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arXiv:1903.08438 · International Journal of Modern Physics B

Characteristic temperatures of a triplon system of dimerized quantum magnets

Abdulla Rakhimov, Mukhtorali Nishonov, Luxmi Rani, Bilal Tanatar

Published Dec 19, 2020• 5 citations
arXivHTMLPDF

Abstract

Exploiting the analogy between ultracold atomic gases and the system of triplons, we study magneto-thermodynamic properties of dimerized quantum magnets in the framework of Bose–Einstein condensation (BEC). Particularly, introducing the inversion (or Joule–Thomson) temperature [Formula: see text] as the point where Joule–Thomson coefficient of an isenthalpic process changes its sign, we show that for a simple paramagnet, this temperature is infinite, while for three-dimensional (3D) dimerized quantum magnets it is finite and always larger than the critical temperature [Formula: see text] of BEC. Below the inversion temperature [Formula: see text], the system of triplons may be in a liquid phase, which undergoes a transition into a superfluid phase at [Formula: see text]. The dependence of the inversion temperature on the external magnetic field [Formula: see text] has been calculated for quantum magnets of TlCuCl3 and Sr3Cr2O8.

DOI
10.1142/s0217979221500181

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Exploiting the analogy between ultracold atomic gases and the system of triplons, we study magneto-thermodynamic properties of dimerized quantum magnets in the framework of Bose–Einstein condensation (BEC). Particularly, introducing the inversion (or Joule–Thomson) temperature [Formula: see text] as the point where Joule–Thomson coefficient of an isenthalpic process changes its sign, we show that for a simple paramagnet, this temperature is infinite, while for three-dimensional (3D) dimerized quantum magnets it is finite and always larger than the critical temperature [Formula: see text] of BEC. Below the inversion temperature [Formula: see text], the system of triplons may be in a liquid phase, which undergoes a transition into a superfluid phase at [Formula: see text]. The dependence of the inversion temperature on the external magnetic field [Formula: see text] has been calculated for quantum magnets of TlCuCl3 and Sr3Cr2O8.
Abstract The temperature dependence of Tan’s contact parameter C and its derivatives for spin gapped quantum magnets are investigated. We use the paradigm of Bose–Einstein condensation (BEC) to describe the low temperature properties of quasiparticles in the system known as triplons. Since the number of particles and the condensate fraction are not fixed we use the μVT ensemble to calculate the thermodynamic quantities. The interactions are treated at the Hartree–Fock–Bogoliubov approximation level. We obtained the temperature dependence of C and its derivative with respect to temperature and applied magnetic field both above and below T c of the phase transition from the normal phase to BEC. We have shown that C is regular, while its derivatives are discontinuous at T c in accordance with Ehrenfest’s classification of phase transitions. Moreover, we have found a sign change in ∂ C /∂ T close to the critical temperature. As to the quantum critical point, C and its derivatives are regular as a function of the control parameter r , which induces the quantum phase transition. At very low temperatures, one may evaluate C simply from the expression C = m 2 μ 2 / a ¯ 4 , where the only parameter effective mass of quasiparticles should be estimated. We propose a method for measuring of Tan’s contact for spin gapped dimerized magnets.
We obtained, within a path-integral formalism (mean-field variational Gaussian approximation), analytical expressions for thermodynamic quantities such as magnetization, heat capacity, and the magnetic Gr\"uneisen parameter ${\mathrm{\ensuremath{\Gamma}}}_{H}$ of the system of triplons in spin gapped quantum magnets. Near the critical temperature ${\mathrm{\ensuremath{\Gamma}}}_{H}$ is discontinuous and changes its sign upon the Bose-Einstein condensation (BEC) of triplons. We predict that in the limit of low temperature TTT and near the critical magnetic field ${H}_{c},\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{H}$ diverges as ${\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremath{\sim}1/{T}^{2}$, while it scales as ${\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremath{\sim}1/(H\ensuremath{-}{H}_{c})$ as the magnetic field approaches Hc{H}_{c}Hc​.
Dimerized quantum magnets provide a useful arena for novel quantum states and phases transitions with the singlet-triplet type of triplon excitations. Here we study the triplon physics and the Bose-Einstein condensation in two isostructural dimerized antiferromagnets AAACu(SeO3_33​)2_22​ (AAA = Hg, Cd). With the systematic measurements, we demonstrate a dimer singlet ground state in HgCu(SeO3_33​)2_22​ with a triplon gap ∼\sim∼ 7.9 K and a triplon Bose-Einstein condensation with an antiferromagnetic order in CdCu(SeO3_33​)2_22​ below 4.4 K. We further adopt the bond-operator technique and show that the elemental replacement preserves the Hamiltonian and allows the study in a unified theoretical framework with tunable interdimer and intradimer interactions on the opposite sides of the quantum critical point. With the peculiar Cu2_22​O8_88​ dimer configuration and effective ferromagnetic interdimer interaction, AAACu(SeO3_33​)2_22​ is distinguished from other SSS = 1/2 dimerized antiferromagnets. Our results represent a global understanding of the magnetic ground states as well as the magnetic transitions in the dimerized magnets of this unusual crystal structure.
We present a study of magnetic field induced quantum phase transitions in insulating systems. A generalized scaling theory is used to obtain the temperature dependence of several physical quantities along the quantum critical trajectory (H=HCH=H_{C}H=HC​, T→0T\to0T→0) where HHH is a longitudinal external magnetic field and HCH_{C}HC​ the critical value at which the transition occurs. We consider transitions from a spin liquid at a critical field HC1H_{C1}HC1​ and from a fully polarized paramagnet, at HC2H_{C2}HC2​, into phases with long range order in the transverse components. The transitions at HC1H_{C1}HC1​ and HC2H_{C2}HC2​ can be viewed as Bose-Einstein condensations of magnons which however belong to different universality classes since they have different values of the dynamic critical exponent zzz. Finally, we use that the magnetic susceptibility is an entanglement witness to discuss how this type of correlation sets in as the system approaches the quantum critical point along the critical trajectory, H=HC2H=H_{C2}H=HC2​, T→0T\to0T→0.
We study properties of magnetic field-induced Bose-Einstein condensate of triplons as a function of temperature and the field within the Hartree-Fock-Bogoliubov approach including the anomalous density. We show that the magnetization is continuous across the transition, in agreement with the experiment. In sufficiently strong fields the condensate becomes unstable due to triplon-triplon repulsion. As a result, the system is characterized by two critical magnetic fields: one producing the condensate and the other destroying it. We show that nonparabolic triplon dispersion arising due to the gapped bare spectrum and the crystal structure has a strong influence on the phase diagram.
We present a theoretical study of Bose-Einstein condensation(BEC) of trapped ideal gas of spin-1 ultracold atoms in tight-binding bands corresponding to simple cubic(SC) optical lattices.Under the constraints that both the total number of atoms (N) and the total magnetization (M) are conserved,we first investigate the phase transitions process of noninteracting spin-1 atomic system,by investigating the critical condensation temperature and condensate fraction,we find BEC with spin degrees of freedom shows richer phase transitions than BEC of scalar atoms.We then extend our studies to the case with a uniform external magnetic field included,the phase transitions for this case make interesting changes again.