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Theory of Magnetic Field-Induced Bose-Einstein Condensation of Triplons in Ba3Cr2O8

Motivated by recent experiments on Ba$_{3}$Cr$_{2}$O$_8$, a new spin-dimer compound with spin-1/2 moments of 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 Ba$_{3}$Cr$_{2}$O$_8$ than in the canonical spin-dimer compound TlCuCl$_{3}$. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons $n_{cr}$ at the critical point. It turns out that the combined effect points to a bigger HFP correction $U n_{cr}$ in Ba$_3$Cr$_2$O$_8$ than in TlCuCl$_{3}$. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific heat data of Ba$_{3}$Cr$_{2}$O$_8$.