Spectroscopic Evidence for the Magnonic Superradiant Phase Transition in Erbium Orthoferrite

The Dicke model predicts that a system of two-level atoms cooperatively coupled with a single mode of cavity photons should exhibit a quantum phase transition as a function of coupling strength. Above a critical coupling strength, the system enters a phase in which atomic inversion and photon number become finite even at zero temperature and without external driving. However, this phenomenon, known as the superradiant phase transition (SRPT), is forbidden by a no-go theorem due to the existence of the so-called A² term (also known as the diamagnetic term) in the light–matter Hamiltonian absent in the Dicke model. Here, we present spectroscopic evidence for a magnonic SRPT in erbium orthoferrite (ErFeO₃). The role of the photonic mode in the Dicke model is played by a magnonic mode of Fe³⁺ spins, which ultrastrongly couples with an ensemble of two-level atoms represented by Er³⁺ spins. These two subsystems interact via exchange interactions, instead of electric dipole interactions; as a result, the no-go theorem does not apply because of the absence of any A² term in the interaction Hamiltonian. Ultrastrong coupling between the two subsystems causes the SRPT, inducing condensation of Fe³⁺ magnons and an Er³⁺ spin polarization. We performed terahertz and gigahertz magnetospectroscopy experiments at low temperatures and observed simultaneously a sharp change and a softening, respectively, of resonance frequencies in the two spin-magnon hybridized modes at the critical point – signatures of the SRPT.