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

TL;DR

This study investigates how Hund's rule coupling and crystal-field splitting influence ferromagnetism and superconductivity in a one-dimensional multi-orbital Hubbard model, revealing phase transitions and orbital fluctuations.

Contribution

It demonstrates the interplay between Hund's rule coupling and crystal-field splitting in stabilizing different magnetic and superconducting phases in the model.

Findings

Ferromagnetism becomes unstable with decreasing Hund's coupling.

Superconductivity with Luttinger parameter K_rho > 1 observed near ferromagnetic phase.

Orbital fluctuations develop due to competition between Hund's coupling and crystal-field splitting.

Abstract

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