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

We demonstrate that Josephson devices with nontrivial phase difference in the ground state can be realized in structures composed from longitudinally oriented normal metal (N) and ferromagnet (F) films in the weak link region. Oscillatory coupling across F-layer makes the first harmonic in the current-phase relation relatively small, while coupling across N-layer provides negative sign of the second harmonic. To derive quantitative criteria for a $φ$-junction, we have solved 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 $φ$-junctions can be fabricated using up-to-date technology.

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