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arXiv:1707.05243 · Physical review. B./Physical review. B

Finite-temperature correlations in a quantum spin chain near saturation

D. Blosser, Noam Kestin, Kirill Yu. Povarov, Robert Bewley, Emanuele Coira, Thierry Giamarchi, A. Zheludev

Published Oct 3, 2017• 20 citations
arXivHTMLPDF

Abstract

Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the $S=1/2$ Heisenberg spin chain compound ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$ at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted $z=2,\phantom{\rule{0.16em}{0ex}}d=1$ quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent nonuniversal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.

DOI
10.1103/physrevb.96.134406

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Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the S=1/2S=1/2S=1/2 Heisenberg spin chain compound K2CuSO4Cl2{\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}K2​CuSO4​Cl2​ at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted z=2,d=1z=2,\phantom{\rule{0.16em}{0ex}}d=1z=2,d=1 quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent nonuniversal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.
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Many phenomena in magnetism can be described using classical models, yet magnetism is a quantum mechanical effect. In addition to thermal fluctuations, quantum fluctuations arise due to the quantum uncertainty of the ground state. These fluctuations are enhanced by low dimensionality and low spin. Spin chains show interesting excitations associated with quasiparticles. Model materials for spin chains can be realized in compounds where the interchain interactions are weak enough. This thesis presents neutron scattering studies of two model materials for spin chains with different spin symmetry. The spin2 Heisenberg antiferromagnetic chain CuSO4*5D2O has a main exchange of J ∼ 3 K, which permits to study its excitation spectrum up to temperatures of ten times the exchange. The spin2 Heisenberg magnet has been studied widely both theoretically and experimentally. The excitation spectrum of the spin2 Heisenberg antiferromagnet consists of quasiparticles called spinons, and calculations for it exist for T = 0 and as a function of temperature. A quantitative comparison between experimental data and theoretical models across a range of temperatures is presented. The excitation spectrum of CuSO4*5D2O is excellently described by the excitation spectrum of a spin2 Heisenberg antiferromagnetic chain at finite temperatures. Energy-temperature scaling is observed at temperatures up to 2J . For these temperatures the Luttinger liquid description of the spin2 Heisenberg antiferromagnetic chain is valid. A spinon continuum is confirmed at all measured temperatures. Therefore, even at ten times the main exchange (T ≈ 10 J), CuSO4*5D2O shows the behavior of a quantum magnet, and not of a classical system at infinite temperatures, for which one would expect single spin flips. The Ising chain is one of the most studied models in magnetism, one model compound for it is RbCoCl3. Optical spectroscopy measurements suggest a lower gap than for similar compounds, which makes it better suited for high resolution neutron spectroscopy. Magnetic correlations along the chains arise in RbCoCl3 below 80 K. A gapped continuum is observed, which arises from isolated antiferromagnetic Ising chains. Below the first magnetic ordering temperature TN1 ≈ 28 K bound states are observed, which arise due to correlations which form between the chains. Strong diffuse scattering leads to the conclusion that disorder is still present. At the second magnetic ordering transition, at TN2 ≈ 14 K, the bound states split as the correlations between the chains change. Fits indicate that the correlations change continuously as a function of temperature. Above TN2 the excitation spectrum of RbCoCl3 can be described by a spin1 2 Ising chain with an XY-component which is treated as a perturbation. Below TN2 the main features are reproduced correctly, but deviations from the details indicate that additional terms in the Hamiltonian may be necessary. This thesis was carried out at the Institut Laue-Langevin, the Laboratory for Neutron Scattering and Imaging at the Paul Scherrer Institute and ETH Zurich.
Inelastic neutron scattering is employed to study transverse spin correlations of a Heisenberg S=1/2S=1/2S=1/2 chain compound in a magnetic field of 7.5 T. The target compound is the antiferromagnetic Heisenberg S=1/2S=1/2S=1/2 chain material 2(1,4-dioxane)$\ifmmode\cdot\else\textperiodcentered\fi{}2({\mathrm{H}}_{2}\mathrm{O})\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{CuCl}}_{2}$, or CuDCl for short. The validity and the limitations of the scaling relation for the transverse dynamic structure factor are tested, discussed, and compared to the Tomonaga-Luttinger spin liquid theory and to Bethe-ansatz results for the Heisenberg model.
Abstract We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of density matrix renormalization group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the dynamical structure factor (DSF), which is related to the inelastic neutron scattering (INS) spectrum and the resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective excitations. Our calculations suggest that the chain can transition between a hidden Z 2 × Z 2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons that can be detected either by INS or L -edge RIXS. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO 5 should be in a Haldane-like phase whose INS or L -edge RIXS spectrum can support observable single-spin excitations including triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the K -edge RIXS spectrum.
Quasi-one-dimensional magnetic materials provide important test beds for rigorous models of interacting many-body systems. Nevertheless, there have been few studies of finite temperature effects on spin correlations in low-spin systems, though these are most likely to exhibit quantum effects. Copper benzoate, Cu(C6D5COO)2⋅3D2O, is a good realization of the S=1/2 Heisenberg antiferromagnetic chain (HAFC). We have performed ac susceptibility and inelastic neutron scattering experiments on this material which establish the Hamiltonian and an excitation spectrum which is consistent with the spinon continuum ansatz of Müller et al. We present inelastic neutron scattering measurements of the temperature evolution of the dynamic spin–spin correlation function Szz(π,ω). Comparison will be made to the classical prediction and to a finite temperature field theory of Schulz as applied to this S=1/2 HAFC.
The low-temperature properties of spin-1/2 one-dimensional (1D) Heisenberg antiferromagnetic (HAF) chains which have relatively small exchange couplings between the spins can be tuned using laboratory-scale magnetic fields. Magnetization measurements, made as a function of temperature, provide phase diagrams for these systems and establish the quantum critical point (QCP). The evolution of the spin dynamics behavior with temperature and applied field in the quantum critical (QC) region, near the QCP, is of particular interest and has been experimentally investigated in a number of 1D HAFs using neutron scattering and nuclear magnetic resonance as the preferred techniques. In the QC phase both quantum and thermal spin fluctuations are present. As a result of extended spin correlations in the chains, magnon excitations are important at finite temperatures. An expression for the NMR spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ of probe nuclei in the QC phase of 1D HAFs is obtained by considering Raman scattering processes which induce nuclear spin flips. The relaxation rate expression, which involves the temperature and the chemical potential, predicts scaling behavior of 1/T11/{T}_{1}1/T1​ consistent with recent experimental findings for quasi-1D HAF systems. A simple relationship between 1/T11/{T}_{1}1/T1​ and the deviation of the magnetization from saturation (${M}_{S}\ensuremath{-}M$) is predicted for the QC region.