Coulomb-Enhanced Spin-Orbit Splitting: The Missing Piece in theSr2RhO4Puzzle

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.PACS numbers: 71.18.+y, 71.20.-b, 71.30.+h Since the discoveries of high-temperature superconductivity and colossal magnetoresistance in Mott insulators 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 lowenergy orbitals and split the corresponding quasiparticle -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 . 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 CuO 4 (2D K 2 NiF 4 -type) and LaMnO 3 (3D perovskite). The relatively small size and strong covalency of the Ca ions cause the RuO 6 octahedra to rotate and tilt. The resulting misalignment of the Ru t 2g Wannier orbitals (WOs) reduces the hopping between them, and so does the deformation of the WOs caused by Ca-O-t 2g covalency [9,10]. As a resu...

Electronic Structure of Low-Dimensional 4d5 Oxides: Interplay of Ligand Distortions, Overall Lattice Anisotropy, and Spin–Orbit Interactions

“…It was later explained that this is the outcome of the interplay of xy and x 2 − y 2 band mixing due to rotations of the RhO 6 octahedra, SOC, and sizable Coulomb interactions. 41,42 We study in more detail the d-level electronic structure and find that even the on-site energy of the Rh xy orbital is lower than the energies of the xz and yz orbitals, despite the apical elongation of the RhO 6 octahedra, which according to basic ligand-field theory should push the xy level higher in energy; 43 see Figure 2. This unexpected order of the Rh t 2g levels is the outcome of low-symmetry potentials related to the anisotropic layered structure of the extended surroundings and represents one ingredient that, in addition to the band effects discussed in refs 40−42 There are 10 alkaline-earth neighboring ions in the twodimensional square-lattice system compounds Sr 2 RhO 4 , Sr 2 IrO 4 , and Ba 2 IrO 4 (see Figure 1) and 12 in the quasi-onedimensional, chainlike compound Ca 3 CoRhO 6 (see Figure 3).…”

“…38,39 The electronic structure of Sr 2 RhO 4 was earlier addressed by both angle-resolved photoemission spectroscopy 40 and DFT calculations within the local-density approximation. 41,42 The particular form of the Fermi surface, with no sheet of xy symmetry, 40 came as a surprise for a system with positive tetragonal distortion of the O cage around the active d-metal site (see Figure 1). It was later explained that this is the outcome of the interplay of xy and x 2 − y 2 band mixing due to rotations of the RhO 6 octahedra, SOC, and sizable Coulomb interactions.…”

“…43 At the MRCI level, the splitting between the xy and xz/yz states is found to be 70 meV (see Table 1), a meaningful number compared to the 100−200 meV energy difference between the upper edges of the xy and xz/yz bands in the periodic DFT calculations. 40,41 The nature of the actual GS is somewhat more complex, however, because of SOCs that are important for 4d electrons. With SOC included, the spectrum of Rh t 2g 5 electronic states is a sequence of three Kramers doublets (KDs).…”

Giant Collective Spin-Orbit Field in a Quantum Well: Fine Structure of Spin Plasmons

“…At first glance, one would expect Coulomb-induced enhancements to be roughly of order r s (Wigner-Seitz radius), which is ≃ 1.3 for the studied sample. On the other hand, recent experiments [25,26] suggest that the interplay of Coulomb and SO interactions could manifest in a mutual boost, leading to significant enhancement of electronic spin splittings especially in low-dimensional systems [27].…”

The electronic structure of epitaxially stabilized 5d perovskite Ca1 −xSrxIrO3 (x= 0, 0.5, and 1) thin films: the role of strong spin–orbit coupling

“…[8][9][10][11] To solve such controversy, previous workers pointed out the importance of the role of the SO coupling. [12][13][14][15] As the strength of the SO coupling is proportional to Z 4 (where Z is the atomic number), it can be as large as 0.3-0.5 eV in 5d…”