  We employ a self-consistent simulation approach based on quantum physics here
to study the magnetism of antiferromagnetic skyrmions formed on manolayer
nanodisk planes. We find that if the disk is small and the Dzyaloshinsky-Moriya
(DM) interaction is weak, a single magnetic vortex may be formed on the disk
plane. In such a case, when uniaxial anisotropy normal to the disk plane is
further considered, the magnetic configuration remains unchanged, but the
magnetization is enhanced in that direction, and reduced in other two
perpendicular orientations. Very similarly, a weak external magnetic field
normal to the disk plane cannot obviously affect the spin structure of the
nanodisk; however, when it is sufficiently strong, it can destroy the AFM
skyrmion completely. On the other hand, by increasing DM interaction so that
the disk diameter is a few times larger than the DM length, more self-organized
magnetic domains, such as vortices and strips, will be formed in the disk
plane. They evolve with decreasing temperature, however always symmetric about
a geometric axis of the square unit cell. We further find that in this case
introducing normal magnetic anisotropy gives rise to the re-construction of AFM
single-vortex structure or skyrmion on the disk plane, which provides a way to
create and/or stabilize such spin texture in experiment.
