Field-dependent superradiant quantum phase transition of molecular magnets in microwave cavities

We study a superradiant quantum phase transition in the model of triangular molecular magnets coupled to the electric component of a microwave cavity field. The transition occurs when the coupling strength exceeds a critical value, dc, which, in sharp contrast to the standard two-level emitters, can be tuned by an external magnetic field. In addition to emitted radiation, the molecules develop an in-plane electric dipole moment at the transition. We estimate that the transition can be detected in state-of-the-art microwave cavities if their electric field couples to a crystal containing a sufficient number of oriented molecules.