  The Dicke model describes the cooperative interaction of an ensemble of
two-level atoms with a single-mode photonic field and exhibits a quantum phase
transition as a function of light--matter coupling strength. Extending this
model by incorporating short-range atom--atom interactions makes the problem
intractable but is expected to produce new phases. Here, we simulate such an
extended Dicke model using a crystal of ErFeO$_3$, where the role of atoms
(photons) is played by Er$^{3+}$ spins (Fe$^{3+}$ magnons). Through
magnetocaloric effect and terahertz magnetospectroscopy measurements, we
demonstrated the existence of a novel atomically ordered phase in addition to
the superradiant and normal phases that are expected from the standard Dicke
model. Further, we elucidated the nature of the phase boundaries in the
temperature--magnetic-field phase diagram, identifying both first-order and
second-order phase transitions. These results lay the foundation for studying
multiatomic quantum optics models using well-characterized many-body condensed
matter systems.
