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I apply the recently developed formalism of generalized quasiclassical theoryto show that using hybrid superconducting systems with non-collinear strongferromagnets one can realize the Josephson junction between Berezinskii-typesuperconductors. The reported calculation reproduces main features observed inthe recent experiment, namely the the slightly asymmetric double-slitFraunhofer interference pattern of the Josephson current through theferromagnetic vortex. The double-slit structure results from the spatiallyinhomogeneous Berezinskii state with the amplitude controlled by the localangle between magnetic moments in two ferromagnetic layers. The criticalcurrent asymmetry by the sign of magnetic field can signal the presence ofspontaneous supercurrents generated by the non-coplanar magnetic texture nearthe core of the ferromagnetic vortex core. I demonstrate that ferromagneticvortex can induce spontaneous vorticity in the odd-frequency order parametermanifesting the possibility of the emergent magnetic field to createtopological defects.

Double-slit Fraunhofer pattern as the signature of the Josephson effect between Berezinskii superconductors through the ferromagnetic vortex