Phase diagrams of F=2 spinor Bose-Einstein condensates

We show that there are three possible phases for a spin-2 spinor Bose condensate, one more compared to the spin-1 case. The order parameters of these phases are the spontaneous magnetization and the singlet pair amplitude. Current estimates of scattering lengths show that all three phases have realizations in optically trapped alkali atoms. There is also a one-to-one correspondence between the structure of a spin-2 spinor Bose condensate and that of a d-wave BCS superfluid.