  In europium-based iron pnictides superconducting Fe-planes can be influenced
by a Zeeman field originated from the neighboring Eu-planes. The field tends to
induce spin-density waves with a ferromagnetic average which coexists with the
superconducting order by forming complementary patterns of the superconducting
and magnetic order parameters in a Fulde-Ferrell-Larkin-Ovchinnikov phase and a
two-dimensional textured-superconducting phase. The hard gap around the Fermi
energy disappears in these fragile inhomogeneous superconducting states, which
features, instead, V-shaped spin-resolved local density of states. The
inhomogeneous states are also competing with either a homogeneous
superconducting or a homogeneous ferromagnetic state, manifesting the
intertwining influences of the magnetic orders in Fe and Eu planes, the
spin-density wave band structure, and the superconducting pairing order.
