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.
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