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Physical review. B, Condensed matter

Effect of vacancy doping on the Haldane spin-liquid state in PbNi2−xMgxV2O8

A. Zorko, Denis Arčon, Alexandros Lappas, John Giapintzakis, Cameron Saylor, Louis Claude Brunel

Published Apr 4, 2002• 12 citations
Publisher

Abstract

The effect of spin-vacancy doping on the ground state of the quasi-one-dimensional $S=1$ quantum antiferromagnet ${\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ is studied by X band as well as high-field ESR. A very broad ESR line is observed at low temperatures in powdered ${\mathrm{PbNi}}_{2\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ for $0<~x<~0.24.$ The frequency dependence of the observed ESR line rules out the possibility that the low-temperature ESR signal comes from the isolated $S=\frac{1}{2}$ spins. Instead, it is proposed that a magnetic coupling (most likely of second order) between the chain-end spins on both sides of the ${\mathrm{Mg}}^{2+}$ impurity plays an important role in this system. Impurity-induced spin states, due to the strong interchain coupling, also induce a staggered magnetization on the neighboring chains with a characteristic length \ensuremath{\xi}. \ensuremath{\xi} increases with decreasing temperature, as suggested by the additional broadening and the shift of the ESR signal at low temperatures. On the other hand the temperature dependence of the low temperature susceptibility suggests a much more complicated picture in which impurity-induced spins are exposed to coupling to thermal excitations on each chain as well as to three-dimensional antiferromagnetic correlations.

DOI
10.1103/physrevb.65.144449

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The effect of spin-vacancy doping on the ground state of the quasi-one-dimensional S=1S=1S=1 quantum antiferromagnet PbNi2V2O8{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}PbNi2​V2​O8​ is studied by X band as well as high-field ESR. A very broad ESR line is observed at low temperatures in powdered PbNi2\ensuremath−xMgxV2O8{\mathrm{PbNi}}_{2\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{V}}_{2}{\mathrm{O}}_{8}PbNi2\ensuremath−x​Mgx​V2​O8​ for 0< x< 0.24.0<~x<~0.24.0< x< 0.24. The frequency dependence of the observed ESR line rules out the possibility that the low-temperature ESR signal comes from the isolated S=12S=\frac{1}{2}S=21​ spins. Instead, it is proposed that a magnetic coupling (most likely of second order) between the chain-end spins on both sides of the Mg2+{\mathrm{Mg}}^{2+}Mg2+ impurity plays an important role in this system. Impurity-induced spin states, due to the strong interchain coupling, also induce a staggered magnetization on the neighboring chains with a characteristic length \ensuremath{\xi}. \ensuremath{\xi} increases with decreasing temperature, as suggested by the additional broadening and the shift of the ESR signal at low temperatures. On the other hand the temperature dependence of the low temperature susceptibility suggests a much more complicated picture in which impurity-induced spins are exposed to coupling to thermal excitations on each chain as well as to three-dimensional antiferromagnetic correlations.
Two quasi-one-dimensional S=1S=1S=1 quantum antiferromagnetic materials, PbNi2V2O8{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}PbNi2​V2​O8​ and SrNi2V2O8,{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8},SrNi2​V2​O8​, are studied by inelastic neutron scattering on powder samples. A simple model Hamiltonian is proposed for the two systems and used to analyze the data. Quantitative information on in-chain and interchain interactions obtained from this analysis is discussed in the context of qualitatively different ground-state properties: magnetic long-range order in SrNi2V2O8{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrNi2​V2​O8​ and disordered ``spin liquid'' Haldane-gap state in PbNi2V2O8.{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}.PbNi2​V2​O8​.
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.
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 study the effect of nonmagnetic Zn2+{\mathrm{Zn}}^{2+}Zn2+ (spin-0) and magnetic Ni2+{\mathrm{Ni}}^{2+}Ni2+ (spin-1) impurities on the ground state and low-lying excitations of the quasi-one-dimensional spin-1/21/21/2 Heisenberg antiferromagnet Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ using inelastic neutron scattering, specific heat, and bulk magnetization measurements. We show that 1% Ni2+{\mathrm{Ni}}^{2+}Ni2+ doping in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ results in a sizable spin gap in the spinon excitations, analogous to the case of Ni doped SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​ previously reported [Simutis et al., Phys. Rev. Lett. 111, 067204 (2013)]. However, a similar level of Zn2+{\mathrm{Zn}}^{2+}Zn2+ doping in SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​, investigated here for comparison, did not reveal any signs of a spin gap. Magnetic ordering temperature was found to be suppressed in the presence of both Zn2+{\mathrm{Zn}}^{2+}Zn2+ and Ni2+{\mathrm{Ni}}^{2+}Ni2+ impurities; however, the rate of suppression due to Ni2+{\mathrm{Ni}}^{2+}Ni2+ was found to be much more pronounced than for Zn2+{\mathrm{Zn}}^{2+}Zn2+. Effect of magnetic field on the ordering temperature is investigated. We found that with increasing magnetic field, not only the magnetic ordering temperature gradually increases but the size of specific heat anomaly associated with the magnetic ordering also progressively enhances, which can be qualitatively understood as due to the field induced suppression of quantum fluctuations.
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.
Motivated by frustrated magnets and quasi-one-dimensional magnetic materials, we study the magnetic properties of one-dimensional (1D) Ising chains with nearest-neighbor (NN) and weaker next-to-nearest-neighbor (NNN) interactions in the presence of vacancy defects. The effect of a vacancy on the magnetic susceptibility of a spin chain is twofold: it reduces the length of the chain by an effective ``vacancy size'' and may also act as a free spin, a ``quasispin,'' with a Curie-type ${\ensuremath{\chi}}_{\text{quasi}}=\ensuremath{\langle}{S}^{2}\ensuremath{\rangle}/T$ contribution to the susceptibility. In chains with antiferromagnetic short-range order, the susceptibility of vacancy-free chains is exponentially suppressed at low temperatures, and quasispins dominate the effect of impurities on the chains' magnetic properties. For chains with antiferromagnetic NN interactions, the quasispin matches the value $\ensuremath{\langle}{S}^{2}\ensuremath{\rangle}=1$ of the Ising spins in the chain for ferromagnetic NNN interactions and vanishes for antiferromagnetic NNN interactions. For chains with ferromagnetic short-range order, quasispin effects are insignificant due to exponentially large low-temperature susceptibilities, and the dominant effect of a vacancy is effectively changing the length of the chain.