Bose-Einstein condensation of magnons and long-range order in coupled S=1 dimers on stacked triangular lattices

The bond operator theory under the mean-field approximations is employed to investigate coupled spin-1 dimers on a stacked triangular lattice. The quantum phase transitions from the gapped spin liquid state to the ferromagnetic state or to the 120 degrees three-sublattice antiferromagnetic state are studied with the idea of Bose-Einstein condensation of related magnons. A quantum phase transition from the spin liquid state to the quintuplet triangularly ordered state is also discussed. With the exchange coupling constants J(i) (i=0,1,2,3) extracted in connection with Ba(3)Mn(2)O(8), the magnetization curve, the temperature dependence of heat capacities, and the H-T (magnetic field-temperature) phase diagram are calculated. These results agree well with the experiments. The critical exponents near the critical fields H(c1) and H(c3) are calculated as 2/3. The incommensurability is estimated as delta=0.02 pi.