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We report the ac magnetic susceptibility $\chi_{ac}$ and resistivity $\rho$measurements of EuFe$_2$As$_2$ under high pressure $P$. By observing nearly100% superconducting shielding and zero resistivity at $P$ = 28 kbar, weestablish that $P$-induced superconductivity occurs at $T_c \sim$~30 K inEuFe$_2$As$_2$. $\rho$ shows an anomalous nearly linear temperature dependencefrom room temperature down to $T_c$ at the same $P$. $\chi_{ac}$ indicates thatan antiferromagnetic order of Eu$^{2+}$ moments with $T_N \sim$~20 K persistsin the superconducting phase. The temperature dependence of the upper criticalfield is also determined.

EuFe$_2$As$_2$ under high pressure: an antiferromagnetic bulk superconductor