  We demonstrate that a spin-orbit-coupled Bose-Einstein condensate can be
effectively rotated by adding a real magnetic field to inputting gauge angular
momentum, which is distinctly different from the traditional ways of rotation
by stirring or Raman laser dressing to inputting canonical angular momentum.
The gauge angular momentum is accompanied by the spontaneous generation of
equal and opposite canonical angular momentum in the ground states, and it
leads to the nucleation of quantized vortices. We explain this by indicating
that the effective rotation with the vortex nucleation results from the
effective magnetic flux induced by the gauge potential, which is essentially
different from the previous scheme of creating vortices by synthetic magnetic
fields. In the weakly interacting regime, symmetrically placed domains
separated by vortex lines as well as half-integer giant vortices are
discovered. With relatively strong interatomic interaction, we predict a
structure of coaxially arranged annular vortex arrays, which is in stark
contrast to the familiar Abrikosov vortex lattice. The developed way of
rotation may be extended to a more general gauge system.
