The kinetic exchange interaction in doubly degenerate narrow bands

Abstract

AbstractA canonical transformation is applied to the doubly‐degenerate‐band Hubbard model with arbitrary n in the strong correlation regime. Projection operators are constructed to project out the splitted subbands. Only the inter‐subband electron hopping is treated as a perturbation which couples different subbands at the second order. In localized picture the coupling is of the Heisenberg type, corresponding to the virtual hopping of electrons and generating the spin waves, the orbital waves, and the coupled spin‐orbital waves. For n = 1 the ground state has ferromagnetic spin and antiferromagnetic orbital ordering. For n = 2 the spins in the ground state have ferromagnetic intra‐site but antiferromagnetic inter‐site ordering. These orderings are due to Hund's rule, the effect of which gets weakened by the intra‐subband electron hopping as n deviates from an integer. This canonical‐transformed effective Hamiltonian is suitable for investigating the phase diagram of the Hubbard model with orbital degeneracy.