Abstract
We explore the competiton of doped holes and defects that leads to the loss of orbital order in vanadate perovskites. In compounds such as La$_{1-{\sf x}}$Ca$_{\,\sf x}$VO$_3$ spin and orbital order result from super-exchange interactions described by an extended three-orbital degenerate Hubbard-Hund model for the vanadium $t_{2g}$ electrons. Long-range Coulomb potentials of charged Ca$^{2+}$ defects and $e$-$e$ interactions control the emergence of defect states inside the Mott gap. The quadrupolar components of the Coulomb fields of doped holes induce anisotropic orbital rotations of degenerate orbitals. These rotations modify the spin-orbital polaron clouds and compete with orbital rotations induced by defects. Both mechanisms lead to a mixing of orbitals, and cause the suppression of the asymmetry of kinetic energy in the $C$-type magnetic phase. We find that the gradual decline of orbital order with doping, a characteristic feature of the vanadates, however, has its origin not predominantly in the charge carriers, but in the off-diagonal couplings of orbital rotations induced by the charges of the doped ions.
Highlights
The discovery that doping holes into Mott insulators (MIs), formed by CuO2 layers, not just leads to a metallic state and to the decay of the antiferromagnetic (AF)order, and yields high-temperature superconductivity [1]was a great surprise
We find that the gradual decline of orbital order with doping, a characteristic feature of the vanadates, has its origin not predominantly in the charge carriers, but in the off-diagonal couplings of orbital rotations induced by the charges of the doped ions
The robustness of the insulating state and of the G-type orbital order in the vanadates, observed in several experiments [41], has two main causes: (i) Doped holes are localized by defects and form small spin-orbital polarons
Summary
The discovery that doping holes (or electrons) into Mott insulators (MIs), formed by CuO2 layers, not just leads to a metallic state and to the decay of the antiferromagnetic (AF). It is the coupling to the extra orbital degree of freedom in the vanadates that leads to the quenching of the kinetic energy and to strong localization and binding of polarons by the Coulomb potential of defects This strong localization creates a new puzzle: How is the orbital order destroyed in these compounds?. It was shown that ORs are an effective perturbation as each defect is surrounded by eight nearest vanadium neighbors [see Fig. 1(b)] It yields a natural explanation for the gradual suppression of G-type orbital order in vanadates as function of doping [59], and the absence of clear signatures of collective phase transitions [60]. The Appendix contains further details of the multiorbital Hubbard-Hund interaction, the Jahn-Teller and other small terms, as well as the derivation of the orbital polarization terms
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