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.

May 29, 20090 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

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

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

Stability and superfluidity of the Bose-Einstein condensate in a two-leg ladder with magnetic field

Yue Jian, Xin Qiao, Jun-Cheng Liang +3 more

The stability and superfluidity of the Bose-Einstein condensate in two-leg ladder with magnetic field are studied. The dispersion relation and the phase diagram of the system are obtained. Three phases are revealed: the Meissner phase, the biased ladder (BL) phase, and the vortex phase. The dispersion relation and phase transition of the system strongly depend on the magnitude of atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. Particularly, the change of the energy band structure in the phase transition region is modified significantly by the atomic interaction strength. Furthermore, based on the Bogoliubov theory, the energetic and dynamical stability of the system are invested. The stability phase diagram in the full parameter space is presented, and the dependence of superfluidity on the dispersion relation is illustrated explicitly. The atomic interaction strength can produce dynamical instability in the energetic unstable region and can expand the superfluid region. The results show that the stability of the system can be controlled by the atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. In addition, the excitation spectrums in the Meissner phase, BL phase and vortex phase are further studied. The modulation of the excitation spectrum and the energetic stability of the system by the atomic interaction strength, the rung-to-leg coupling ratio and magnetic flux is discussed. Finally, through the numerical simulation, the dynamical instability of the system is verified by the time evolution of the Bloch wave and rung current. This provides a theoretical basis for controlling the superfluidity of the system.The stability and superfluidity of the Bose-Einstein condensate in two-leg ladder with magnetic field are studied. The dispersion relation and the phase diagram of the system are obtained. Three phases are revealed: the Meissner phase, the biased ladder (BL) phase, and the vortex phase. The dispersion relation and phase transition of the system strongly depend on the magnitude of atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. Particularly, the change of the energy band structure in the phase transition region is modified significantly by the atomic interaction strength. Furthermore, based on the Bogoliubov theory, the energetic and dynamical stability of the system are invested. The stability phase diagram in the full parameter space is presented, and the dependence of superfluidity on the dispersion relation is illustrated explicitly. The atomic interaction strength can produce dynamical instability in the energetic unstable region and can expand the superfluid region. The results show that the stability of the system can be controlled by the atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. In addition, the excitation spectrums in the Meissner phase, BL phase and vortex phase are further studied. The modulation of the excitation spectrum and the energetic stability of the system by the atomic interaction strength, the rung-to-leg coupling ratio and magnetic flux is discussed. Finally, through the numerical simulation, the dynamical instability of the system is verified by the time evolution of the Bloch wave and rung current. This provides a theoretical basis for controlling the superfluidity of the system.

Physical review. EAug 13, 20216 citations

The effects of disorder in dimerized quantum magnets in mean field approximations

Abdulla Rakhimov, Shuhrat Mardonov, E Ya Sherman +1 more

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.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.

arXiv:1206.4143New Journal of PhysicsNov 7, 20128 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}