and $$\chi \approx \pi +\varphi -\frac{2q\Gamma }{(p-q)\Gamma _{BI}}\sin \left(
\varphi \right)$$in $\pi $-state ($d_{F}>d_{F1}$). Substitution of these expressions into (\[Jsymm1\]) results in $$J_{S}(\varphi )=\pm \frac{J_{G}}{\Gamma _{BI}}\left[ \sin \varphi -\frac{\Gamma }{\Gamma _{BI}}\frac{1\mp \beta }{2\beta }\sin \left( 2\varphi
\right) \right]  \label{SISIotFI3}$$for $0$- and $\pi $- states, respectively. It is seen that for $d_{F}<d_{F1}$ the CPR (\[SISIotFI3\]) has typical for SIS tunnel junctions sinusoidal shape with small correction taking into account the suppression of superconductivity in the s layer due to proximity with FS part of complex sFS electrode. Its negative sign is typical for the tunnel Josephson structures with composite NS or FS electrodes [@KuperD; @CurPh]. For $d_{F}>d_{F1}$ the supercurrent changes its sign thus exhibiting the transition of SIsFS junction into $\pi $ state. It’s important to note that in this mode the SIsFS structure may have almost the same value of the critical current both in $0$ and $\pi $ states. It is unique property, which can not be realized in SFS devices studied before. For this reason we have identified this mode as “Switchable $0-\pi $ SIS junction”.

### Mode (1b): sFS junction

Another limiting case is realized under the condition $\Gamma _{BI}^{-1}\gg
|\beta |\Gamma ^{-1}.$ It fulfills in the 