  The relative stability of various axisymmetric vortices in a spinor
Bose-Einstein condensate with F=1 is examined within extended Bogoliubov
theory. This yields the phase diagram in the plane of external rotation
frequency vs magnetization. We compare antiferromagnetic, nonmagnetic, and
ferromagnetic cases. The excitation spectrum is evaluated under rotation to
investigate the local stability of the possible vortices and the vortex
nucleation frequency.
