Ferromagnetism and Superconductivity in the Multi-orbital Hubbard Model: Hund's Rule Coupling versus Crystal-Field Splitting

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of crystal-field splitting △, the fully polarized ferromagnetism, which is observed in the strong coupling regime, becomes unstable against the partially polarized ferromagnetism when Hund's rule coupling J is smaller than a certain critical value of order of △. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between Hund's rule coupling and crystal-field splitting. The superconducting phase with the Luttinger liquid parameter K_ρ> 1 is observed for the singlet ground state in this region..