Resistivity and Hall effect measurements of EuFe$_2$As$_2$ up to 3.2,GPa indicate no divergence of quasiparticle effective mass at the pressure $P_mathrm{c}$ where the magnetic and structural transition disappears. This is corroborated by analysis of
the temperature ($T$) dependence of the upper critical field. $T$-linear resistivity is observed at pressures slightly above $P_mathrm{c}$. The scattering rates for both electrons and holes are shown to be approximately $T$-linear. When a field is applied, a $T^2$ dependence is recovered, indicating that the origin of the $T$-linear dependence is spin fluctuations.
We have constructed a pressure$-$temperature ($P-T$) phase diagram of $P$-induced superconductivity in EuFe$_2$As$_2$ single crystals, via resistivity ($rho$) measurements up to 3.2 GPa. As hydrostatic pressure is applied, an antiferromagnetic (AF) t
ransition attributed to the FeAs layers at $T_mathrm{0}$ shifts to lower temperatures, and the corresponding resistive anomaly becomes undetectable for $P$ $ge$ 2.5 GPa. This suggests that the critical pressure $P_mathrm{c}$ where $T_mathrm{0}$ becomes zero is about 2.5 GPa. We have found that the AF order of the Eu$^{2+}$ moments survives up to 3.2 GPa without significant changes in the AF ordering temperature $T_mathrm{N}$. The superconducting (SC) ground state with a sharp transition to zero resistivity at $T_mathrm{c}$ $sim$ 30 K, indicative of bulk superconductivity, emerges in a pressure range from $P_mathrm{c}$ $sim$ 2.5 GPa to $sim$ 3.0 GPa. At pressures close to but outside the SC phase, the $rho(T)$ curve shows a partial SC transition (i.e., zero resistivity is not attained) followed by a reentrant-like hump at approximately $T_mathrm{N}$ with decreasing temperature. When nonhydrostatic pressure with a uniaxial-like strain component is applied using a solid pressure medium, the partial superconductivity is continuously observed in a wide pressure range from 1.1 GPa to 3.2 GPa.
We have carried out high-field resistivity measurements up to 27,T in EuFe$_2$As$_2$ at $P$,=,2.5,GPa, a virtually optimal pressure for the $P$-induced superconductivity, where $T_mathrm{c}$,=,30,K. The $B_mathrm{c2}-T_mathrm{c}$ phase diagram has be
en constructed in a wide temperature range with a minimum temperature of 1.6 K ($approx 0.05 times T_mathrm{c}$), for both $B parallel ab$ ($B_mathrm{c2}^mathrm{ab}$) and $B parallel c$ ($B_mathrm{c2}^mathrm{c}$). The upper critical fields $B_mathrm{c2}^mathrm{ab}$(0) and $B_mathrm{c2}^mathrm{c}$(0), determined by the onset of resistive transitions, are 25 T and 22 T, respectively, which are significantly smaller than those of other Fe-based superconductors with similar values of $T_mathrm{c}$. The small $B_mathrm{c2}(0)$ values and the $B_mathrm{c2}(T)$ curves with positive curvature around 20 K can be explained by a multiple pair-breaking model that includes the exchange field due to the magnetic Eu$^{2+}$ moments. The anisotropy parameter, $Gamma=B_mathrm{c2}^{ab}/B_mathrm{c2}^{c}$, in EuFe$_2$As$_2$ at low temperatures is comparable to that of other 122 Fe-based systems.
