Exact results for itinerant ferromagnetism in a $t_{2g}$ orbital system on cubic and square lattices

Abstract

We study itinerant ferromagnetism in a $t_{2g}$ multi-orbital Hubbard system in the cubic lattice, which consists of three planar oriented orbital bands of $d_{xy}$, $d_{yz}$, and $d_{zx}$. Electrons in each orbital band can only move within a two-dimensional plane in the three-dimensional lattice parallel to the corresponding orbital orientation. Electrons of different orbitals interact through the on-site multi-orbital interactions including Hund's coupling. The strong coupling limit is considered in which there are no doubly occupied orbitals but multiple on-site occupations are allowed. We show that, in the case in which there is one and only one hole for each orbital band in each layer parallel to the orbital orientation, the ground state is a fully spin-polarized itinerant ferromagnetic state, which is unique apart from the trivial spin degeneracy. When the lattice is reduced into a single two-dimensional layer, the $d_{zx}$ and $d_{yz}$ bands become quasi-one-dimensional while the $d_{xy}$ band remains two-dimensional. The ground state ferromagnetism also appears in the strong-coupling limit as a generalization of the double exchange mechanism. Possible applications to the systems of SrRuO${}_3$ and LaAlO${}_3$/SrTiO${}_3$ interface are discussed.

References in corpus (19)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO3/SrTiO3 interface
• Coexistence of Magnetic Order and Two-dimensional Superconductivity at LaAlO${}_3$/SrTiO${}_3$ Interfaces
• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions
• Superconductivity and Ferromagnetism in Oxide Interface Structures: Possibility of Finite Momentum Pairing
• Ferromagnetic exchange, spin-orbit coupling and spiral magnetism at the LaAlO_3/SrTiO_3 interface
• Itinerant Ferromagnetism in an Ultracold Atom Fermi Gas
• Proposed realization of itinerant ferromagnetism in optical lattices
• Phases of the infinite U Hubbard model
• Ground-State Ferromagnetic Transition in Strongly Repulsive One-Dimensional Fermi Gases
• Ferromagnetism in the Hubbard model: A constructive approach
• Ferromagnetism in itinerant two-dimensional t2g systems
• Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices
• Temperature Evolution of Itinerant Ferromagnetism in SrRuO3 Probed by Optical Spectroscopy
• Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: a Quantum Monte Carlo Study
• Metallic ferromagnetism in the Hubbard model: A rigorous example
• Itinerant Ferromagnetism in an Atom Trap
• Itinerant ferromagnetism in a Fermi gas with contact interaction: Magnetic properties in a dilute Hubbard model

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• Fingerprints of spin-orbital polarons and of their disorder in the photoemission spectra of doped Mott insulators with orbital degeneracy
• Sign problem free quantum Monte-Carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets
• Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models
• Anisotropic moiré band flattening in twisted bilayers of M-valley MXenes
• Stability of the Nagaoka-type Ferromagnetic State in a $t_{2g}$ Orbital System on a Cubic Lattice