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

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.

arXiv comment26 pages, 26 figures

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• Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
• Spin-orbit fluctuations in frustrated heavy-fermion metal LiV${}_2$O${}_4$
• Magnetic molecular orbitals in MnSi
• Charge-spin-orbital Fluctuations in Mixed Valence Spinels: Comparative Study of AlV2O4 and LiV2O4
• Microscopic theory of Dzyaloshinsky-Moriya interaction in pyrochlore oxides with spin-orbit coupling
• Epitaxial growth and scanning tunneling microscopy of LiV${}_2$O${}_4$ thin films on SrTiO${}_3$(111)