Interplay between crystal-field splitting and superexchange interaction in thet2gorbital Mott insulator

Abstract

With a model of the d 1 (t 2g )-electron antiferromagnetic Mott insulator a competition of two typical interactions for orbital states of the t 2g -triplet levels has been investigated: The on-site electronic coupling with a local crystal field (LCF) tends orbitals to order, while the intersite superexchange (SE) induces their fluctuations. Both interactions coexist in perovskites: The LCF is induced by GdFeO 3 -type structural deformations. In turn, the SE originates from virtual electronic hoppings, allowed by the Pauli principle, between nonorthogonal orbital states of adjacent sites. The dependence of the state of the orbitals (namely, a dispersion of their excitations and the quadrupole polarization) on a relation between the energy of the triplet level splitting, caused by the D 3d -symmetry LCF, and the exchange energy J SE is analyzed. Two qualitatively different regimes of the collective orbital behavior have been established: the induced order and fast fluctuations. It has been found that a crossover between them occurs when comes close to J SE , and in the parameter region about ≈ J SE the order and fluctuations affect the wave function in a comparable extent. Previous approaches based on either of the interactions fail in this window. The present study identifies validity ranges of the former theories, embracing the physics of the orbitals by the unified description.

Structural phase transitions of the metal oxide perovskites SrTiO3, LaAlO3, and LaTiO3studied with a scree

“…90,94 This small CFS is a shared feature between semilocal functionals and might be at the origin of the unsettled theoretical description of the orbital state of bulk LaTiO 3 . 88,89 With HSE06, CF = 190 meV which is high compared to the nearly degenerate doublet observed experimentally. 69 This difference probably comes from the higher orthorhombic distortion we observe in our defect-free relaxed structures which is known experimentally to increase with decreasing defect concentration.…”

“…5 shows more details about the O-2p and Ti-3d band separation where the t 2g triplet states 87,88 can be distinguished by their colors. The GdFeO 3 -type distortion causes a large crystal-field splitting ( CF ) defined as the separation between the two first t 2g triplet 035107-6 TABLE IV.…”

Orbital superexchange and crystal field simultaneously at play in YVO3: Resonant inelastic x-ray scattering at the VLedge and the OKedge

“…However, this complex problem has hardly been addressed thus far. [9][10][11][12] Therefore we focus on the two limiting cases, either a dominant crystal field or dominant superexchange interactions. Both, superexchange and the noncubic crystal field lift the threefold orbital degeneracy of the cubic 3 T 1 ground state, giving rise to low-energy intra-t 2g excitations.…”

“…If both, superexchange interactions and the coupling to the lattice are relevant, the spectral signatures become more difficult to interpret, a complex situation that has hardly been studied thus far. [9][10][11][12] The experimental observation of orbitons at low energies 250 meV has been claimed based on Raman data of LaMnO 3 , RTiO 3 , and RVO 3 with R = rare earth. [13][14][15][16][17] However, the orbiton interpretation of these data has caused controversy.…”

Evolution of Co charge disproportionation with Na order inNaxCoO2

“…31 Such effect could explain the recovery of the isotropy of the local wave functions. 30,32 A plausible possibility for the reduction could come from the band structure of the holes in the triangular CoO 2 layers, which would intermix the three planar t 2g orbitals (xy, yz, xz). 33,34 The quantitative description of this situation is a challenge for future theoretical developments.…”