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Journal of Physics Conference Series

Nonquasiparticle states in the half-metallic ferromagnet simulated by the two-band Hubbard model

K Nakano, Tomonori Shirakawa, Y. Ohta

Published Jan 1, 2010• 0 citations
Publisher

Abstract

The density-matrix renormalization group method is used to study the three-band zigzag ladder model that simulates the electronic state of the t 2g -orbital system of the double string of the edge-shared CrO 6 octahedra in the half-metallic ferromagnet K 2 Cr 8 O 16 . The saturated ferromagnetism caused by the double-exchange mechanism is thereby demonstrated. We also use the Lanczos exact-diagonalization technique on small clusters to study the two Hubbard chains coupled with the ferromagnetic exchange interaction, whereby we consider the nonquasiparticle states in the half-metallic ferromagnet that appear in the single-particle spectral function.

DOI
10.1088/1742-6596/200/1/012143

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We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet dxy{d}_{xy}dxy​-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet py{p}_{y}py​-wave-like pairing correlation is most dominant.
We examined a one-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping with up to 32 sites by means of the density-matrix renormalization-group method. The model has two energy bands and includes the flat-band model studied by Tasaki as a special case. The model with finite band dispersion is found to show metallic (saturated) ferromagnetism for a sufficiently strong interaction. No partially polarized ground state is found. The interaction necessary to realize a ferromagnetic ground state becomes weak when the electron density is decreased from the quarter-filling.
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 a ladder system with two inequivalent legs, namely, a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density-matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wave numbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.
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).
We study the Hubbard model on three coupled chains which has the saturated ferromagnetic ground states in a finite range of the electron filling factor . In the case that both the single-electron band gap between the highest and lower two bands and the on-site Coulomb interaction are infinitely large, we will rigorously show that the present model exhibits ferromagnetism for 0 < <(1/3), where 0 0 (1/6) depending on the band structure. We will also give numerical results, which indicate that, even in the case that the band gap and the Coulomb interaction are not so large, the present ferromagnetism will survive for suitable electron filling factors.