Controllable magnetic states in chains of coupled φ0 Josephson junctions with ferromagnetic weak links

A superconductor/ferromagnet/superconductor Josephson junction with anomalous phase shift (φ₀-S/F/S JJ) is a system in which the anomalous ground state shift φ₀ provides direct magnetoelectric coupling between a magnetic moment and a phase of the superconducting condensate. If a chain of such φ₀-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 Mᵢ 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 ∑Mᵢ 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 ∑Mᵢ can be fully controlled by a supercurrent and the response of the magnetic system to local external perturbations is highly nonlocal.