Ferromagnetic-semiconductor–singlet-(or triplet) superconductor–ferromagnetic-semiconductor systems as possible logic circuits and switches

We consider thin superconducting (S) films of thickness $d\ll {\xi }_0,$ sandwiched between two ferromagnetic semiconducting insulators (FI) with differently orientated magnetizations—the $\mathrm{F}\mathrm{I}-S-\mathrm{F}\mathrm{I}$ system. We calculate the dependence of the superconducting critical temperature on the orientation of the magnetization in the insulators and on the thickness of the superconducting film. The calculations are done for singlet as well as triplet superconductors. In the singlet case $T_c$ depends on the relative orientation of the left and right magnetization only, while in the triplet case $T_c$ depends on the absolute orientation of magnetization. The latter property can serve as a kind of spin spectroscopy of triplet and unconventional superconductors, for instance in resolving the structure of the triplet order parameter in the recently discovered layered superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4.$ The possibility of logic circuits and switches, which are based on the $\mathrm{F}\mathrm{I}-S-\mathrm{F}\mathrm{I}$ systems with arbitrary orientation of magnetizations in FI films, is analyzed too.