Quantum Statistics of Interacting Dimer Spin Systems

Abstract

The compound TlCuCl 3 represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Würtz [Phys. Rev. B 50, 13 515 (1994)] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important. DOI: 10.1103/PhysRevLett.95.267201 PACS numbers: 75.10.Jm, 05.30.Jp, 78.70.Nx The temperature is without doubt the key control parameter in solid-state physics, for both historical and technical reasons. Historically, the study of thermal fluctuations created the discipline of statistical mechanics. As one technical example, the liquefaction of helium in 1908 enabled the discovery of superconductivity in 1911 [1]. While control parameters such as the magnetic field or applied pressure may seem rather abstract by comparison, in certain classes of system they have a profound effect on the quantum mechanical fluctuations of the dominant degrees of freedom. In this respect, dimer spin systems such as BaCuSi 2 O 6 [2 -4], TlCuCl 3 [5-9], and Cs 3 Cr 2 Br 9 [10] have recently attracted considerable attention as they exhibit both field-and (in TlCuCl 3 ) pressure-induced magnetic quantum phase transitions. The ordered phases have also been described as a novel state resulting from BoseEinstein condensation of magnons [11,12].To date, the primary experimental and theoretical studies of these systems have focused on elucidating the parameter dependence of the ground and excited states at ''T 0 K' ' [3,4,6 -10]. However, the temperature dependence of the spin-spin correlation function S Q; ! in such dimer-based compounds is also of fundamental interest. At finite temperatures, thermal fluctuations populating the excited triplet states above the energy gap, 7:5 K, in the spin excitation spectrum of TlCuCl 3 become significant and compete with the intrinsic quantum fluctuations. The absence of a classical ordering transition in zero field and at ambient pressure, and the strong interdimer interactions, make TlCuCl 3 an ideal candidate for an experimental investigation of the quantum statistical description for such a spin system.In TlCuCl 3 , the antiferromagnetic (AF) dimer unit is formed by the two S 1=2 magnetic moments in a pair of Cu 2 ions, and has a singlet ground state (total spin S 0) with triplet (S 1) excited states which may be considered as bosonic quasiparticles. Only in the high-temperature limit, relative to the intradimer exchange constant J 56 K [5,13], is the system better described in terms of S 1=2 fermions whose interactions are weak compared to the thermal fluctuations, and AF dimer correlations are strongly suppressed. In the intermediate regime, < T < J, a singlet-triplet description remains valid but the number of excited triplets becomes significan...

Microscopic model for Bose-Einstein condensation and quasiparticle decay

“…We apply the mean-field approach in Refs. [40,46,[52][53][54] to H 1D,eff +H inter,eff from Eqs. (2,4).…”

“…We attribute the discrepancy at higher temperatures to the insufficient treatment of the hardcore constraint by the above approach (for 15 K the condensate fraction s 2 is only 0.77). Note that we only apply the mean-field theory to the dispersion obtained from CUT, not to the original spin model as done previously [40,53] because IPA-CuCl 3 is not far enough in the dimer limit.…”

Extended Universal Finite-TRenormalization of Excitations in a Class of One-Dimensional Quantum Magnets

“…Extensive finite-T data exist for the S 1=2 dimer systems CuNO 3 2 [20] and TlCuCl 3 [21]. Unfortunately, in the former compound v , while the latter is by no measure one-dimensional.…”

Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field

“…This could be used to study different effects such as the interesting shifts and damping of the triplet modes with temperature that have been observed in 3D gapped systems. 90 A second important step would be to improve the description of the quasi-1D systems, by including in a mean-field way the effect of the other ladders in the numerical study. This is something we already partly performed, but the extension to the dynamical quantities remains to be done.…”