  We show that the low-temperature phase transition in ErFeO3 that occurs at a
critical temperature of ~ 4 K can be described as a magnonic version of the
superradiant phase transition (SRPT). The role of photons in the
quantum-optical SRPT is played by Fe magnons, while that of two-level atoms is
played by Er spins. Our spin model, which is reduced to an extended Dicke
model, takes into account the short-range, direct exchange interactions between
Er spins in addition to the long-range Er-Er interactions mediated by Fe
magnons. By using realistic parameters determined by recent terahertz
magnetospectroscopy and magnetization experiments, we demonstrate that it is
the cooperative, ultrastrong coupling between Er spins and Fe magnons that
causes the phase transition. This work thus proves ErFeO3 to be a unique system
that exhibits a SRPT in thermal equilibrium, in contrast to previous
observations of laser-driven non-equilibrium SRPTs.
