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arXiv:cond-mat/0310645 · Physical Review B

Comparison of S=0 and S=12 impurities in the Haldane chain compound Y2BaNiO5

J. Das, A. V. Mahajan, Julien Bobroff, H. Alloul, Fabien Alet, Erik Schwartz Sørensen

Published Apr 2, 2004• 44 citations
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Abstract

We present the effect of Zn $(S=0)$ and Cu $(S=1/2)$ substitution at the Ni site of $S=1$ Haldane chain compound ${\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5}.$ ${}^{89}\mathrm{Y}$ nuclear-magnetic resonance (NMR) allows us to measure the local magnetic susceptibility at different distances from the defects. The ${}^{89}\mathrm{Y}$ NMR spectrum consists of one central peak and several less intense satellite peaks. The central peak represents the chain sites far from the defect. Its shift measures the uniform susceptibility, which displays a Haldane gap $\ensuremath{\Delta}\ensuremath{\approx}100\mathrm{K}$ and it corresponds to an antiferromagnetic (AF) coupling $J\ensuremath{\approx}260\mathrm{K}$ between the nearest neighbor Ni spins. Zn or Cu substitution does not affect the Haldane gap. The satellites, which are evenly distributed on the two sides of the central peak, probe the antiferromagnetic staggered magnetization near the substituted site. The spatial variation of the induced magnetization is found to decay exponentially from the impurity for both Zn and Cu for $T>50\mathrm{K}.$ Its extension is found identical for both impurities and corresponds accurately to the correlation length $\ensuremath{\xi}(T)$ determined by Monte Carlo simulations for the pure compound. In the case of nonmagnetic Zn, the temperature dependence of the induced magnetization is consistent with a Curie law with an ``effective'' spin $S=0.4$ on each side of Zn. This staggered effect is quantitatively well accounted for in all the explored range by quantum Monte Carlo (QMC) computations of the spinless-defect-induced magnetism. In the case of magnetic Cu, the similarity of the induced magnetism to the Zn case implies a weak coupling of the Cu spin to the nearest-neighbor Ni spins. The slight reduction of about $20\ensuremath{-}30%$ of the induced polarization with respect to Zn is reproduced by QMC computations by considering an antiferromagnetic coupling of strength ${J}^{\ensuremath{'}}=0.1J\ensuremath{-}0.2J$ between the $S=1/2$ Cu spin and nearest-neighbor Ni spin. Macroscopic susceptibility measurements confirm these results as they display a clear Curie contribution due to the impurities nearly proportional to their concentration. This contribution is indeed close to that of two spin half for Zn substitution. The Curie contribution is smaller in the Cu case, which confirms that the coupling between Cu and near-neighbor Ni is antiferromagnetic.

DOI
10.1103/physrevb.69.144404

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We present the effect of Zn (S=0)(S=0)(S=0) and Cu (S=1/2)(S=1/2)(S=1/2) substitution at the Ni site of S=1S=1S=1 Haldane chain compound Y2BaNiO5.{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5}.Y2​BaNiO5​. 89Y{}^{89}\mathrm{Y}89Y nuclear-magnetic resonance (NMR) allows us to measure the local magnetic susceptibility at different distances from the defects. The 89Y{}^{89}\mathrm{Y}89Y NMR spectrum consists of one central peak and several less intense satellite peaks. The central peak represents the chain sites far from the defect. Its shift measures the uniform susceptibility, which displays a Haldane gap \ensuremathΔ\ensuremath≈100K\ensuremath{\Delta}\ensuremath{\approx}100\mathrm{K}\ensuremathΔ\ensuremath≈100K and it corresponds to an antiferromagnetic (AF) coupling J\ensuremath≈260KJ\ensuremath{\approx}260\mathrm{K}J\ensuremath≈260K between the nearest neighbor Ni spins. Zn or Cu substitution does not affect the Haldane gap. The satellites, which are evenly distributed on the two sides of the central peak, probe the antiferromagnetic staggered magnetization near the substituted site. The spatial variation of the induced magnetization is found to decay exponentially from the impurity for both Zn and Cu for T>50K.T>50\mathrm{K}.T>50K. Its extension is found identical for both impurities and corresponds accurately to the correlation length \ensuremathξ(T)\ensuremath{\xi}(T)\ensuremathξ(T) determined by Monte Carlo simulations for the pure compound. In the case of nonmagnetic Zn, the temperature dependence of the induced magnetization is consistent with a Curie law with an ``effective'' spin S=0.4S=0.4S=0.4 on each side of Zn. This staggered effect is quantitatively well accounted for in all the explored range by quantum Monte Carlo (QMC) computations of the spinless-defect-induced magnetism. In the case of magnetic Cu, the similarity of the induced magnetism to the Zn case implies a weak coupling of the Cu spin to the nearest-neighbor Ni spins. The slight reduction of about 20\ensuremath−3020\ensuremath{-}30%20\ensuremath−30 of the induced polarization with respect to Zn is reproduced by QMC computations by considering an antiferromagnetic coupling of strength J\ensuremath′=0.1J\ensuremath−0.2J{J}^{\ensuremath{'}}=0.1J\ensuremath{-}0.2JJ\ensuremath′=0.1J\ensuremath−0.2J between the S=1/2S=1/2S=1/2 Cu spin and nearest-neighbor Ni spin. Macroscopic susceptibility measurements confirm these results as they display a clear Curie contribution due to the impurities nearly proportional to their concentration. This contribution is indeed close to that of two spin half for Zn substitution. The Curie contribution is smaller in the Cu case, which confirms that the coupling between Cu and near-neighbor Ni is antiferromagnetic.
We present a 31P^{31}\text{P}31P NMR study of the coupled spin 12\frac{1}{2}21​ ladder compound BiCu2PO6{\text{BiCu}}_{2}{\text{PO}}_{6}BiCu2​PO6​. In the pure material, intrinsic susceptibility, and dynamics show a spin gap of about $\ensuremath{\Delta}\ensuremath{\approx}35--40\text{ }\text{K}$. Substitution of nonmagnetic Zn or magnetic Ni impurity at Cu site induces a staggered magnetization which results in a broadening of the 31P^{31}\text{P}31P NMR line while susceptibility far from the defects is unaffected. The effect of Ni on the NMR line broadening is twice that of Zn, which is consistent with quantum Monte Carlo calculations assuming that Ni couples ferromagnetically to its adjacent Cu. The induced moment follows a 1/T1/T1/T temperature dependence due to the Curie-type development of the moment amplitude while its extension saturates and does not depend on impurity content or nature. This allow us to verify the generically expected scenario for impurity doping and to extend it to magnetic impurity case: in an antiferromagnetically correlated low-dimensional spin system with antiferromagnetic correlations, any type of impurity induces a staggered moment at low temperature, whose extension is not linked to the impurity nature but to the intrinsic physics at play in the undoped pure system, from one-dimensional to two-dimensional systems.
We present a static, model-independent, experimental determination of the spin-spin correlation length $\ensuremath{\xi}$ in a quantum spin system. This is achieved in the doped Haldane (i.e., S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 Heisenberg antiferromagnetic) chain ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}$ by 89Y{}^{89}\mathrm{Y}89Y NMR imaging of the staggered magnetization induced around the Mg impurities (i.e., chain boundaries) by a magnetic field. The magnitude of this magnetization is found to decay exponentially, with $\ensuremath{\xi}$ equal to the theoretical prediction for an infinite S=1S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1S=1 chain and the staggered magnetic moment at the edge site showing the Curie behavior of an effective S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 spin.
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.
Open segments of S=1S=1S=1 antiferromagnetic spin chains are studied at finite temperatures and fields using continuous time quantum Monte Carlo techniques. By calculating the resulting magnetization profiles for a large range of chain lengths with fixed field and temperature we reconstruct the experimentally measured NMR spectrum of impurity doped ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}.$ For temperatures above the gap the calculated NMR spectra are in excellent agreement with the experimental results, confirming the existence of S=1/2S=1/2S=1/2 excitations at the end of open S=1S=1S=1 chain segments. At temperatures below the gap, neglecting interchain couplings, we still find well defined peaks in the calculated NMR spectra corresponding to the S=1/2S=1/2S=1/2 chain end excitations. At low temperatures, interchain couplings could become important, resulting in a more complicated phase.
The response of an open spin chain with isotropic antiferromagnetic interactions to a uniform magnetic field is studied by classical Monte Carlo simulations. It is observed how the induced on-site magnetization is nonuniform, due to the occurrence of edge staggered terms which decay exponentially over a distance equal to the zero-field correlation length of the infinite chain. The total magnetic moment associated to each staggered term is found to be about half of the original single-spin magnitude and to decrease as the inverse of temperature (i.e., to behave as a Curie-like moment). The numerical results are compared to recent NMR findings in spinless-doped Y2BaNiO5;{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5};Y2​BaNiO5​; the remarkable agreement found shows that, for temperatures above the Haldane gap, the classical approach gives a correct picture of the boundary effects observed in the Heisenberg S=1S=1S=1 chain.
Nuclear magnetic resonance and magnetization measurements were used to probe the magnetic features of single-crystalline Bi(Cu(1-x)Zn(x))(2)PO(6) with 0<x<0.05 at temperatures between 2.6 K and 300 K. The simple line shape of the (31)P NMR signals of the pristine compound changes considerably for x>0 and we present clear evidence for a temperature-dependent variation of the local magnetization close to the Zn sites. The generic nature of this observation is indicated by results of model calculations on appropriate spin systems of limited size employing quantum Monte Carlo methods.