Hidden Symmetries and their Consequences in $t_{2g}$ Cubic Perovskites

Abstract

The five-band Hubbard model for a $d$ band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e. g. cubic) symmetry. In that case, if the crystal field splitting is large one may consider excitations confined to the lowest threefold degenerate $t_{2g}$ orbital states. When the electron hopping matrix element ($t$) is much smaller than the on-site Coulomb interaction energy ($U$), the Hubbard model can be mapped onto the well-known effective Hamiltonian (at order $t^2/U$) derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support long range spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying three-band Hubbard model. Using these symmetries we develop a rigorous Mermin-Wagner construction, which shows that the three-band Hubbard model does not support spontaneous long-range spin order at any nonzero temperature and at any order in $t/U$ -- despite the three-dimensional lattice structure. Introduction of spin-orbit coupling does allow spin ordering, but even then the excitation spectrum is gapless due to a subtle continuous symmetry. Finally we showed that these hidden symmetries dramatically simplify the numerical exact diagonalization studies of finite clusters.

26 pages, 3 figures, 520 KB, submitted Phys. Rev. B

References in corpus (5)

• Magnetic Order and Dynamics in an Orbitally Degenerate Ferromagnetic Insulator
• Quantum behavior of Orbitals in Ferromagnetic Titanates: Novel Orderings and Excitations
• Unusual Symmetries in the Kugel-Khomskii Hamiltonian
• Magnetic Ordering, Orbital Ordering and Resonant X-ray Scattering in Perovskite Titanates
• Damped orbital excitations in the titanates

Cited by in corpus (14)

• Orbital Physics in the Perovskite Ti Oxides
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• Novel magnetic state in $d^4$ Mott insulators
• Theory of Half-metallic Ferrimagnetism in Double Perovskites
• Theory of Half-Metallic Double Perovskites I: Double Exchange Mechanism
• Optical study of orbital excitations in transition-metal oxides
• Orbital liquid in ferromagnetic manganites: The orbital Hubbard model for $e_g$ electrons
• Theory of Half-Metallic Double Perovskites II: Effective Spin Hamiltonian and Disorder Effects
• The magnetic structure of the Jahn-Teller System LaTiO3
• Orbitally induced string formation in the spin-orbital polarons
• Orbital order, stacking defects and spin-fluctuations in the $p$-electron molecular solid RbO${}_2$
• Spin-orbital locked magnetic excitations in a half-metallic double perovskite Ba2FeReO6
• The spin-wave spectrum of the Jahn-Teller system LaTiO3
• Landau Expansion for the Kugel-Khomskii $t_{2g}$ Hamiltonian