  Single monolayer FeSe film grown on Nb-doped SrTiO$_3$(001) substrate shows
the highest superconducting transition temperature (T$_C$ $\sim$ 100 K) among
the iron-based superconductors (iron-pnictide), while T$_C$ of bulk FeSe is
only $\sim$ 8 K. Antiferromagnetic spin fluctuations were believed to be
crucial in iron-pnictides, which has inspired several proposals to understand
the FeSe/SrTiO$_3$ system. Although bulk FeSe does not show the
antiferromagnetic order, calculations suggest that the parent FeSe/SrTiO$_3$
films are AFM. Experimentally, due to lacking of direct probe, the magnetic
state of FeSe/SrTiO$_3$ films remains mysterious. Here, we report the direct
evidences of the antiferromagnetic order in the parent FeSe/SrTiO$_3$ films by
the magnetic exchange bias effect measurements. The phase transition
temperature is $\geq$ 140 K for single monolayer film. The AFM order disappears
after electron doping.
