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Motivated by recent experiments on Ba$_{3}$Cr$_{2}$O$_8$, a new spin-dimercompound with spin-1/2 moments of Cr$^{5+}$ ions, we theoretically investigatethe field-induced magnetic ordering in this material in view of theBose-Einstein condensation (BEC) of triplet excitations (triplons). We applythe self-consistent Hartree-Fock-Popov (HFP) approach to a microscopicHamiltonian, using the realistic triplon dispersion measured in an inelasticneutron scattering experiment. In particular, we ask to what extent the BEC ofdilute triplons near the critical field can explain the magnetic ordering inthis material. For example, we investigate the temperature range where the BECpicture of triplons can be applied via the HFP approach. We also determine thetemperature regime where a quadratic approximation of the triplon dispersionworks. It is found that the strength of the effective repulsive interactionbetween triplons is much weaker in Ba$_{3}$Cr$_{2}$O$_8$ than in the canonicalspin-dimer compound TlCuCl$_{3}$. Small effective repulsive interaction incombination with the narrow band of triplons leads to higher density oftriplons $n_{cr}$ at the critical point. It turns out that the combined effectpoints to a bigger HFP correction $U n_{cr}$ in Ba$_3$Cr$_2$O$_8$ than inTlCuCl$_{3}$. Nonetheless, the HFP approach provides a reasonable explanationof the transverse magnetization and the specific heat data ofBa$_{3}$Cr$_{2}$O$_8$.

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