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arXiv:cond-mat/9711229 · Physical review. B, Condensed matter

Effect of spin-1 impurities in dimerized Heisenberg chains

P. Hansen, José A. Riera, A. Delia, Elbio R. Dagotto

Published Sep 1, 1998• 6 citations
arXivHTMLPDF

Abstract

The effects of spin-1 impurities introduced in dimerized antiferromagnetic spin chains are studied using Lanczos diagonalization and quantum Monte Carlo simulations. First, the magnitude of the interaction between a Ni ion replacing a Cu ion is derived for the case study system Cu-O-Cu. Then, it is shown that the introduction of $S=1$ impurities leads to the suppression of the original spin gap of the dimerized system and to the enhancement of the antiferromagnetic correlations close to the impurity. These features are interpreted in terms of a valence bond picture of the ground state of both the pure and the doped system. The similitudes and differences between the underlying mechanisms that produce these effects in the cases of nonmagnetic and $S=1$ impurities are analyzed. It is stressed that a singlet formed between the spin-1 impurity site and the two spin-1/2 neighbors spins behaves as an effective nonmagnetic vacancy which may be partially responsible for the enhancement of the antiferromagnetic correlations on the whole system. Implications of these results for experiment are also discussed.

DOI
10.1103/physrevb.58.6258

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The effects of spin-1 impurities introduced in dimerized antiferromagnetic spin chains are studied using Lanczos diagonalization and quantum Monte Carlo simulations. First, the magnitude of the interaction between a Ni ion replacing a Cu ion is derived for the case study system Cu-O-Cu. Then, it is shown that the introduction of S=1S=1S=1 impurities leads to the suppression of the original spin gap of the dimerized system and to the enhancement of the antiferromagnetic correlations close to the impurity. These features are interpreted in terms of a valence bond picture of the ground state of both the pure and the doped system. The similitudes and differences between the underlying mechanisms that produce these effects in the cases of nonmagnetic and S=1S=1S=1 impurities are analyzed. It is stressed that a singlet formed between the spin-1 impurity site and the two spin-1/2 neighbors spins behaves as an effective nonmagnetic vacancy which may be partially responsible for the enhancement of the antiferromagnetic correlations on the whole system. Implications of these results for experiment are also discussed.
Spin models that have been proposed to describe dimerized chains, ladders, two-dimensional antiferromagnets, and other compounds are studied here when some spins are replaced by spinless vacancies, such as it occurs by Zn doping. A small percentage of vacancies rapidly destroys the spin gap, and their presence induces enhanced antiferromagnetic correlations near those vacancies. The study is performed with computational techniques which includes Lanczos, world-line Monte Carlo, and the density-matrix renormalization-group methods. Since the phenomenon of enhanced antiferromagnetism is found to occur in several models and cluster geometries, a common simple explanation for its presence may exist. It is argued that the resonating-valence-bond character of the spin correlations at short distances of a large variety of models is responsible for the presence of robust staggered spin correlations near vacancies and lattice edges. The phenomenon takes place regardless of the long distance properties of the ground state, and it is caused by a ``pruning'' of the available spin singlets in the vicinity of the vacancies. The effect produces a broadening of the low-temperature NMR signal for the compounds analyzed here. This broadening should be experimentally observable in the structurally dimerized chain systems $\mathrm{Cu}({\mathrm{NO}}_{3}{)}_{2}\ensuremath{\cdot}2.5{\mathrm{H}}_{2}\mathrm{O}$, CuWO4{\mathrm{CuWO}}_{4}CuWO4​, (VO)2P2O7(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}(VO)2​P2​O7​, and Sr14Cu24O41,{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},Sr14​Cu24​O41​, in ladder materials such as SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​, in the spin-Peierls systems CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ and NaV2O5{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}NaV2​O5​, and in several others since it is a universal effect common to a wide variety of models and compounds. In addition, it is argued that the N\'eel order observed in SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ upon Zn doping is induced by the local antiferromagnetic order discussed in this paper, enhanced by a favorable ratio between the actual Heisenberg couplings along chains and rungs, as reported in recent experimental literature. Based on this reasoning it is predicted here that other ladder materials such as Zn-doped Cu2(C5H12N2)2Cl4{\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}Cu2​(C5​H12​N2​)2​Cl4​ will not present N\'eel order at small Zn concentrations.
We are considering the interplay between several non-magnetic impurities in the spin-(1/2) Heisenberg antiferromagnet in chains, ladders and planes by introducing static vacancies in numerical quantum Monte Carlo simulations. The effective potential between two and more impurities is accurately determined, which gives a direct measure of the quantum correlations in the systems. Large effective interaction potentials are an indication of strong quantum correlations in the system and reflect the detailed nature of the valence bond ground states. In two-dimensions (2D) the interactions are smaller, but can still be analyzed in terms of valence bonds.
We are considering the interplay between several non-magnetic impurities in the spin-(1/2) Heisenberg antiferromagnet in chains, ladders and planes by introducing static vacancies in numerical quantum Monte Carlo simulations. The effective potential between two and more impurities is accurately determined, which gives a direct measure of the quantum correlations in the systems. Large effective interaction potentials are an indication of strong quantum correlations in the system and reflect the detailed nature of the valence bond ground states. In two-dimensions (2D) the interactions are smaller, but can still be analyzed in terms of valence bonds.
Low-lying excited states as well as the ground state of the spin-1 antiferromagnetic Heisenberg chain with a spin-1/2 impurity are studied by means of a method of numerical diagonalization. The isotropic nearest-neighbor exchange coupling plus the uniaxial single-ion-type anisotropy energy is assumed for the host-system Hamiltonian. The energy differences between the ground state and the low-lying excited states, which appear in the Haldane gap, are estimated in the thermodynamic limit. The results are used to analyze the electron-spin-resonance experimental data on Ni(C2_22​H8_88​N2_22​)2_22​NO2_22​(ClO4_44​), abbreviated NENP, containing a small amount of spin-1/2 Cu2+^{2+}2+ impurities. It is found that in this system, the impurity-host (\bigl((Cu2+^{2+}2+-Ni2+^{2+}2+)\bigr)) coupling is ferromagnetic and its magnitude is about 5 \,\% of the magnitude of the host-host (\bigl((Ni2+^{2+}2+-Ni2+^{2+}2+)\bigr)) coupling.
The influence of nonmagnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ is studied. A simple extension to Zn-doped Sr Cu2{\mathrm{Cu}}_{2}Cu2​ O3{\mathrm{O}}_{3}O3​ is also discussed. Using exact diagonalization techniques and intuitive arguments we show that Zn doping introduces states in the spin-Peierls gap of CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​. This effect can be understood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn doping according to the numerical data presented here. As recent numerical calculations have shown, similar arguments apply to ladders with nonmagnetic impurities simply replacing the tendency to dimerization in CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ by the tendency to form spin singlets along the rungs in SrCu2{\mathrm{SrCu}}_{2}SrCu2​O3{\mathrm{O}}_{3}O3​. \textcopyright{} 1996 The American Physical Society.
The doping of quantum Heisenberg antiferromagnets on the kagome lattice by nonmagnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing (a) the valence-bond crystal (VBC), (b) the dimer liquid, and (c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the kagome lattice to account for spontaneous creation of mobile S=1/2S=1/2S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos exact diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small-size spinon-impurity bound state appears in some region of the dimer-liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the valence-bond glass scenario [R. R. P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the nuclear magnetic resonance spectra of the Herbertsmithite compound are outlined.