  Temperature dependence of resistivity under high pressures with magnetic
fields parallel and perpendicular to the FeSe planes are measured in FeSe
single crystals. It is found that the structural transition (nematic)
temperature is suppressed by pressure and ends at around $P$ = 1.18 GPa. Below
around 0.85 GPa, the superconducting transition shows a narrow width with no
indication of antiferromagnetic order. While above this pressure, the
superconducting transition temperature drops slightly forming a small dome of
superconducting region with the maximum $T_c$ at around 0.825 GPa. Furthermore,
just above this pressure, the superconducting transition exhibits an unusual
large transition width which reaches about 6-8 K. This wide transition width is
an intrinsic feature and does not change with magnetic field. In the high
pressure region above 1.18 GPa, just accompanying the onset of superconducting
transition, an upturn of resistivity immediately occurs, which is attributed to
the formation of an antiferromagnetic order. This closely attached behavior of
superconductivity and antiferromagnetic order indicates that these two orders
have a synergy feature. Near the critical pressure 0.825 GPa and below, our
data illustrate that an antiferromagnetic order emerges when superconductivity
is suppressed. From the weak influence of magnetic field to the
antiferromagnetic order, we conclude that it exists already below the small
superconducting dome in the low pressure region. This shows a competing feature
between superconductivity and antiferromagnetic order. Our results show duality
features, namely synergy and competition between superconductivity and
antiferromagnetic order under pressure in FeSe.
