Broken Symmetry States of Doubly Degenerate Orbital Systems with Cubic Structure—Group Theoretical Classification

Abstract

For the e_g Hubbard model on a simple cubic lattice group theoretical classification of mean field solutions have been made by assuming four kinds of single-Q wave vectors (0,0,0), (0,0,π), (π,π,0) and (π,π,π), and collinear magnetic states. Twenty-one broken symmetry states have been obtained in detail. Besides the usual charge and spin ordering states the so-called orbital orders of the two e_g states, φ₁=(3z²−r²)⁄\\sqrt3 and φ₂=x²−y², or their linear combinations have been derived. It is shown that the broken symmetry states corresponding to ordering of the complex orbital states Ψ₁=\\frac1\\sqrt2(φ₁−iφ₂) and Ψ₂=\\frac1\\sqrt2(φ₁+iφ₂) represent octupole ordering. Finally quite exotic broken symmetry states consisting of combination of charge, spin and orbital orderings are derived.