  The ultrastrong coupling of (quasi-)particles has gained considerable
attention due to its application potential and richness of the underlying
physics. Coupling phenomena arising due to electromagnetic interactions are
well explored. In magnetically ordered systems, the quantum-mechanical
exchange-interaction should furthermore enable a fundamentally different
coupling mechanism. Here, we report the observation of ultrastrong intralayer
exchange-enhanced magnon-magnon coupling in a compensated ferrimagnet. We
experimentally study the spin dynamics in a gadolinium iron garnet single
crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic
compensation temperature, we observe ultrastrong coupling of clockwise and
anticlockwise magnon modes. The magnon-magnon coupling strength reaches more
than 30% of the mode frequency and can be tuned by varying the direction of the
external magnetic field. We theoretically explain the observed phenomenon in
terms of an exchange-enhanced mode-coupling mediated by a weak cubic
anisotropy.
