  We study the magnetic phase diagram and hysteresis behavior of weakly coupled
spin dimers on a triangular lattice using the cluster mean-field method with
cluster-size scaling. We find that the magnetization curve has plateaus at 1/3
and 2/3 of the total magnetization, in which local singlet and triplet states
form a superlattice pattern. Moreover, if increasing (decreasing) the magnetic
field from the 1/3 (2/3) plateau, the Bose-Einstein condensation (BEC) of
triplons occurs on the superlattice background, leading to the transition into
magnon supersolid phase. We also find that the first-order transition between
these solid states and the standard magnon BEC state exhibits an anomalous
hysteresis upon cycling the magnetic field; the transition can occur only from
solid to BEC, and the system cannot return to the initial solid state in the
reverse process.
