Cooper pair splitting in diffusive magnetic SQUIDs

We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties – ferromagnetic, half-metallic or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realises a ${\phi }_0$ junction with sample-dependent ${\phi }_0$ and critical current. Cooper pair splitting between the two arms plays a major role and leads to $2{\mathrm{\Phi }}_0$ periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the three types of magnetic links.