We study the Josephson effect in junctions composed of two ferromagnetic insulator/diffusive superconductor bilayers separated by an insulating barrier. By computing the free energy of the system, we identify two distinct contributions: (i) The work performed by a current source to create a supercurrent through the junction, and (ii) an antiferromagnetic coupling between ferromagnetic insulators, mediated by the superconducting condensate across the insulating barrier. The competition between these contributions allows for switching between parallel and antiparallel configurations of the magnetizations of the ferromagnetic insulators. We explicitly show that the switching occurs at finite temperatures and for superconducting phase differences satisfying $\pi /2<\varphi <3\pi /2$. Importantly, this effect can be realized in ferromagnetic insulators with sufficiently large easy-plane anisotropy energy. Using realistic junction parameters, we demonstrate that the switching can be controlled by phase bias and triggered by half-flux-quantum voltage pulses or external magnetic field pulses on the microsecond timescale. These results provide a route towards controllable Josephson-based superconducting memory devices based on EuS/Al heterostructures.

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• Magnetization switching
• Superconductivity
• Josephson junctions
• Magnetic insulators
• Landau-Lifschitz-Gilbert equation
• Usadel equation