Cooperative exchange coupling of rare-earth spins with a vacuum magnon field in ErFeO₃

Dicke cooperativity is a many-body effect in quantum optics describing the process of N oscillators in a photonic cavity developing macroscopic coherence amongst themselves by interacting with a single light field, while exhibiting a N^1/2 enhancement of the light-matter coupling rate. Here, we have discovered that cooperatively enhanced coupling similar to this canonical light-matter interaction effect occurs in a magnetic solid in the form of matter-matter interaction. We studied an ErFeO₃ single crystal with terahertz magnetospectroscopy at low temperatures and high magnetic fields, and discovered that the exchange coupling of the paramagnetic Er³⁺ ions with a Fe³⁺ magnon field within the crystal quantitatively follows the scaling behavior expected by the Dicke cooperativity effect. This scaling behavior also enables quantitative determination of the Er³⁺-Fe³⁺ exchange coupling coefficients. Our finding provides a novel route for understanding, controlling, or predicting new phases of condensed matter using concepts and tools available in quantum optics.