  Ba3Mn2O8 is a spin-dimer compound based on pairs of S=1, 3d^2, Mn^{5+} ions
arranged on a triangular lattice. Antiferromagnetic intradimer exchange leads
to a singlet ground state in zero-field. Here we present the first results of
thermodynamic measurements for single crystals probing the high-field ordered
states of this material associated with closing the spin gap to the excited
triplet states. Specific heat, magnetocaloric effect, and torque magnetometry
measurements were performed in magnetic fields up to 32 T and temperatures down
to 20 mK. For fields above H_{c1} ~ 8.7 T, these measurements reveal a single
magnetic phase for H parallel to c, but two distinct phases (approximately
symmetric about the center of the phase diagram) for H perpendicular to c.
Analysis of the simplest possible spin Hamiltonian describing this system
yields candidates for these ordered states corresponding to a simple spiral
structure for H parallel to c, and to two distinct modulated phases for H
perpendicular to c. Both single-ion anisotropy and geometric frustration play
crucial roles in defining the phase diagram.
