Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1801.00642 · Physical review. B./Physical review. B

Magnetocaloric effect and Grüneisen parameter of quantum magnets with a spin gap

Abdulla Rakhimov, Alsu Gazizulina, Zabardast Narzikulov, A. Schilling, Eugene Ya. Sherman

Published Oct 10, 2018• 12 citations
arXivHTMLPDF

Abstract

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 $T$ 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 ${H}_{c}$.

DOI
10.1103/physrevb.98.144416

Related papers

Critical behavior of Tan’s contact for bosonic systems with a fixed chemical potential

Abdulla Rakhimov, Tolibjon Abdurakhmonov, B. Tanatar

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.

arXiv:2104.11894•Journal of Physics Condensed Matter•Aug 18, 2021•6 citations

Quantum magnetization plateau and sign change of the magnetocaloric effect in a ferrimagnetic spin chain.

A. S. Boyarchenkov, Irina Gennad'evna Bostrem, Alexander S. Ovchinnikov

The magnetocaloric effect in the $(5∕2,1)$ ferrimagnetic chain is investiagted using a finite-cluster solver with central spin selection to reduce finite-size effects. We found that an enhanced magnetocaloric effect occurs at the boundary of the ground-state magnetization plateau. The calculated magnetic Gr\"uneisen parameter ${\ensuremath{\Gamma}}_{H}$ exhibits strong signatures of a field-induced quantum phase transition at the critical magnetic field ${H}_{c}$ destroying the plateau. We obtain the characteristic increase ${\ensuremath{\Gamma}}_{H}\ensuremath{\sim}{T}^{\ensuremath{-}1∕\ensuremath{\nu}z}$ near ${H}_{c}$ and the sign change ${\ensuremath{\Gamma}}_{H}\ensuremath{\approx}\ensuremath{-}{G}_{r}∕(H\ensuremath{-}{H}_{c})$, in accordance with scaling theory predictions.

Physical Review B•Dec 14, 2007•26 citations

Characteristic temperatures of a triplon system of dimerized quantum magnets

Abdulla Rakhimov, Mukhtorali Nishonov, Luxmi Rani +1 more

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.

arXiv:1903.08438•International Journal of Modern Physics B•Dec 19, 2020•5 citations

Universal Magnetocaloric Effect near Quantum Critical Point of Magnon Bose-Einstein Condensation

Junsen Xiang, Enze Lv, Qinxin Shen +19 more

Bose-Einstein condensation (BEC), a macroscopic quantum phenomenon arising from phase coherence and bosonic statistics, has been realized in quantum magnets. Here, we report the observation of a universal magnetocaloric effect (MCE) near a BEC quantum critical point (QCP) in copper sulfate crystal ($CuSO_4 \cdot 5H_2O$). By conducting magnetocaloric and nuclear magnetic resonance measurements, we uncover a field-driven BEC QCP, evidenced by the universal scaling law $T_c \propto (B_c - B)^{2/3}$ and the perfect data collapse of the magnetic Grüneisen ratio. Thermal excitation triggers a dimensional crossover to a 1D quantum-critical regime, where the MCE scaling strictly matches the universality class of 1D Fermi gases. Notably, the quantum-critical MCE enables cooling down to 12.8 mK without helium-3, with very fast thermal relaxation rate that is critical for high cooling power. This work demonstrates the universal MCE in magnon BEC systems, using a common copper sulfate compound as a paradigmatic example, and paves the way for next-generation sub-Kelvin cooling.

arXiv:2508.05750•Aug 7, 2025•0 citations

The magnetocaloric effect in integrable spin-schains

G A P Ribeiro

We study the magnetocaloric effect for the integrable antiferromagnetic high spin chain. We present an exact computation of the Grüneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin- s chain in the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the ( H , T ) plane. We have been able to identify the quantum critical points H c ( s ) = 2/( s + 1/2) looking at the isentropes and/or the characteristic behaviour of the Grüneisen parameter.

arXiv:1009.4411•Journal of Statistical Mechanics Theory and Experiment•Dec 6, 2010•8 citations

Thermal expansion and Grüneisen parameter in quantum Griffiths phases

Thomas Vojta

We consider the behavior of the Gr\"uneisen parameter, the ratio between thermal expansion and specific heat, at pressure-tuned infinite-randomness quantum-critical points and in the associated quantum Griffiths phases. We find that the Gr\"uneisen parameter diverges as $\text{ln}({T}_{0}/T)$ with vanishing temperature $T$ in the quantum Griffiths phases. At the infinite-randomness critical point itself, the Gr\"uneisen parameter behaves as ${[\text{ln}({T}_{0}/T)]}^{1+1/(\ensuremath{\nu}\ensuremath{\psi})}$ where $\ensuremath{\nu}$ and $\ensuremath{\psi}$ are the correlation length and tunneling exponents. Analogous results hold for the magnetocaloric effect at magnetic-field-tuned transitions. We contrast clean and dirty systems, we discuss subtle differences between Ising and Heisenberg symmetries, and we relate our findings to recent experiments on ${\text{CePd}}_{1\ensuremath{-}x}{\text{Rh}}_{x}$.

arXiv:0905.2106•Physical Review B•Jul 1, 2009•12 citations
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 \ensuremathΓH{\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremathΓH​ of the system of triplons in spin gapped quantum magnets. Near the critical temperature \ensuremathΓH{\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremathΓH​ 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 Hc,\ensuremathΓH{H}_{c},\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{H}Hc​,\ensuremathΓH​ diverges as \ensuremathΓH\ensuremath∼1/T2{\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremath{\sim}1/{T}^{2}\ensuremathΓH​\ensuremath∼1/T2, while it scales as \ensuremathΓH\ensuremath∼1/(H\ensuremath−Hc){\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremath{\sim}1/(H\ensuremath{-}{H}_{c})\ensuremathΓH​\ensuremath∼1/(H\ensuremath−Hc​) as the magnetic field approaches Hc{H}_{c}Hc​.
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.
The magnetocaloric effect in the (5∕2,1)(5∕2,1)(5∕2,1) ferrimagnetic chain is investiagted using a finite-cluster solver with central spin selection to reduce finite-size effects. We found that an enhanced magnetocaloric effect occurs at the boundary of the ground-state magnetization plateau. The calculated magnetic Gr\"uneisen parameter ${\ensuremath{\Gamma}}_{H}$ exhibits strong signatures of a field-induced quantum phase transition at the critical magnetic field Hc{H}_{c}Hc​ destroying the plateau. We obtain the characteristic increase ${\ensuremath{\Gamma}}_{H}\ensuremath{\sim}{T}^{\ensuremath{-}1∕\ensuremath{\nu}z}$ near Hc{H}_{c}Hc​ and the sign change ${\ensuremath{\Gamma}}_{H}\ensuremath{\approx}\ensuremath{-}{G}_{r}∕(H\ensuremath{-}{H}_{c})$, in accordance with scaling theory predictions.
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.
Bose-Einstein condensation (BEC), a macroscopic quantum phenomenon arising from phase coherence and bosonic statistics, has been realized in quantum magnets. Here, we report the observation of a universal magnetocaloric effect (MCE) near a BEC quantum critical point (QCP) in copper sulfate crystal (CuSO4⋅5H2OCuSO_4 \cdot 5H_2OCuSO4​⋅5H2​O). By conducting magnetocaloric and nuclear magnetic resonance measurements, we uncover a field-driven BEC QCP, evidenced by the universal scaling law Tc∝(Bc−B)2/3T_c \propto (B_c - B)^{2/3}Tc​∝(Bc​−B)2/3 and the perfect data collapse of the magnetic Grüneisen ratio. Thermal excitation triggers a dimensional crossover to a 1D quantum-critical regime, where the MCE scaling strictly matches the universality class of 1D Fermi gases. Notably, the quantum-critical MCE enables cooling down to 12.8 mK without helium-3, with very fast thermal relaxation rate that is critical for high cooling power. This work demonstrates the universal MCE in magnon BEC systems, using a common copper sulfate compound as a paradigmatic example, and paves the way for next-generation sub-Kelvin cooling.
We study the magnetocaloric effect for the integrable antiferromagnetic high spin chain. We present an exact computation of the Grüneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin- s chain in the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the ( H , T ) plane. We have been able to identify the quantum critical points H c ( s ) = 2/( s + 1/2) looking at the isentropes and/or the characteristic behaviour of the Grüneisen parameter.
We consider the behavior of the Gr\"uneisen parameter, the ratio between thermal expansion and specific heat, at pressure-tuned infinite-randomness quantum-critical points and in the associated quantum Griffiths phases. We find that the Gr\"uneisen parameter diverges as ln(T0/T)\text{ln}({T}_{0}/T)ln(T0​/T) with vanishing temperature TTT in the quantum Griffiths phases. At the infinite-randomness critical point itself, the Gr\"uneisen parameter behaves as ${[\text{ln}({T}_{0}/T)]}^{1+1/(\ensuremath{\nu}\ensuremath{\psi})}$ where $\ensuremath{\nu}$ and $\ensuremath{\psi}$ are the correlation length and tunneling exponents. Analogous results hold for the magnetocaloric effect at magnetic-field-tuned transitions. We contrast clean and dirty systems, we discuss subtle differences between Ising and Heisenberg symmetries, and we relate our findings to recent experiments on ${\text{CePd}}_{1\ensuremath{-}x}{\text{Rh}}_{x}$.