$0\text{−}\pi$ transition in superconductor-ferromagnet-superconductor junctions with strongly spin-dependent scattering

We develop a theory of the critical current in superconductor–ferromagnetic alloy–superconductor trilayers, which takes into account the strong spin dependence of electron scattering on compositional disorder in a diluted ferromagnetic alloy. We show that in such a system the critical current oscillations as a function of the thickness of the ferromagnetic layer, with period of $v_F∕2I$, $v_F$ and $I$ being the Fermi velocity and exchange splitting, respectively, decay exponentially with a characteristic length of the order of the mean free path.

Figure 1

Dependence of the factor $\mid Z\mid$ determined in Eq. (18) on $\alpha =({\tau }_J-{\tau }_V)∕({\tau }_V+{\tau }_J)$ for various values of $I\tau$. From top to bottom: $I\tau =0,0.3,1,10$. The results show that outside the diffusive regime, $I\tau ⪡1$ and ${\tau }_J⪢{\tau }_V$, $Z$ is a smooth function of $\alpha$ of order 1.

Figure 2

Dependence of the critical current in a SFS trilayer on ferromagnetic layer thickness. Here, we normalize the current using a notional $j_0=2\pi e\nu v_F{\Theta }^2\Delta$, and show it for $T=0$, $\Delta \tau =0.1$ and several values of parameters $\alpha$ and $I\tau$: $\alpha =0$ (dashed lines) and 0.3 (solid lines). Dips in the value of $j_c$ indicate positions where it disappears and changes sign, thus resulting in a sequence of $0\text{−}\pi$ transitions. Neighboring dips always correspond to the same value of $I\tau$, demonstrating only weak dependence of the results on the parameter $\alpha$. For comparison, we also show the decay of the Josephson proximity effect in a SNS structure heavily doped by magnetic scatterers $(I\tau =0)$.