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arXiv:cond-mat/0211299 · Physical review. B, Condensed matter

Effect of ring exchange on an orbital antiferromagnet

C. H. Chung, Hae‐Young Kee, Yong Baek Kim

Published Jun 10, 2003• 5 citations
arXivHTMLPDF

Abstract

We study the effect of four-particle ring exchange process on an orbital antiferromagnetic state that occurs in some correlated electron systems in two dimensions. The primary question is whether the ring exchange process enhances or suppresses the orbital antiferromagnetic ordering. Using the fact that the orbital antiferromagnetic state arises in the large-$N$ limit of the $\mathrm{SU}(N)$ generalization of the $t\ensuremath{-}J$ model, we consider the large-$N$ limit of the $t\ensuremath{-}J\ensuremath{-}K$ model where K represents the four-particle ring exchange term. The phase diagrams in the large-$N$ mean-field theory are obtained for the half-filling and finite hole concentrations at zero temperature. It is found that the ring exchange in general favors dimerized states or the inhomogeneous orbital antiferromagnetic state and suppresses the homogeneous orbital antiferromagnetic state. We compare our results with other related models of strongly correlated systems with ring exchange processes.

DOI
10.1103/physrevb.67.224405

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We study the effect of four-particle ring exchange process on an orbital antiferromagnetic state that occurs in some correlated electron systems in two dimensions. The primary question is whether the ring exchange process enhances or suppresses the orbital antiferromagnetic ordering. Using the fact that the orbital antiferromagnetic state arises in the large-NNN limit of the SU(N)\mathrm{SU}(N)SU(N) generalization of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model, we consider the large-NNN limit of the t\ensuremath−J\ensuremath−Kt\ensuremath{-}J\ensuremath{-}Kt\ensuremath−J\ensuremath−K model where K represents the four-particle ring exchange term. The phase diagrams in the large-NNN mean-field theory are obtained for the half-filling and finite hole concentrations at zero temperature. It is found that the ring exchange in general favors dimerized states or the inhomogeneous orbital antiferromagnetic state and suppresses the homogeneous orbital antiferromagnetic state. We compare our results with other related models of strongly correlated systems with ring exchange processes.
We study an effective one-dimensional (1-D) orbital $t\text{\ensuremath{-}}J$ model derived for strongly correlated eg{e}_{g}eg​ electrons in doped manganites. The ferromagnetic spin order at half filling is supported by orbital superexchange $\ensuremath{\propto}J$ which stabilizes orbital order with alternating ${x}^{2}\ensuremath{-}{y}^{2}$ and $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals. In a doped system it competes with the kinetic energy $\ensuremath{\propto}t$. When a single hole is doped to a half-filled chain, its motion is hindered and a localized orbital polaron is formed. An increasing doping generates either separated polarons or phase separation into hole-rich and hole-poor regions, and eventually polarizes the orbitals and gives a metallic phase with occupied $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals. This crossover, investigated by exact diagonalization at zero temperature, is demonstrated both by the behavior of correlation functions and by spectral properties, showing that the orbital chain with Ising superexchange is more classical and thus radically different from the 1-D spin $t\text{\ensuremath{-}}J$ model. At finite temperature we derive and investigate an effective 1-D orbital model using a combination of exact diagonalization with classical Monte Carlo for spin correlations. A competition between the antiferromagnetic and ferromagnetic spin order was established at half filling, and localized polarons were found for antiferromagnetic interactions at low hole doping. Finally, we clarify that the Jahn-Teller alternating potential stabilizes the orbital order with staggered orbitals, inducing the ferromagnetic spin order, and enhancing the localized features in the excitation spectra. Implications of these findings for colossal magnetoresistance manganites are discussed.
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We examine the superfluid phase of a hard-core boson model with nearest-neighbor exchange JJJ and four-particle ring-exchange KKK at half filling on the square lattice. At zero temperature we find that the uniform superfluid in the pure-JJJ model is quickly destroyed by the inclusion of negative-KKK ring-exchange interactions, favoring a state with a $(\ensuremath{\pi},\ensuremath{\pi})$ ordering wave vector. Minimization of the mean-field energy suggests that another type of superfluid state, characterized by nonzero bond chirality, is formed. We also study the behavior of the finite-TTT Kosterlitz-Thouless phase transition in the uniform superfluid phase, by forcing the Nelson-Kosterlitz universal jump condition on the finite-TTT spin-wave superfluid density. Away from the pure JJJ point, TKT{T}_{KT}TKT​ decreases rapidly for negative KKK, while for positive KKK, TKT{T}_{KT}TKT​ reaches a maximum at some $K\ensuremath{\ne}0$ in agreement with recent quantum Monte Carlo simulations.
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An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region and a suppression in the composite ordered phase. The doping-dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro-orbital order dominates the filling range $2\ensuremath{\lesssim}n\ensuremath{\le}3$ and ferro-orbital order dominates the strongly interacting region for $1\ensuremath{\lesssim}n<2$, we find superconductivity with a remarkably high Tc{T}_{c}Tc​ around n=1.5n=1.5n=1.5 (quarter filling). Also in the doped system, there is a close connection between the orbital-freezing crossover and superconductivity.