A system of magnetic molecules coupled to microwave cavities ($LC$ resonators) undergoes the equilibrium superradiant phase transition. The transition is experimentally observable. The effect of the coupling is first illustrated by the vacuum-induced ferromagnetic order in a quantum Ising model and then by the modification of the magnetic phase diagram of ${\mathrm{Fe}}_8$ dipolar crystals, exemplifying the cooperation between intrinsic and photon-induced spin-spin interactions. Finally, a transmission experiment is shown to resolve the transition, measuring the quantum electrodynamical control of magnetism.

• Received 1 December 2020
• Revised 25 August 2021
• Accepted 25 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.167201