Low-Temperature Phases of Er_1-<i>_x</i>Y<i>_x</i>FeO₃ Mapped Out by Terahertz Time-Domain Spectroscopy

When the strength of coupling between an ensemble of two-level atoms and a single mode of light becomes a significant fraction of the natural frequencies in the system, a novel regime of light-matter interaction, known as the ultrastrong coupling regime, emerges. As the coupling is further increased, a quantum phase transition, referred to as the superradiant phase transition (SRPT), is theoretically predicted to occur. To date, a SRPT in thermal equilibrium has never been realized experimentally, and even its observability is a topic of ongoing debate in the literature. However, there remains a strong possibility to observe a phase transition analogous to the SRPT in magnetically ordered systems, which would provide new insight into the underlying physics behind the original photon SRPT. In the present work, we performed an extensive study of the low-temperature phases of Er_1-xY_xFeO₃ as a function of temperature, magnetic field and x through terahertz time-domain magnetospectroscopy. Through comparison with our detailed calculations, we found that there is a phase transition that can be interpreted as a magnon analogue of the SRPT in an extended Dicke model and that the cooperative coupling of spins and magnons plays a key role in the experimental realization of this phenomenon.