Effective Hamiltonian of Three-orbital Hubbard Model on Pyrochlore Lattice: Application to LiV_2O_4

TL;DR

This paper derives an effective Hamiltonian for a three-orbital Hubbard model on the pyrochlore lattice to understand heavy fermion behavior in LiV_2O_4, revealing competing magnetic interactions and persistent fluctuations.

Contribution

It introduces a low-energy effective Hamiltonian incorporating spin and orbital exchanges for the pyrochlore lattice, advancing understanding of heavy fermion phenomena in LiV_2O_4.

Findings

Competing ferromagnetic and antiferromagnetic exchange processes.

Absence of phase transition down to very low temperatures.

Large fluctuations in spin and orbital sectors at low energies.

Abstract

We investigate heavy fermion behaviors in the vanadium spinel LiV_2O_4. We start from a three-orbital Hubbard model on the pyrochlore lattice and derive its low-energy effective Hamiltonian by an approach of real-space renormalization group type. One important tetrahedron configuration in the rochlore lattice has a three-fold orbital degeneracy and spin S=1, and correspondingly, the effective Hamiltonian has spin and orbital exchange interactions of Kugel-Khomskii type as well as correlated electron hoppings. Analyzing the effective Hamiltonian, we find that ferromagnetic double exchange processes compete with antiferromagnetic superexchange processes and various spin and orbital exchange processes are competing to each other. These results suggest the absence of phase transition in spin and orbital spaces down to very low temperatures and their large fluctuations in the low-energy sector, which are key issues for understanding the heavy fermion behavior in LiV_2O_4.