Layered ferromagnet-superconductor structures: The π state and proximity effects

We investigate clean mutilayered structures of the SFS and SFSFS type (where the S layer is intrinsically superconducting and the F layer is ferromagnetic), at low temperature, through numerical solution of the self-consistent Bogoliubov-de Gennes equations for these systems. We obtain results for the pair amplitude, the local density of states, and the local magnetic moment. We find that as a function of the thickness dF of the magnetic layers separating adjacent superconductors, the ground state energy varies periodically between two stable states. The first state is an ordinary “ 0 state,” in which the order parameter has a phase difference of zero between consecutive S layers, and the second is a “ π state,” where the sign alternates, corresponding to a phase difference of π between adjacent S layers. This behavior can be understood from simple arguments. The density of states and the local magnetic moment also reflect this periodicity.