High-field instability of low-temperature magnon Bose-Einstein condensate

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 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.

arXiv:0905.4817Physical Review BJan 19, 201018 citations

Bose–Einstein condensation of triplons with a weakly broken U(1) symmetry

Asliddin Khudoyberdiev, Abdulla Rakhimov, A. Schilling

The low-temperature properties of certain quantum magnets can be described in terms of a Bose–Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl 3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree–Fock–Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl 3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., of T c in H = 6 T and for .The low-temperature properties of certain quantum magnets can be described in terms of a Bose–Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl 3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree–Fock–Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl 3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., of T c in H = 6 T and for .

arXiv:1701.08009New Journal of PhysicsSep 4, 201716 citations

Metastable spin-phase diagrams in antiferromagnetic Bose-Einstein condensates

Eduardo Serrano-Ensástiga, Francisco Mireles

Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.

arXiv:2109.01986Physical Review ADec 13, 20214 citations

Theory of magnetic-field-induced Bose-Einstein condensation of triplons in Ba3Cr2O8

Tyler Dodds, Bohm‐Jung Yang, Yong Baek Kim

Motivated by recent experiments on ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ , a new spin-dimer compound with spin-1/2 moments of ${\text{Cr}}^{5+}$ 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 ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in the canonical spin-dimer compound ${\text{TlCuCl}}_{3}$ . Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons ${n}_{\text{cr}}$ at the critical point. The combined effect points to a bigger HFP correction $U{n}_{\text{cr}}$ in ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in ${\text{TlCuCl}}_{3}$ . Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ .Motivated by recent experiments on ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$, a new spin-dimer compound with spin-1/2 moments of ${\text{Cr}}^{5+}$ 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 ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in the canonical spin-dimer compound ${\text{TlCuCl}}_{3}$. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons ${n}_{\text{cr}}$ at the critical point. The combined effect points to a bigger HFP correction $U{n}_{\text{cr}}$ in ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in ${\text{TlCuCl}}_{3}$. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$.

arXiv:0910.0247Physical Review BFeb 9, 201013 citations

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.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:2104.11894Journal of Physics Condensed MatterAug 18, 20216 citations

Double Phase Transitions in Magnetized Spinor Bose-Einstein Condensation

Tomoya Isoshima, Tetsuo Ohmi, Kazushige Machida

It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always double BEC transitions from single component BEC to multiple component BEC. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase diagram for the temperature vs the polarization, the spatial spin structure, the distribution of non-condensates and the excitation spectrum are examined for the harmonically trapped systems.It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always double BEC transitions from single component BEC to multiple component BEC. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase diagram for the temperature vs the polarization, the spatial spin structure, the distribution of non-condensates and the excitation spectrum are examined for the harmonically trapped systems.

arXiv:cond-mat/0005289Journal of the Physical Society of JapanDec 15, 200038 citations

Motivated by recent experiments on

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}

, a new spin-dimer compound with spin-1/2 moments of

{\text{Cr}}^{5+}

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

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}

than in the canonical spin-dimer compound

{\text{TlCuCl}}_{3}

. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons

{n}_{\text{cr}}

at the critical point. The combined effect points to a bigger HFP correction

U{n}_{\text{cr}}

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}

than in

{\text{TlCuCl}}_{3}

. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}