High Magnetic Field Studies of Pressure-induced Superconductor EuFe$_2$As$_2$

We have performed resistivity and susceptibility measurements of the pressure-induced superconductor EuFe$_2$As$_2$ under high magnetic fields up to 27 T. The upper critical field $B_{c2}$ and its pressure evolution up to 3.2 GPa were determined in a wide temperature range down to 1.6 K. At 2.5 GPa, nearly the optimal pressure with $T_c$=30 K, $B_{c2}$(0) obtained by the onset of resistive transitions are 25 T and 22 T for $B\parallel ab$ and $B\parallel c$, respectively, which are appreciably smaller than those for other Fe-based superconductors with similar $T_c$. The small $B_{c2}$(0) values and the peculiar $B_ {c2}$($T$) curves in EuFe$_2$As$_2$ can be explained by a multiple pair-breaking model including the exchange field due to the magnetic Eu$^{2+}$ moments. We will also present the results of quantum oscillations observed above the optimal pressure.