  Motivated by the recent experimental realization of a Bose-Einstein
condensate (BEC) of europium atoms, we investigate the self-bound droplet state
of a europium BEC with spin degrees of freedom. Under a sufficiently weak
magnetic field, the droplet has a torus shape with circulating spin vectors,
which is referred to as a magnetic vortex. The ground state transforms from the
torus to cigar shape through bistability with an increase in the magnetic
field. Dynamical change of the magnetic field causes the torus to rotate due to
the Einstein-de Haas effect. The magnetic vortices form a supersolid in a
confined system.
