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arXiv:cond-mat/0304620 · Journal of the Physical Society of Japan

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

Kazuhiro Sano, Yoshiaki Ōno

Published Aug 15, 2003• 18 citations
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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 $Δ$, 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 $Δ$. 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 $K_ρ>1$ is observed for the singlet ground state in this region.

DOI
10.1143/jpsj.72.1847

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The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting ΔΔΔ, 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 JJJ is smaller than a certain critical value of order of ΔΔΔ. 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 Kρ>1K_ρ>1Kρ​>1 is observed for the singlet ground state in this region.
Using the numerical diagonalization method, we investigate the ferromagnetism and the superconductivity in the multi-orbital Hubbard model in one-dimension. To examine the superconductivity, we calculate the critical exponent Kρ based on the Luttinger liquid theory and the anomalous flux quantization in the superconducting region. Analyzing the value of Kρ, we obtain the phase diagram on the U′ - J parameter plane including the superconducting phase and the fully polarized ferromagnetic phase.
Using the numerical diagonalization method, we investigate superconductivity and related ferromagnetism in the one-dimensional two-orbital Hubbard model with a finite band splitting at less than half filling. We obtain superconducting (SC) region with the Luttinger liquid parameter Kρ > 1 and confirm anomalous flux quantization in the SC state. It is found that the SC phase appears near partially polarized ferromagnetic phase. We also calculate various pairing correlation functions to clarify the nature of the SC phase. Detailed analysis of these functions indicates that the triplet pairing between the nearest neighbor sites is relevant to the superconductivity. It suggests that the ferromagnetic fluctuation plays an important role for the superconductivity.
Using the numerical diagonalization method, we investigate superconductivity and related ferromagnetism in the one-dimensional two-orbital Hubbard model with a finite band splitting at less than half filling. We obtain superconducting (SC) region with the Luttinger liquid parameter Kρ and confirm anomalous flux quantization in the SC statenear partially polarized ferromagnetic phase. We also calculate various pairing correlation functions to clarify the nature of the SC phase. Detailed analysis of these functions indicates that the triplet pairing between the nearest neighbor sites is relevant to the superconductivity.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75)(0<n<1.75)(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1),(n=1),(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1),(n<1),(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1),(n>1),(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).(n=2).(n=2).
Role of the double exchange for appearance of partial ferromagnetism in a semimetal is explored for a semimetallic two-band Hubbard model in one-dimension. In a strong coupling limit, a ferromagnetic exchange interaction between two neighboring triplet excitons becomes dominant compared with anti-ferromagnetic couplings and a partial spin polarization is shown to appear. Exact evaluation of magnetization is possible for the partially ferromagnetic ground state in this limit. Obtained phase diagram has a doping dependence similar to our DMRG results for finite interactions. The ferromagnetism is favored in semimetallic systems by the interplay of the intra-orbital Coulomb repulsion and the inter-orbital Hund-rule coupling.
We investigate the effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising-type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.