Josephson φ-junctions based on structures with complex normal/ferromagnet bilayer

We demonstrate that Josephson devices with a nontrivial phase difference 0 < phi(g) < pi in the ground state can be realized in structures composed of longitudinally oriented normal metal (N) and ferromagnet (F) films in the weak link region. Oscillatory coupling across the F-layer makes the first harmonic in the current-phase relation relatively small, while coupling across the N-layer provides a negative sign of the second harmonic. To derive quantitative criteria for a phi-junction, we have solved the two-dimensional boundary-value problem in the frame of Usadel equations for overlap and ramp geometries of S-NF-S structures. Our numerical estimates show that phi-junctions can be fabricated using up-to-date technology.