Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a non-frustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This counterintuitive result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The mechanism proposed here should be common to other correlated oxides as well. PACS numbers: 75.10.Jm, 75.30.Ds, 78.70.Nx Impurities are known to be an effective tool to locally perturb quantum systems, thereby revealing important information about their microscopic interactions and correlations [1]. A well studied example of a strongly correlated quantum system in which effects of such impurity doping can be investigated is La 2 CuO 4 -one of the most important cuprate superconductor parent compounds. In its pristine form, this material is a two-dimensional (2D) spin-1 2 Heisenberg antiferromagnet (AF) [2]. It is believed that the substitution of Cu 2+ (S = 1 2 ) ions by spinless Zn 2+ represents a good realization of the site-diluted Heisenberg hamiltonian [3,4,5,6]. In this Letter, we demonstrate that there exists a significant qualitative correction to the dilution picture. Impurities can induce substantial frustrating interactions between nearby spins. Not only does this effect explain discrepancies between experimental data and the dilution-only theories for La 2 Cu 1−x Zn x O 4 , but it may also be important for a variety of other phenomena in diluted magnets and doped Mott insulators. Our mechanism for such an effect should be common to many charge-transfer insulators, including oxides of transition metals.We propose that the presence of extra degrees of freedom due to oxygen orbitals necessarily results in frustrating terms in the corresponding low-energy spin hamiltonian of the Zndoped system, which are absent in the dilution-only models. Utilizing quantum Monte Carlo (QMC) and analytic T -matrix approaches, we calculate the doping dependence of the staggered magnetization for such a low-energy model. We show that this model, with the parameters appropriate for the CuO 2 planes given by a three-band Hubbard model calculation, naturally explains experimental data.Experiments and theories.-Comprehensive studies of the problem of La 2 CuO 4 diluted by spinless Zn impurities have been performed using neutron scattering, magnetometry, and NMR (NQR) on the experimental side [3,4], and QMC and T -matrix approaches of the diluted Heisenberg model on the theoretical side [5,6,7]. These studies allow for extensive cross-checks. The unbiased QMC data agree with the Tmatrix results closely up to x ≃ 15%, supporting the validity of the latter in the low-doping regime [5,6]. However, there are serious discrepancies between theoretical and experimental results. Fig. 1 shows the average magnetic moment M per Cu site versus the Zn doping fraction x. The experimental data a...
We study the effect of spin anisotropies on a frustrated quantum antiferromagnet using the J1-J XXZ 2 model on the square lattice. The T = 0 and finite-T phase diagrams of this model are obtained utilizing spin-wave theory, exact diagonalization, and quantum Monte Carlo. We find that anisotropic frustration tends to stabilize XY -and Ising-like ordered phases, while the disordered spin-liquid phase is restricted to a small region of the phase diagram. The ordered phases are separated by first-order transitions and exhibit a non-trivial reentrance phenomenon.
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. To obtain the low-energy effective model, we first determine hybridized electronic states of CuO4 and ZnO4 plaquets within the CuO2 planes. Qualitatively, we find that the hybridization of zinc and oxygen orbitals can result in an impurity state with the energy ε, which is lower than the effective Hubbard gap U . In the limit of the effective hopping integral t ≪ ε, U , the low-energy, spin-only Hamiltonian includes terms of the order t 2 /U and t 4 /ε 3 . That is, besides the usual nearest-neighbor superexchange Jterms 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, denoted as J ′ Zn and J ′′ Zn , are of order t 4 /ε 3 and can be substantial when ε ∼ 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.
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