Competing ferromagnetic superconducting states in europium-based iron pnictides

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.