The magnetic dipole-dipole interaction couples the spin and orbital angular momenta so that spin relaxation causes the system to rotate mechanically (Einstein-de Haas effect) or, conversely, a solid-body rotation of the system leads to its magnetization (Barnett effect). We show that these effects also occur in a dipolar Bose-Einstein condensate in which atoms undergo scalar, spinor, and dipolar interactions. General properties of the order parameter for a dipolar spinor Bose-Einstein condensate is discussed based on symmetries of the interactions, and an initially spin-polarized dipolar condensate is shown to dynamically generate a new type of non-singular vortex via spin-orbit interactions. We also discuss the effect of the external magnetic field and that of the trap geometry on the properties of the condensate. |