Bose-einstein condensation in spin dimer compounds

The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.

arXiv:cond-mat/0607465Physical Review LettersJan 4, 200764 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

Bose-Einstein Condensation in Some Interacting Systems

Joseph V. Pulé

NATO ASI series. Series B : PhysicsJan 1, 19860 citations

Bose-Einstein Condensation of Molecules

Johannes Hecker Denschlag

APSMar 1, 20041 citation

Nuclear magnetic resonance evidence for a strong modulation of the Bose-Einstein condensate in BaCuSi 2 O 6

S. Krämer, Raivo Stern, M. Horvatić +3 more

We present a $^{63,65}\mathrm{Cu}$ and $^{29}\mathrm{Si}$ NMR study of the quasi-2D coupled spin 1/2 dimer compound ${\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}$ in the magnetic field range $13--26\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ and at temperatures as low as $50\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ . NMR data in the gapped phase reveal that below $90\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ different intradimer exchange couplings and different gaps $({\ensuremath{\Delta}}_{\mathrm{B}}∕{\ensuremath{\Delta}}_{\mathrm{A}}=1.16)$ exist in every second plane along the $c$ axis, in addition to a planar incommensurate (IC) modulation. $^{29}\mathrm{Si}$ spectra in the field induced magnetic ordered phase reveal that close to the quantum critical point at ${H}_{\mathrm{c}1}=23.35\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ the average boson density $\overline{n}$ of the Bose-Einstein condensate is strongly modulated along the $c$ axis with a density ratio for every second plane ${\overline{n}}_{\mathrm{A}}∕{\overline{n}}_{\mathrm{B}}\ensuremath{\simeq}5$. An IC modulation of the local density is also present in each plane.We present a $^{63,65}\mathrm{Cu}$ and $^{29}\mathrm{Si}$ NMR study of the quasi-2D coupled spin 1/2 dimer compound ${\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}$ in the magnetic field range $13--26\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ and at temperatures as low as $50\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. NMR data in the gapped phase reveal that below $90\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ different intradimer exchange couplings and different gaps $({\ensuremath{\Delta}}_{\mathrm{B}}∕{\ensuremath{\Delta}}_{\mathrm{A}}=1.16)$ exist in every second plane along the $c$ axis, in addition to a planar incommensurate (IC) modulation. $^{29}\mathrm{Si}$ spectra in the field induced magnetic ordered phase reveal that close to the quantum critical point at ${H}_{\mathrm{c}1}=23.35\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ the average boson density $\overline{n}$ of the Bose-Einstein condensate is strongly modulated along the $c$ axis with a density ratio for every second plane ${\overline{n}}_{\mathrm{A}}∕{\overline{n}}_{\mathrm{B}}\ensuremath{\simeq}5$. An IC modulation of the local density is also present in each plane.

arXiv:0704.0888Physical Review BSep 18, 200733 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}

We present a

^{63,65}\mathrm{Cu}

and

^{29}\mathrm{Si}

NMR study of the quasi-2D coupled spin 1/2 dimer compound

{\mathrm{BaCuSi}}_{2}{\mathrm{O}}_{6}

in the magnetic field range

13--26\phantom{\rule{0.3em}{0ex}}\mathrm{T}

and at temperatures as low as

50\phantom{\rule{0.3em}{0ex}}\mathrm{mK}

. NMR data in the gapped phase reveal that below

90\phantom{\rule{0.3em}{0ex}}\mathrm{K}

different intradimer exchange couplings and different gaps $({\ensuremath{\Delta}}_{\mathrm{B}}∕{\ensuremath{\Delta}}_{\mathrm{A}}=1.16)$ exist in every second plane along the

c

axis, in addition to a planar incommensurate (IC) modulation.

^{29}\mathrm{Si}

spectra in the field induced magnetic ordered phase reveal that close to the quantum critical point at

{H}_{\mathrm{c}1}=23.35\phantom{\rule{0.3em}{0ex}}\mathrm{T}

the average boson density

\overline{n}

of the Bose-Einstein condensate is strongly modulated along the

c

axis with a density ratio for every second plane ${\overline{n}}_{\mathrm{A}}∕{\overline{n}}_{\mathrm{B}}\ensuremath{\simeq}5$. An IC modulation of the local density is also present in each plane.