  The influence of antiferromagnetic order on the mixed state of a
superconductor may result in creation of spin-flop domains along vortices. This
may happen when an external magnetic field is strong enough to flip over
magnetic moments in the vortex core from their ground state configuration. The
formation of domain structure causes modification of the surface energy
barrier, and creation of the new state in which magnetic flux density is
independent of the applied field. The modified surface energy barrier has been
calculated for parameters of the antiferromagnetic superconductor
DyMo$_{6}$S$_{8}$. The prediction of two-step flux penetration process has been
verified by precise magnetization measurements performed on the single crystal
of DyMo$_{6}$S$_{8}$ at milikelvin temperatures. A characteristic plateau on
the virgin curve $B(H_0)$ has been found and attributed to the modified surface
energy barrier. The end of the plateau determines the critical field, which we
call the second critical field for flux penetration.
