Long-range interaction of magnetic moments in a coupled system of S/F/S Josephson junctions with anomalous ground-state phase shift

TL;DR

This paper proposes a superconductivity-mediated long-range magnetic interaction in coupled S/F/S Josephson junctions with spin-orbit coupling, enabling control over magnetic states at macroscopic distances.

Contribution

It introduces a novel long-range magnetic coupling mechanism based on anomalous phase shifts and superconducting phase control in S/F/S junctions.

Findings

Interaction favors antiparallel magnetization alignment.

Coupling strength remains significant over millimeter scales.

Interaction exhibits a 1/l power law decay at large distances.

Abstract

A mechanism of a superconductivity-mediated interaction of two magnets in a system of coupled superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions (JJs) with spin-orbit interaction is proposed. The predicted indirect magnetic interaction favors the antiparallel orientation of the magnets. Its spatial scale is not restricted by the proximity length scales of the superconductor. Our estimates suggest that the interaction strength is not reduced considerably even at the macroscopic scales of the order of millimeters. At larger distances $l$ between the magnets the coupling constant exhibits the long-range power law $1/l$ behavior. The mechanism of the interaction is based on two key ingredients: (i) the anomalous ground state phase shift in the S/F/S JJ provides a magnetoelectric coupling between the condensate phase and the magnetization and (ii) the interaction is mediated by the condensate phase of the superconducting region connecting both JJs. In addition we demonstrate high tunability of the total magnetic configuration of the system by the externally controlled superconducting phase between the leads.