  The iron-based superconductors represent a promising platform for
high-temperature superconductivity, but the interactions underpinning their
pairing present a puzzle. The EuFe$_2$As$_2$ family is unique among these
materials for having magnetic order which onsets within the superconducting
state, just below the superconducting transition. Superconductivity and
magnetic order are normally antagonistic and often vie for the same unpaired
electrons, but in this family the magnetism arises from largely localized Eu
moments and they coexist, with the competition between these evenly-matched
opponents leading to reentrant superconducting behavior. To help elucidate the
physics in this family and the interactions between the magnetic order and
superconductivity, we investigate the $H$--$T$ phase diagram near optimal Rh
doping through specific heat, resistivity, and magnetization measurements, and
study the electronic structure by angular-resolved photoemission spectroscopy.
The competition between the Eu and FeAs layers may offer a route to directly
accessing the electronic structure under effective magnetic fields via ARPES,
which is ordinarily a strictly zero-field technique.
