Calorimetric determination of magnetic phase diagram of Ba$_{3}$CoSb$_{2}$O$_{9}$*

We report heat capacity measurements as a function of temperature, magnetic field, and field angle for the spin 1/2 triangular antiferromagnet Ba$_{3}$CoSb$_{2}$O$_{9}$, for fields up to the saturation field of 32.5 T and temperatures down to 0.1 K. The system behaves as a frustrated Heisenberg antiferromagnet with weak xy anisotropy. For magnetic fields applied along the a axis, 3 main magnetic phases are expected [1], each corresponding to a different spin arrangement: a low field ``Y'' phase, an intermediate ``up - up - down'' phase, and a high field 'V' phase. We find instead 5 distinct magnetic phase transitions with increasing field, suggesting that the ``Y' and ``V'' phases split into alternating and non-alternating co-planar subphases. \\[4pt] [1] A.V. Chubukov \& D.I. Golosov, J.Phys.Cond.Mat 3, 69 (1991).