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arXiv:1208.5921 · Physical Review Letters

Asymmetric Thermal Line Shape Broadening in a Gapped 3D Antiferromagnet: Evidence for Strong Correlations at Finite Temperature

Diana Lucia Quintero-Castro, B. Lake, A. T. M. N. Islam, Elisa M. Wheeler, Christian Balz, Martin Må̊nsson, K. C. Rule, S. N. Gvasaliya, A. Zheludev

Published Sep 19, 2012• 21 citations
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Abstract

It is widely believed that magnetic excitations become increasingly incoherent as the temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric-indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature activated coherent state of quasiparticles is not confined to special cases like the highly dimerized spin-1/2 chain but is found generally in dimerized antiferromagnets of all dimensionalities and perhaps gapped magnets in general.

DOI
10.1103/physrevlett.109.127206

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It is widely believed that magnetic excitations become increasingly incoherent as the temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric-indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature activated coherent state of quasiparticles is not confined to special cases like the highly dimerized spin-1/2 chain but is found generally in dimerized antiferromagnets of all dimensionalities and perhaps gapped magnets in general.
Dimerized magnets forming alternating Heisenberg chains exhibit quantum coherence and entanglement and thus can find potential applications in quantum information and computation. However, magnetic systems typically undergo thermal decoherence at finite temperatures. Here, we show inelastic neutron scattering results on an alternating antiferromagnetic-ferromagnetic chain compound Na2Cu2TeO6{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}Na2​Cu2​TeO6​ that the excited quasiparticles can counter thermal decoherence and maintain strong correlations at elevated temperatures. At low temperatures, we observe clear dispersive singlet-triplet excitations arising from the dimers formed along the crystalline bbb axis. The excitation gap is of $\ensuremath{\sim}18\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ and the bandwidth is about half of the gap. The band top energy has a weak modulation along the [100] direction, indicative of a small interchain coupling. The gap increases while the bandwidth decreases with increasing temperature, leading to a strong reduction in the available phase space for the triplons. As a result, the Lorentzian-type energy broadening becomes highly asymmetric as the temperature is raised. These results are associated with a strongly correlated state resulting from hard-core constraint and quasiparticle interactions. We consider these results to be not only evidence for strong correlations at finite temperatures in Na2Cu2TeO6{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}Na2​Cu2​TeO6​, but also for the universality of the strongly correlated state in a broad range of quantum magnetic systems.
The effect of thermal fluctuations on the dynamics of a gapped quantum magnet is studied using inelastic neutron scattering on copper nitrate, a model material for the spin-1/2, one-dimensional (1D) bond alternating Heisenberg chain. A large, highly deuterated, single-crystal sample of copper nitrate is produced using a solution growth method and measurements are made using the high-resolution backscattering spectrometer OSIRIS at the ISIS Facility. Theoretical calculations and numerical analysis are combined to interpret the physical origin of the thermal effects observed in the magnetic spectra. The primary observations are (1) a thermally induced central peak due to intraband scattering, which is similar to Villain scattering familiar from soliton systems in 1D, and (2) the one-magnon quasiparticle pole is seen to develop with temperature into an asymmetric continuum of scattering. We relate this asymmetric line broadening to a thermal strongly correlated state caused by hard-core constraints and quasiparticle interactions. These findings are a counter example to recent assertions of the universality of line broadening in 1D systems and are applicable to a broad range of quantum systems.
Unlike most quantum systems which rapidly become incoherent as temperature is raised, strong correlations persist at elevated temperatures in S=12S=\frac{1}{2}S=21​ dimer magnets, as revealed by the unusual asymmetric line shape of their excitations at finite temperatures. Here, we quantitatively explore and parametrize the strongly correlated magnetic excitations at finite temperatures using high-resolution inelastic neutron scattering of the model compound BaCu2V2O8{\mathrm{BaCu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCu2​V2​O8​ which we show to be an alternating antiferromagnetic-ferromagnetic $\mathrm{spin}\ensuremath{-}\frac{1}{2}$ chain. Comparison to state of the art computational techniques shows excellent agreement over a wide temperature range. Our findings hence demonstrate the possibility to quantitatively predict coherent behavior at elevated temperatures in quantum magnets.
We use the density matrix renormalization group method to compute the frequency and momentum-resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero-temperature case, the finite-temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one-dimensional quantum chains.
We have mapped from the quantum to the classical limit the spin excitation spectrum of the antiferromagnetic spin-1 Heisenberg chain system CsNiCl3{\mathrm{CsNiCl}}_{3}CsNiCl3​ in its paramagnetic phase from T=5T=5T=5 to 200K.200\mathrm{K}.200K. Neutron scattering shows that the excitations are resonant and dispersive up to at least $T=70\mathrm{K}\ensuremath{\simeq}2.7J,$ but broaden considerably with increasing temperature. The dispersion flattens out with increasing temperature as the resonance energy $\ensuremath{\Delta}$ at the antiferromagnetic wave vector increases and the maximum in the dispersion decreases. The correlation length $\ensuremath{\xi}$ between T=12T=12T=12 and 50K50\mathrm{K}50K is in agreement with quantum Monte Carlo calculations for the spin-1 chain. $\ensuremath{\xi}$ is also consistent with the single mode approximation, suggesting that the excitations are short-lived single particle excitations. Below T=12KT=12\mathrm{K}T=12K where three-dimensional spin correlations are important, $\ensuremath{\xi}$ is shorter than predicted and the experiment is not consistent with the random phase approximation for coupled quantum chains. At T=200K,T=200\mathrm{K},T=200K, the structure factor and second energy moment of the excitation spectrum are in excellent agreement with the high-temperature series expansion.
The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here, we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line shape is found to be asymmetric at elevated temperatures and the bandwidth of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced that can also be applied to more sophisticated and higher dimensional models.