partly incoherent– bands away from the chemical potential. According to recent calculations using the local density-functional plus dynamical mean-field approximation (LDA+DMFT), such Coulomb-enhanced crystal-field splitting seems to be the mechanism triggering the expansion-induced metal-insulator transition in undoped LaMnO 3 [1] and in V 2 O 3 [2], long considered the prototype Mott transition. The low-temperature, antiferromagnetically-ordered, insulating phase of V 2 O 3 is well described [3] in the LDA+U static mean-field approximation, which yields the configuration t 2 2g → e π ↑↑ g a 0 1g. Although this approximation exaggerates the tendency towards symmetry breaking, it does give a reasonable description of the shape of the Fermi surface (FS) on the metallic side of the transition [1, 2]. When going from 3d to 4d transition-metal oxides, the larger extent of the 4d orbitals cause the hopping, t, and the coupling to the lattice to increase, and U and J to decrease. This is reflected in the rich electronic properties of e.g. the t 4 2g ruthenates in the Ruddlesden-Popper series (Ca 1−x Sr x) ν+1 Ru ν O 3ν+1 [4, 5, 6, 7, 8]. Here, the end-members (ν=1 and ν=∞) have the same structures as respectively La 2 …

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