Specific heat of theS=1spin-dimer antiferromagnetBa3Mn2O8in high magnetic fields

We have measured the specific heat of the coupled spin-dimer antiferromagnet ${\mathrm{Ba}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{8}$ to $50\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ in temperature and to $29\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ in the magnetic field. The experiment extends to the midpoint of the field region $(25.9\phantom{\rule{0.3em}{0ex}}\mathrm{T}\ensuremath{\leqslant}H\ensuremath{\leqslant}32.3\phantom{\rule{0.3em}{0ex}}\mathrm{T})$ of the magnetization plateau at $1∕2$ of the saturation magnetization, and reveals the presence of three ordered phases in the field region between that of the magnetization plateau and the low-field spin-liquid region. The exponent of the phase boundary with the thermally disordered region is smaller than the theoretical value based on the Bose-Einstein condensation of spin triplets. At zero field and $29\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, the specific-heat data show gapped behaviors characteristic of spin liquids. The zero-field data indicate that the gapped triplet excitations form two levels whose energies differ by nearly a factor of 2. At least the lower level is well localized. The data at $29\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ reveal that the low-lying excitations at the magnetization plateau are weakly delocalized.