  We investigate a Bose-Einstein condensate of $F= 1$ $^{87}$Rb atoms in a 2D
spin-dependent optical lattice generated by intersecting laser beams with a
superposition of polarizations. For $^{87}$Rb the effective interaction of an
atom with the electromagnetic field contains a scalar and a vector (called as
fictitious magnetic field, $B_{fic}$) potentials. The Rb atoms behave as a
quantum rotor (QR) with angular momentum given by the sum of the atomic
rotational motion angular momentum and the hyperfine spin. The ground state of
the QR is affected upon applying an external magnetic field, $B_{ext}$,
perpendicular to the plane of QR motion and a sudden change of its topology
occurs as the ratio $B_{ext}/B_{fic}$ exceeds critical value. It is shown that
the change of topology of the QR ground state is a result of combined action of
Zeeman and Einstein-de Haas effects. The first transfers atoms to the largest
hyperfine component to polarize the sample along the field as the external
magnetic field is increased. The second sweeps spin to rotational angular
momentum, modifying the kinetic energy of the atoms.
