  We will show the importance of coexistence of oppositely flowing
$\varphi$-currents for magnetized stars to sustain strong toroidal magnetic
fields within the stars by an- alyzing stationary states of magnetized stars
with surface currents which flow in the opposite direction with respect to the
bulk currents within the stars. We have imposed boundary conditions for
currents and toroidal magnetic fields to vanish outside the stars. It is
important to note that these boundary conditions set an upper limit for the
total current within the stars. This upper limit for the total current results
in the presence of an upper limit for the magnitude of the energy for the
toroidal magnetic fields of the stars. If the stars could have the toroidal
surface currents which flow in the opposite directions to the internal toroidal
currents, the positively flowing inter- nal toroidal currents can become
stronger than the upper limit value of the current for configurations without
surface toroidal currents. Thus the energies for the toroidal magnetic fields
can become much larger than those for the magnetized stars with- out surface
toroidal currents. We have also analyzed the same phenomena appearing in
spherical incompressible stars for dipole-like magnetic fields with or without
sur- face toroidal currents by employing the zero-flux-boundary method. We have
applied those configurations with surface toroidal currents to magnetars and
discussed their flares through which magnetic helicities could arise outside
the stellar surfaces.
