Interaction of magnons with plasmons in a system of antiferromagnetic insulators coupled to a superconductor microwave cavity through interfacial exchange interaction

A superconductor can interact with magnets through the magnetic field which is induced by the supercurrent. However, this interaction is rather weak and requires relatively large magnets to reach a sizable hybridization of microwave electromagnetic modes with magnons. The size of the device can be drastically reduced by means of the large interfacial exchange interaction between spins in a magnet and a superconductor. In the spin-orbit coupled superconductor this interaction can be transmitted to the s-wave condensate through a mixing of triplet and singlet Cooper pairs. In this paper we theoretically consider thin antiferromagnetic films, which make a spin compensated contact to a superconducting wire, which forms a cavity for Mooij-Schon plasma waves. The effective Lagrangian is derived where the interaction of these waves with magnons is taken into account. Frequencies of hybrid magnon-plasmon modes are calculated. A system of two micromagnets placed far apart are also considered and their mutual coupling through the cavity mode is calculated.