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arXiv:1009.3375 · Europhysics Letters (EPL)

Microscopic model for Bose-Einstein condensation and quasiparticle decay

T. Fischer, Stefanie Duffe, Götz Silvester Uhrig

Published Nov 1, 2011• 21 citations
arXivHTMLPDF

Abstract

Sufficiently dimerized quantum antiferromagnets display elementary S =1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl 3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J 1 ≈− 2.3 meV, J 2 ≈1.2 meV, J 3 ≈2.9 meV and J 4 ≈− 0.3 meV. These couplings determine IPA-CuCl 3 as system of coupled asymmetric S =1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.

DOI
10.1209/0295-5075/96/47001

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Sufficiently dimerized quantum antiferromagnets display elementary S =1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl 3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J 1 ≈− 2.3 meV, J 2 ≈1.2 meV, J 3 ≈2.9 meV and J 4 ≈− 0.3 meV. These couplings determine IPA-CuCl 3 as system of coupled asymmetric S =1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.
In sufficiently dimerized quantum antiferromagnets the elementary excitations are given by gapped spin S = 1 triplon quasiparticles. Although these triplons are protected by a gap at low energies they may decay spontaneously at higher energies where the one-triplon dispersion merges with the two-triplon continuum. First, we illustrate and characterize such a spontaneous decay in low-dimensional quantum antiferromagnets on the basis of a simple one-dimensional bosonic model. The decay implies the breakdown of the quasiparticle picture. No quantitative description by a Lorentzian resonance is possible. In particular, three qualitatively different scenarios are identified depending on the one-triplon dispersion and the two-triplon interaction. To describe unstable quasiparticles in more complex models we introduced an adapted generator for continuous unitary transformations. Its general properties are derived and discussed. Next, we investigate asymmetric antiferromagnetic and asymmetric ferroantiferromagnetic spin S = ½ Heisenberg ladders, which allow for spontaneous triplon decay, to illustrate this approach. Results for the low-energy spectra and the dynamical structure factors for these systems are presented. We show that quasiparticle decay is more pronounced in the case of ferro-antiferromagnetic ladders than in solely antiferromagnetic ladders. Finally, we use continuous unitary transformations and high temperature series expansions to determine a quantitative model for the compound IPA-CuCl3 based on data of inelastic neutron scattering and measurements of the magnetic susceptibility. Our calculations reveal IPA-CuCl3 as system of coupled asymmetric spin S = ½ Heisenberg ladders with the four magnetic couplings J 1 ˜ -2.3 meV, J2 ˜ 1.2 meV, J3 ˜ 2.9 meV and J4 ˜ -0.3 meV. Based on this microscopic model for IPA-CuCl3 the adapted continuous unitary transformation is used to describe the quasiparticle decay in IPA-CuCl3. The results agree very well with the experimental data. In addition the magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate our microscopic model.
We provide a theory of triplon dynamics in the valence bond solid ground state of the coupled spin ladders modeled for BiCu2PO6{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}BiCu2​PO6​. Utilizing the recent high-quality neutron scattering data [K. W. Plumb et al., Nat. Phys. 12, 224 (2016)] as guides and a theory of interacting triplons via the bond operator formulation, we determine a minimal spin Hamiltonian for this system. It is shown that the splitting of the low-energy triplon modes and the peculiar magnetic field dependence of the triplon dispersions can be explained by including substantial Dzyaloshinskii-Moriya and symmetric anisotropic spin interactions. Taking into account the interactions between triplons and the decay of the triplons to the two-triplon continuum via anisotropic spin interactions, we provide a theoretical picture that can be used to understand the main features of the recent neutron scattering experimental data.
We study theoretically the effects of disorder on Bose–Einstein condensates (BEC) of bosonic triplon quasiparticles in doped dimerized quantum magnets. The condensation occurs in a magnetic field, where the concentration of bosons in the random potential is sufficient to form the condensate. The effect of doping is partly modeled by a δ -correlated distribution of impurities, which (i) leads to a uniform renormalization of the system parameters and (ii) produces disorder in the system with renormalized parameters. This approach can explain qualitatively the available magnetization data on the Tl 1− x K x CuCl 3 compound taken as an example. In addition to the magnetization, we found that the speed of the Bogoliubov mode has a maximum as a function of x . No evidence of the pure Bose glass phase has been found in the BEC regime.
Motivated by recent experiments on Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​, a new spin-dimer compound with spin-1/2 moments of Cr5+{\text{Cr}}^{5+}Cr5+ ions, we theoretically investigate the field-induced magnetic ordering in this material in view of the Bose-Einstein condensation (BEC) of triplet excitations (triplons). We apply the self-consistent Hartree-Fock-Popov (HFP) approach to a microscopic Hamiltonian, using the realistic triplon dispersion measured in an inelastic neutron-scattering experiment. In particular, we ask to what extent the BEC of dilute triplons near the critical field can explain the magnetic ordering in this material. For example, we investigate the temperature range where the BEC picture of triplons can be applied via the HFP approach. We also determine the temperature regime where a quadratic approximation of the triplon dispersion works. It is found that the strength of the effective repulsive interaction between triplons is much weaker in Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​ than in the canonical spin-dimer compound TlCuCl3{\text{TlCuCl}}_{3}TlCuCl3​. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons ncr{n}_{\text{cr}}ncr​ at the critical point. The combined effect points to a bigger HFP correction UncrU{n}_{\text{cr}}Uncr​ in Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​ than in TlCuCl3{\text{TlCuCl}}_{3}TlCuCl3​. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​.
We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy, fine structure, and linewidth of the magnon resonance in the model spin-1/2 ladder antiferromagnet IPA-CuCl(3) at temperatures T≪Δ(0)/k(B), where Δ(0) is the spin gap at T=0. In this low-temperature regime we find that the results deviate substantially from the predictions of the nonlinear sigma model proposed as a description of magnon excitations in one-dimensional quantum magnets and attribute these deviations to real-space and spin-space anisotropies in the spin Hamiltonian as well as scattering of magnon excitations from a dilute density of impurities. These effects are generic to experimental realizations of one-dimensional quantum magnets.
Structural and magnetic properties of a quasi-one-dimensional spin-12\frac{1}{2}21​ compound NaVOPO4{\mathrm{NaVOPO}}_{4}NaVOPO4​ are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and 31P^{31}\mathrm{P}31P nuclear magnetic resonance measurements, as well as complementary ab initio calculations. Whereas magnetic susceptibility of NaVOPO4{\mathrm{NaVOPO}}_{4}NaVOPO4​ may be compatible with the gapless uniform spin chain model, detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio $\ensuremath{\alpha}\ensuremath{\simeq}0.98$ and the ensuing zero-field spin gap ${\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{\mathrm{B}}\ensuremath{\simeq}2.4\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50 mK in zero field. However, applied fields above the critical field ${H}_{c1}\ensuremath{\simeq}1.6\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ give rise to a magnetic ordering transition with the phase boundary ${T}_{N}\ensuremath{\propto}{(H\ensuremath{-}{H}_{c1})}^{\frac{1}{\ensuremath{\phi}}}$, where $\ensuremath{\phi}\ensuremath{\simeq}1.8$ is close to the value expected for Bose-Einstein condensation of triplons. With its weak alternation of the exchange couplings and small spin gap, NaVOPO4{\mathrm{NaVOPO}}_{4}NaVOPO4​ lies close to the quantum critical point.