Impurity-induced frustration: low-energy model of diluted oxides

Abstract

We provide a detailed derivation of the low-energy model for Zn-diluted La2CuO4 in the limit of low doping together with a study of the ground-state properties of that model. We consider Zn-doped La2CuO4 within a framework of the three-band Hubbard model, which closely describes high-Tc cuprates on the energy scale of the most relevant atomic orbitals. Qualitatively, we find that the hybridization of zinc and oxygen orbitals can result in an impurity state with the energy \varepsilon, which is lower than the effective Hubbard gap U. The low-energy, spin-only Hamiltonian includes terms of the order t^2/U and t^4/\varepsilon^3. That is, besides the usual nearest-neighbor superexchange J-terms of order t^2/U, the low-energy model contains impurity-mediated, further-neighbor frustrating interactions among the Cu spins surrounding Zn-sites in an otherwise unfrustrated antiferromagnetic background. These terms can be substantial when \varepsilon ~ U/2, the latter value corresponding to the realistic CuO2 parameters. In order to verify this spin-only model, we subsequently apply the T-matrix approach to study the effect of impurities on the antiferromagnetic order parameter. Previous theoretical studies, which include only the dilution effect of impurities, show a large discrepancy with experimental data in the doping dependence of the staggered magnetization at low doping. We demonstrate that this discrepancy is eliminated by including impurity-induced frustrations into the effective spin model with realistic CuO2 parameters. Recent experimental study shows a significantly stronger suppression of spin stiffness in the case of Zn-doped La2CuO4 compared to the Mg-doped case and thus gives a strong support to our theory. We argue that the proposed impurity-induced frustrations should be important in other strongly correlated oxides and charge-transfer insulators.

arXiv comment16 pages, 12 figures, related work: arXiv:0812.1023, a few clarifications added, published version

References in corpus (31)

• Correlated Electrons in High Temperature Superconductors
• Local Ordering in the Pseudogap State of the High-T${}_c$ Superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Quantum Impurities in the Two-Dimensional Spin One-Half Heisenberg Antiferromagnet
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Independent freezing of charge and spin dynamics in La1.5Sr0.5CoO4
• Consistent low-energy reduction of the three-band model for copper oxides with O-O hopping to the effective t-J model
• Quantum Phase Transition of Randomly-Diluted Heisenberg Antiferromagnet on a Square Lattice
• Diluted quantum antiferromagnets: spin excitations and long-range order
• Higher order effective low-energy theories
• Generalized $t$-$t^{\prime }$-$J$ model: parameters and single-particle spectrum for electrons and holes in copper oxides
• Low energy theory of the t-t'-t''-U Hubbard Model at half-filling: interaction strengths in cuprate superconductors and an effective spin-only description of La_2CuO_4
• Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet
• Non-magnetic Impurities in Spin Gap Systems
• Reduction of three-band model for copper oxides to single-band generalized t~-~J model
• Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet
• Range of the t--J model parameters for CuO${}_2$ plane: experimental data constraints
• Excitations and Quantum Fluctuations in Site Diluted Two-Dimensional Antiferromagnets
• Ab Initio Calculation of Impurity Effects in Copper Oxide Materials
• Long-range order and low-energy spectrum of diluted 2D quantum AF
• Magnetic properties of spin diluted iron pnictides from muSR and NMR in LaFe1-xRuxAsO
• Spin Dilution in Frustrated Two-Dimensional s=1/2 Antiferromagnets on a Square Lattice
• Impurity-induced frustration in correlated oxides
• Neutron Scattering, Magnetometry, and Quantum Monte Carlo Study of the Randomly-Diluted Spin-1/2 Square-Lattice Heisenberg Antiferromagnet
• Spin Dependence of the Critical Concentration for the Neel State of 2D Impure Heisenberg Antiferromagnets
• Evidence for impurity-induced frustration in La2CuO4
• Microscopic Hamiltonian for Zn or Ni substituted high temperature cuprate superconductors
• Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4
• On the Self-Consistent Spin-Wave Theory of Two-Dimensional Magnets With Impurities
• Theoretical Analysis of the Reduction of Neel Temperature in La${}_2$(Cu${}_{1-x}$Zn(or Mg)${}_x)$O${}_4$

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• Magnetic phase diagram of low-doped La{2-x}SrxCuO4 thin films studied by low-energy muon-spin rotation
• Magnetic structure of the frustrated S=1/2 chain magnet LiCu2O2 doped with nonmagnetic Zn
• Influence of applied electric and magnetic fields on a thermally-induced reentrance of a coupled spin-electron model on a decorated square lattice
• Magnetic order and disorder in a quasi-two-dimensional quantum Heisenberg antiferromagnet with randomized exchange
• The influence of further-neighbor spin-spin interaction on a ground state of 2D coupled spin-electron model in a magnetic field
• Magnetic properties of LiCu${}_3$O${}_3$ -- quasi-two-dimensional antiferromagnet on depleted square lattice