Fraunhofer patterns in magnetic Josephson junctions with non-uniform magnetic susceptibility

The development of superconducting memory and logic based on magnetic Josephson junctions relies on an understanding of junction properties and, in particular, the dependence of critical current on external magnetic flux (i.e. Fraunhofer patterns). With the rapid development of Josephson junctions with various forms of inhomogeneous barrier magnetism, Fraunhofer patterns are increasingly complex. In this paper we model Fraunhofer patterns for magnetic Josephson junctions in which the barrier magnetic susceptibility is position- and external-magnetic-field dependent. The model predicts anomalous Fraunhofer patterns in which local minima in the Josephson critical current can be nonzero and non-periodic with external magnetic flux due to an interference effect between magnetised and demagnetised regions.