arXiv:0811.2106 · Europhysics Letters (EPL)

NMR response in quasi–one-dimensional spin-\chem{\frac{1}{2}} antiferromagnets

Jesko Sirker, Nicolas Laflorencie

Published Jun 1, 2009• 13 citations

Abstract

Non-magnetic impurities break a quantum spin chain into finite segments and induce Friedel-like oscillations in the local susceptibility near the edges. The signature of these oscillations has been observed in Knight shift experiments on the high-temperature superconductor YBa 2 Cu 3 O 6.5 and on the spin chain compound Sr 2 CuO 3 . Here we analytically calculate NMR spectra, compare with the available experimental data for Sr 2 CuO 3 , and show that the interchain coupling is responsible for the complicated and so far unexplained lineshape. Our results are based on a parameter-free formula for the local susceptibility of a finite spin chain obtained by bosonization which is checked by comparing with quantum Monte Carlo and density matrix renormalization group calculations.

DOI: 10.1209/0295-5075/86/57004

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Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift

Sebastian Eggert, Ian K. Affleck

arXiv:cond-mat/9505092Physical Review LettersJul 31, 1995153 citations

arXiv:0811.2106 · Europhysics Letters (EPL)

NMR response in quasi–one-dimensional spin-\chem{\frac{1}{2}} antiferromagnets

Jesko Sirker, Nicolas Laflorencie

Published Jun 1, 2009• 13 citations

arXiv HTML PDF

Abstract

DOI: 10.1209/0295-5075/86/57004

Related papers

Chain Breaks and the Susceptibility of Sr2Cu1−xPdxO3+δ and Other Doped Quasi-One-Dimensional Antiferromagnets

Jesko Sirker, Nicolas Laflorencie, Satoshi Fujimoto +2 more

We study the magnetic susceptibility of one-dimensional S=1/2 antiferromagnets containing nonmagnetic impurities which cut the chain into finite segments. For the susceptibility of long anisotropic Heisenberg chain segments with open boundaries we derive a parameter-free result at low temperatures using field-theory methods and the Bethe ansatz. The analytical result is verified by comparing with quantum Monte Carlo calculations. We then show that the partitioning of the chain into finite segments can explain the Curie-like contribution observed in recent experiments on Sr2Cu(1-x)PdxO(3+delta). Possible additional paramagnetic impurities seem to play only a minor role.We study the magnetic susceptibility of one-dimensional S=1/2 antiferromagnets containing nonmagnetic impurities which cut the chain into finite segments. For the susceptibility of long anisotropic Heisenberg chain segments with open boundaries we derive a parameter-free result at low temperatures using field-theory methods and the Bethe ansatz. The analytical result is verified by comparing with quantum Monte Carlo calculations. We then show that the partitioning of the chain into finite segments can explain the Curie-like contribution observed in recent experiments on Sr2Cu(1-x)PdxO(3+delta). Possible additional paramagnetic impurities seem to play only a minor role.

arXiv:cond-mat/0610165Physical Review LettersMar 27, 200750 citations

Consequences of lattice imperfections and interchain couplings for the critical properties of spin-1/2 chain compounds

Sirker

To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account.Here we present the field theory for finite spin chains at finite temperature and calculate experimentally measurable quantities like susceptibilities and nuclear magnetic resonance spectra.For the interchain couplings we concentrate on geometries relevant for cuprate spin chains like Sr 2 CuO 3 and SrCuO 2 .The field theoretical results are compared to experimental as well as numerical data obtained by the density matrix renormalization group.To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account.Here we present the field theory for finite spin chains at finite temperature and calculate experimentally measurable quantities like susceptibilities and nuclear magnetic resonance spectra.For the interchain couplings we concentrate on geometries relevant for cuprate spin chains like Sr 2 CuO 3 and SrCuO 2 .The field theoretical results are compared to experimental as well as numerical data obtained by the density matrix renormalization group.

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Sebastian Eggert

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Jan 1, 20091 citation

Magnetization profiles and NMR spectra of doped Haldane chains at finite temperatures

Fabien Alet, Erik Schwartz Sørensen

Open segments of $S=1$ 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 $S=1/2$ excitations at the end of open $S=1$ chain segments. At temperatures below the gap, neglecting interchain couplings, we still find well defined peaks in the calculated NMR spectra corresponding to the $S=1/2$ chain end excitations. At low temperatures, interchain couplings could become important, resulting in a more complicated phase.Open segments of $S=1$ 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 $S=1/2$ excitations at the end of open $S=1$ chain segments. At temperatures below the gap, neglecting interchain couplings, we still find well defined peaks in the calculated NMR spectra corresponding to the $S=1/2$ chain end excitations. At low temperatures, interchain couplings could become important, resulting in a more complicated phase.

arXiv:cond-mat/0006282Physical review. B, Condensed matterDec 1, 200013 citations

Enhancement of antiferromagnetic correlations induced by nonmagnetic impurities: Origin and predictions for NMR experiments

Markus Laukamp, George Balster Martins, C. J. Gazza +5 more

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 $\mathrm{Cu}({\mathrm{NO}}_{3}{)}_{2}\ensuremath{\cdot}2.5{\mathrm{H}}_{2}\mathrm{O}$, ${\mathrm{CuWO}}_{4}$ , $(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}$ , and ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},$ in ladder materials such as ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ , in the spin-Peierls systems ${\mathrm{CuGeO}}_{3}$ and ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5}$ , 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 ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ 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 ${\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}$ will not present N\'eel order at small Zn concentrations.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 $\mathrm{Cu}({\mathrm{NO}}_{3}{)}_{2}\ensuremath{\cdot}2.5{\mathrm{H}}_{2}\mathrm{O}$, ${\mathrm{CuWO}}_{4}$, $(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}$, and ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},$ in ladder materials such as ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$, in the spin-Peierls systems ${\mathrm{CuGeO}}_{3}$ and ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5}$, 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 ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ 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 ${\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}$ will not present N\'eel order at small Zn concentrations.

arXiv:cond-mat/9707261Physical review. B, Condensed matterMay 1, 199889 citations

Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift

Sebastian Eggert, Ian K. Affleck

Nonmagnetic impurities in an $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function, ${S}_{\mathrm{imp}}(k)$ , measured in neutron scattering and the local susceptibility, ${\ensuremath{\chi}}_{i}$ measured in Knight shift experiments. ${S}_{\mathrm{imp}}(k)$ becomes quite large near the antiferromagnetic wave vector, and exhibits much stronger temperature dependence than the bulk structure function. ${\ensuremath{\chi}}_{i}$ has a large component which alternates and increases as a function of distance from the impurity.Nonmagnetic impurities in an $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function, ${S}_{\mathrm{imp}}(k)$, measured in neutron scattering and the local susceptibility, ${\ensuremath{\chi}}_{i}$ measured in Knight shift experiments. ${S}_{\mathrm{imp}}(k)$ becomes quite large near the antiferromagnetic wave vector, and exhibits much stronger temperature dependence than the bulk structure function. ${\ensuremath{\chi}}_{i}$ has a large component which alternates and increases as a function of distance from the impurity.

arXiv:cond-mat/9505092Physical Review LettersJul 31, 1995153 citations

Open segments of

S=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=1/2

excitations at the end of open

S=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=1/2

chain end excitations. At low temperatures, interchain couplings could become important, resulting in a more complicated phase.

{\mathrm{CuWO}}_{4}

(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}

, and

{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},

in ladder materials such as

{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}

, in the spin-Peierls systems

{\mathrm{CuGeO}}_{3}

and

{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}

, 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

{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}

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

{\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}

will not present N\'eel order at small Zn concentrations.

Nonmagnetic impurities in an

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function,

{S}_{\mathrm{imp}}(k)

, measured in neutron scattering and the local susceptibility, ${\ensuremath{\chi}}_{i}$ measured in Knight shift experiments.

{S}_{\mathrm{imp}}(k)

becomes quite large near the antiferromagnetic wave vector, and exhibits much stronger temperature dependence than the bulk structure function. ${\ensuremath{\chi}}_{i}$ has a large component which alternates and increases as a function of distance from the impurity.