Spin-1 effective Hamiltonian with three degenerate orbitals: An application to the case of V2O3

Abstract

Motivated by recent neutron and x-ray observations in V2O3, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t2g states containing two electrons coupled to spin S = 1, and use it to re-examine the low-temperature ground-state properties of this compound. An axial trigonal distortion of the cubic states is also taken into account. Since there are no assumptions about the symmetry properties of the hopping integrals involved, the resulting spin-orbital Hamiltonian can be generally applied to any crystallographic configuration of the transition metal ion giving rise to degenerate t2g orbitals.Specializing to the case of V2O3 we consider the low temperature antiferromagnetic insulating phase. We find two variational regimes, depending on the relative size of the correlation energy of the vertical pairs and the in-plane interaction energy. The former favors the formation of stable molecules throughout the crystal, while the latter tends to break this correlated state. Using the appropriate variational wave functions we determine in both cases the minimizing orbital solutions for various spin configurations, compare their energies and draw the corresponding phase diagrams in the space of the relevant parameters of the problem. We find that none of the symmetry-breaking stable phases with the real spin structure presents an orbital ordering compatible with the magnetic space group indicated by very recent observations of non-reciprocal x-ray gyrotropy in V2O3. We do however find a compatible solution with very small excitation energy in two distinct regions of the phase space, which might turn into the true ground state of V2O3 due to the favorable coupling with the lattice. We illustrate merits and drawbacks of the various solutions and discuss them in relation to the present experimental evidence.

Application of theS=1underscreened Anderson lattice model to Kondo uranium and neptunium compounds

“…30,31 This model describes the Kondo interaction, J K , between localized S=1 spins and s = 1/2 spins of conduction electrons, and an inter-site ferromagnetic exchange interaction between the f -spins, J H . The mean-field treatment of the UKL model gives an analog of the Doniach phase diagram, and qualitatively accounts for the coexistence of ferromagnetism and Kondo effect.…”

On the Nature of the Magnetic Ground-State Wave Function of V2O3

“…My answer is negative, and is motivated by the results of Refs. 16,24,25,26 , that I summarize here.…”

“…Soon after, its experimental detection was claimed to be found 13 . The subsequent theoretical and experimental debate led to the abandonment of the CNR model, that was based on a spin S V = 1/2 on each vanadium ion and thus in contradiction with the experimental result of S V = 1 13,14 , in favour of a picture where the two nearest V-ions are linked together in a stable molecule with spin S M = 2 15,16,17 . This picture has been recently criticized by Elfimov et al 18 .…”

Slave boson theory for transport through magnetic molecules with vibronic states

“…Following Refs. [39,40] we define two states with quantum numbers i = 1, 2 and σ =↑, ↓ . The operators f † iσ create a fermion in these states.…”