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A superconductor/ferromagnet/superconductor Josephson junction with anomalous phase shift (₀-S/F/S JJ) is a system in which the anomalous ground state shift ₀ provides direct magnetoelectric coupling between a magnetic moment and a phase of the superconducting condensate. If a chain of such ₀-S/F/S JJs are coupled via superconducting leads, the condensate phase, being a macroscopic quantity, mediates a long-range interaction between the magnetic moments M₈ of the weak links. We study the static and dynamic magnetic properties of such a system. It is shown that it manifests properties of an n-level system, in which the energies of the levels are determined by only projections of the total magnetic moment M₈ onto the easy magnetic axis. It is similar to a magnetic atom in a Zeeman field, but the role of the field is played by the magnetoelectric coupling. However, unlike an atom in a magnetic field, the relative order of energies of different states is controlled by electrical means. It is also demonstrated that M₈ can be fully controlled by a supercurrent and the response of the magnetic system to local external perturbations is highly nonlocal.
Bobkov et al. (Tue,) studied this question.