  We investigate the relation of the critical current density (Jc) and the
remarkably increased superconducting transition temperature (Tc) for the FeSe
single crystals under pressures up to 2.43 GPa, where the Tc is increased by ~8
K/GPa. The critical current density corresponding to the free flux flow is
monotonically enhanced by pressure which is due to the increase in Tc, whereas
the depinning critical current density at which the vortex starts to move is
more influenced by the pressure-induced magnetic state compared to the increase
of Tc. Unlike other high-Tc superconductors, FeSe is not magnetic, but
superconducting at ambient pressure. Above a critical pressure where magnetic
state is induced and coexists with superconductivity, the depinning Jc abruptly
increases even though the increase of the zero-resistivity Tc is negligible,
directly indicating that the flux pinning property compared to the Tc
enhancement is a more crucial factor for an achievement of a large Jc. In
addition, the sharp increase in Jc in the coexisting superconducting phase of
FeSe demonstrates that vortices can be effectively trapped by the competing
antiferromagnetic order, even though its antagonistic nature against
superconductivity is well documented. These results provide new guidance toward
technological applications of high-temperature superconductors.
