Utilizing a microscopic Bogoliubov-de Gennes approach we study Josephson effect in arbitrarily oriented d-wave superconductors connected through two ferromagnets with noncollinear magnetizations, by solving scattering problem. The critical Josephson current is calculated for various parameters of the junction. Mutual influence of d-wave superconducting electrodes orientation and angle α between magnetization in ferromagnetic bilayer of thickness d is analyzed. For various orientation of superconducting electrodes, we calculate (d,α) phase diagram, and discuss the possibility to achieve except coexistence of two stable states 0 and π, also coexistence of three stable states 0, π and π∕2, by varying the angle between magnetizations. We observe also areas of coexistence of stable and metastable states.

中文翻译：

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d波超导体取向对非均匀铁磁结处约瑟夫森电流和相位差的影响

利用微观 Bogoliubov-de Gennes 方法，我们通过解决散射问题研究了通过两个具有非共线磁化强度的铁磁体连接的任意定向 d 波超导体中的约瑟夫森效应。针对结的各种参数计算临界约瑟夫森电流。分析了厚度为d的铁磁双层中d波超导电极取向和磁化角α的相互影响。对于不同取向的超导电极，我们计算了（d，α）相图，并讨论了实现除了两个稳定态 0 和 π 共存之外，还实现三个稳定态 0、π 和 π∕2 共存的可能性，通过改变磁化之间的角度。我们还观察到稳定和亚稳态共存的区域。