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

A superconductor/ferromagnet/superconductor Josephson junction with anomalous phase shift $({\ensuremath{\varphi}}_{0}\text{\ensuremath{-}}\mathrm{S}/\mathrm{F}/\mathrm{S} \mathrm{JJ})$ is a system in which the anomalous ground state shift ${\ensuremath{\varphi}}_{0}$ provides direct magnetoelectric coupling between a magnetic moment and a phase of the superconducting condensate. If a chain of such ${\ensuremath{\varphi}}_{0}\text{\ensuremath{-}}\mathrm{S}/\mathrm{F}/\mathrm{S}$ JJs are coupled via superconducting leads, the condensate phase, being a macroscopic quantity, mediates a long-range interaction between the magnetic moments ${\mathbit{M}}_{i}$ 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 $\ensuremath{\sum}{\mathbit{M}}_{i}$ 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 $\ensuremath{\sum}{\mathbit{M}}_{i}$ can be fully controlled by a supercurrent and the response of the magnetic system to local external perturbations is highly nonlocal.