  We study a square plaquette of four optical microtraps containing ultracold
$^{87}$Rb atoms in F=1 hyperfine state. In a presence of external resonant
magnetic field the dipolar interactions couple initial $m_F=1$ component to
other Zeeman sublevels. This process is a generalization of the Einstein-de
Haas effect to the case when the external potential has only $C_4$
point-symmetry. We observe that vortex structures appear in the initially empty
$m_F=0$ state. Topological properties of this state are determined by
competition between the local axial symmetry of the individual trap and the
discrete symmetry of the plaquette. For deep microtraps vortices are localized
at individual sites whereas for shallow traps only one discrete vortex appears
in the plaquette. States created in these two opposite cases have different
topological properties related to $C_4$ point-symmetry.
