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.
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 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
b 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, but also for the universality of the strongly correlated state in a broad range of quantum magnetic systems.
We discuss the theory of the nonzero temperature
(T) spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap $\ensuremath{\Delta}$. For $T\ensuremath{\ll}\ensuremath{\Delta}$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle
S matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the
O(3) $\ensuremath{\sigma}$ model, and strong- and weak-coupling expansions (the latter using a Majorana fermion representation) for the two-leg
S=1/2 Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals an
S=1, two-particle bound state which leads to the presence of a second peak in the
T=0 inelastic neutron-scattering (INS) cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate
1/T1 of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit $T\ensuremath{\ll}\ensuremath{\Delta}$. The results for
1/T1 are compared with the experimental findings of Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] and the agreement is quite good. In the regime $\ensuremath{\Delta}<T<$(a typical microscopic exchange) and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.
The effect of temperature dependent asymmetric line broadening is investigated in $\mathrm{Cu}({\mathrm{NO}}_{3}{)}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2.5{\mathrm{D}}_{2}\mathrm{O}$, a model material for a one-dimensional bond alternating Heisenberg chain, using the high resolution neutron-resonance spin echo (NRSE) technique. Inelastic neutron scattering experiments on dispersive excitations including phase sensitive measurements demonstrate the potential of NRSE to resolve line shapes, which are non-Lorentzian, opening up a new and hitherto unexplored class of experiments for the NRSE method beyond standard linewidth measurements. The particular advantage of NRSE is its direct access to the correlations in the time domain without convolution with the resolution function of the background spectrometer. This application of NRSE is very promising and establishes a basis for further experiments on different systems, since the results for Cu(
NO3)${}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2.5{\mathrm{D}}_{2}\mathrm{O}$ are applicable to a broad range of quantum systems.
Temperature dependencies of gap energies and magnon lifetimes are measured in the quasi-1-dimensional S=1/2 gapped quantum magnets IPA-CuCl3 and Sul-Cu2Cl4 using inelastic neutron scattering. The results are compared to those found in literature for S=1 Haldane spin chain materials and to theoretical calculations for the O(3)- and O(N)- quantum non-linear sigma-models. It is found that when the T=0 energy gap Delta is used as the temperature scale, all experimental and theoretical curves are identical to within system-dependent but temperature-independent scaling factors of the order of unity. This quasi-universality extends over a surprising broad T range, at least up to kappa T ~ 1.5 Delta.
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.