  Bose-Einstein condensates of dilute atomic gases, characterized by a
macroscopic population of the quantum mechanical ground state, are a new,
weakly interacting quantum fluid. In most experiments condensates in a single
weak field seeking state are magnetically trapped. These condensates can be
described by a scalar order parameter similar to the spinless superfluid 4He.
Even though alkali atoms have angular momentum, the spin orientation is not a
degree of freedom because spin flips lead to untrapped states and are therefore
a loss process. In contrast, the recently realized optical trap for sodium
condensates confines atoms independently of their spin orientation. This opens
the possibility to study spinor condensates which represent a system with a
vector order parameter instead of a scalar. Here we report a study of the
equilibrium state of spinor condensates in an optical trap. The freedom of spin
orientation leads to the formation of spin domains in an external magnetic
field. The structure of these domains are illustrated in spin domain diagrams.
Combinations of both miscible and immiscible spin components were realized.
