Zero phase difference supercurrent in ferromagnetic Josephson junctions

We analyse both analytically and numerically a ballistic ferromagnetic Josephson junction with spin active interfaces, focusing on the zero phase difference supercurrent that appears when the magnetizations of the intermediate layer and the interfaces form a non-coplanar set of vectors. We claim that the presence of even one magnetization vector in the system breaks the time reversal invariance of the Hamiltonian, which can lead to a zero phase difference supercurrent, unless the symmetry is restored by a combination of time reversal and a rotational symmetry. This is the case when the magnetizations of the junction form a coplanar set of vectors. We also derive a new formula for the equilibrium supercurrent which is a generalization of our previous work.