  The structure of a superconducting vortex has been studied theoretically for
a dirty antiferromagnetic superconductor (AFSC), modelling an AFSC as a doped
semi-metal with s-wave superconducting pairing and antiferromagnetic
(dielectric) interaction between electrons (holes). It is also supposed that
the quasiparticles dispersion law possesses the property of nesting. The
distribution of the superconducting and magnetic order parameters near the
vortex core is calculated. It is shown that the antiferromagnetic order, been
suppressed at large distances, is restored around the superconducting flux and
the vortex core is in fact insulating and antiferromagnetic, in stark contrast
to the normal metal cores of traditional superconductors. Moreover, our model
calculations predict that as the temperature decreases the flux region of the
superconductivity and antiferromagnetism coexistence increases.
