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arXiv:cond-mat/9912273 · Physical Review Letters

Spin-1 Chain Doped with Mobile S=1/2 Fermions

Beat Ammon, Masatoshi Imada

Published Jul 31, 2000• 11 citations
arXivHTMLPDF

Abstract

We investigate the doping of a two-orbital chain with mobile $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ fermions as a valid model for ${\mathrm{Y}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{BaNiO}}_{5}$. The $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ spins are stabilized by strong, ferromagnetic Hund's rule couplings. We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Gapless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ chain accompanied by a finite string order parameter.

DOI
10.1103/physrevlett.85.1056

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We investigate the doping of a two-orbital chain with mobile S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 fermions as a valid model for Y2\ensuremath−xCaxBaNiO5{\mathrm{Y}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{BaNiO}}_{5}Y2\ensuremath−x​Cax​BaNiO5​. The S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 spins are stabilized by strong, ferromagnetic Hund's rule couplings. We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Gapless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 chain accompanied by a finite string order parameter.
Different models for doping of two-orbital chains with mobile S=1/2S=1/2S=1/2 fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with a level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.
Doping of a two-orbital chain with mobile S=1/2 Fermions and strong Hund's rule couplings stabilizing the S=1 spins strongly depends on the presence of a level difference among these orbitals. By DMRG methods we find a finite spin gap upon doping and dominant pairing correlations without level-difference, whereas the presence of a level difference leads to dominant charge density wave (CDW) correlations with gapless spin-excitations. The string correlation function also shows qualitative differences between the two models.
We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths UUU and for degenerate orbitals. At half filling and large UUU, the ferromagnetic Hund's coupling, JH{J}_{\mathrm{H}}JH​, generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U=1.6U=1.6U=1.6 in units of the noninteracting bandwidth and for ${J}_{\mathrm{H}}/U\ensuremath{\gtrsim}0.275$, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.
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.
A proper theoretical description of doped antiferromagnets is until now an unresolved issue. In this work we study chain and ladder systems, and in particularly we focus on the physically most interesting two leg ladder. Our starting point is the Spin Fermion model in which an antiferromagnetic background of localized spins interacts with mobile holes via a rotation invariant Kondo-like term. The interesting region of the phase diagram is that close to the Mott-insulator transition where the doping delta is zero. At zero doping in fact the system is an insulator and the spins organize themselves in a spin liquid, a rotational invariant state characterized by a finite correlation length and an energy gap (a spin gap) above the ground state. Such a state is also the ground state of a field theory, the non linear sigma model (NLsigmaM) which is recognized as the low energy effective theory for antiferromagnetic spin ladder. The first question we answer is how such a spin state evolves as one moves off from the Mott phase by increasing the doping. Integrating out the fermions in our model we obtain an effective theory for the spins which we are able to evaluate in the continuum limit. The effective theory is again a NLsigmaM with coupling constants which depend on the concentration of dopant holes. In contrast to existing mean field calculation our theory predicts a lowering of the spin gap with doping and a consequent increase in the correlation length. Indeed a lowering of the spin gap due to doping is also observed in numerical simulation and on NMR experiments on $Sr14-xCaxCu24O41 with which we obtain very good agreement. Secondly we concentrated on the behavior of the fermions. The general paradigm of interacting fermions in one dimension is that of the Luttinger Liquid characterized by bosonic excitations and spin charge separation. By generalizing our approach we are able to access the one particle fermion propagator as a quantity averaged over the NLsigmaM which controls the spin background. We see that in the limit of zero doping the quasiparticle weight Z is non-zero in a neighborhood of the Fermi energy. This in turn implies that the Luttinger liquid parameter Krho goes to one as the doping delta goes to zero as was first argued by Schulz. Our stronger result allows us to assert that in the very low doping regime the fermions constitute a Fermi liquid.
Using the density matrix renormalization-group technique, we calculate the impurity energy levels for two different effective models of off-chain doping for quasi-one-dimensional Heisenberg chain compound Y2BaNiO5:{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5}:Y2​BaNiO5​: ferromagnetic bond doping and antiferromagnetic site spin-1/2 doping. Thresholds of the impurity strength for the appearance of localized states are found for both models. However, the ground-state and low-energy excitations for weak impurity strength are different for these two models and the difference can be detected by experiments.