Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behavior of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation $T_{\mathrm{BEC}}$ increases with magnetic field. In particular the system is ferromagnetic below $T_{\mathrm{BEC}}$ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetization with regard to temperature or magnetic field are discontinuous along the phase boundary.

• Received 16 March 1998

DOI:https://doi.org/10.1103/PhysRevA.59.1528