0- and π-states in Josephson coupling through magnetic layers

We study the Josephson coupling energy, EJ, between two superconductors (SCs) through magnetic layers, i.e., ferromagnetic metal (FM) and antiferromagnetic insulator (AFI). By the tunneling Hamiltonian approach, analytical formulae of EJ are given in the fourth order perturbation theory as to the tunneling matrix element. In the former case, the EJ exhibits a damped oscillatory dependence on the thickness of the FM, and shows a transition between the 0- and the π-Josephson couplings. In the latter case, the magnetic exchange interaction in the AFI plane suppresses the π-Josephson coupling, and the 0-Josephson coupling leads to coexistence between SC and AFI. It is found that the origin of π-Josephson coupling in the SC/AFI/SC junction is different from that in the SC/FM/SC one.