We have observed hysteresis in superconducting resistive transition curves of Ba$_{0.07}$K$_{0.93}$Fe$_2$As$_2$ ($T_csim$8 K) below about 1 K for in-plane fields. The hysteresis is not observed as the field is tilted away from the $ab$ plane by 20$^{
circ}$ or more. The temperature and angle dependences of the upper critical field indicate a strong paramagnetic effect for in-plane fields. We suggest that the hysteresis can be attributed to a first-order superconducting transition due to the paramagnetic effect. Magnetic torque data are also shown.
We show that the Fermi surface (FS) in the antiferromagnetic phase of BaFe$_2$As$_2$ is composed of one hole and two electron pockets, all of which are three dimensional and closed, in sharp contrast to the FS observed by angle-resolved photoemission
spectroscopy. Considerations on the carrier compensation and Sommerfeld coefficient rule out existence of unobserved FS pockets of significant sizes. A standard band structure calculation reasonably accounts for the observed FS, despite the overestimated ordered moment. The mass enhancement, the ratio of the effective mass to the band mass, is 2--3.
We present the magnetic and superconducting phase diagram of EuFe$_2$As$_2$ for $B parallel c$ and $B parallel ab$. The antiferromagnetic phase of the Eu$^{2+}$ moments is completely enclosed in the superconducting phase. The upper critical field vs.
temperature curves exhibit strong concave curvatures, which can be explained by the Jaccarino-Peter compensation effect due to the antiferromagnetic exchange interaction between the Eu$^{2+}$ moments and conduction electrons.
