Double phase transitions in magnetized spinor Bose-Einstein condensation

It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with; the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always doub le BEC transitions from single component BEC to multiple component BEG. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase dia,sram for the temperat ure vs the polarization, the spatial spin structure, the distribution of no n-condensates and the excitation spectrum are examined for the harmonically trapped systems.