Magnetospectroscopic Evidence for the Magnonic Superradiant Phase Transition in Erbium Orthoferrite

The superradiant phase transition (SRPT) occurs when the strength of the cooperative coupling of an ensemble of two-level atoms with a bosonic excitation exceeds a critical value, creating a new ground state that possesses a finite atomic polarization with concomitant boson condensation. Photonic SRPTs have been realized only in nonequilibrium situations. Recently, a magnonic SRPT has been theoretically demonstrated for erbium orthoferrite, ErFeO₃, in thermal equilibrium. This material consists of two subsystems: (i) Er³⁺ ions, which can be viewed as an ensemble of two-level atoms, and (ii) Fe³⁺ ions with magnons, which are bosonic excitations. Ultrastrong coupling between the two subsystems causes a SRPT, inducing condensation of Fe³⁺ magnons and an Er³⁺ spin polarization. Here, we provide experimental evidence for the phase transition through GHz magnetospectroscopy. We varied the detuning between the lowest Er³⁺ atomic transition and the Fe³⁺ magnon excitation via an applied DC magnetic field. This process is equivalent to the threshold modulation of the Er³⁺–Fe³⁺ coupling strength for the SRPT, which allows us to measure a rapid decrease of the resonance frequency of Er³⁺ spins as the system crosses the superradiant-to-normal phase boundary. Our measurements relied on minute temperature changes of an ErFeO₃ crystal owing to spin–lattice coupling, by which we were able to precisely monitor peak positions as a function of magnetic field.