Ground State of the Two Orbital Hubbard Model on the Pyrochlore Lattice with Competing Double Exchange and Superexchange Interactions

Abstract

The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials, controlling phase transitions from a ferromagnetic metal to a spin glass metal and then a spin glass (Mott) insulator. We provide a comprehensive description of the ground state of this model using an unrestricted Hartree-Fock scheme implemented via a simulated annealing procedure. We establish the metal-insulator transition line for varying Hubbard interaction and superexchange. The orbital disorder already present in the ferromagnetic case is further enhanced by antiferromagnetic coupling and the resulting magnetic disorder. This suppresses the kinetic energy and shifts the metal-insulator transition to lower Hubbard interaction. We characterise the changing nature of the metal-insulator transition by tracking the magnetic and orbital correlations, the density of states, and the optical conductivity. The metal-insulator transition shows increasing 'Anderson' character as the antiferromagnetic coupling is increased. This paper is focused on the ground state, a companion paper will discuss the finite temperature physics involving magnetic and orbital thermal fluctuations.

Mott transition and anomalous resistive state in the pyrochlore molybdates

“…We opt to handle the problem in real space as follows: (i) We use a Hubbard-Stratonovich (HS) [27][28][29] transformation that decouples U n iα n iβ in terms of an auxiliary orbital moment Γ i (τ ), coupling to O i = µν c † iµ σ µν c iν , and a scalar field Φ i (τ ) coupling to n i at each site [30]. (ii) An exact treatment of the resulting functional integral requires quantum Monte Carlo.…”