  Hybrid magnonics involving coupling between magnons and different quantum
particles have been extensively studied during past few years for varied
interests including quantum electrodynamics. In such systems, magnons in
magnetic materials with high spin density are utilized where the coupling
strength is collectively enhanced by the square root of the number of spins to
overcome the weaker coupling between individual spins and the microwave field.
However, achievement of strong magnon-magnon coupling in a confined nanomagnets
would be essential for on-chip integration of such hybrid systems. Here,
through intensive study of interaction between different magnon modes in a
Ni80Fe20 (Py) nanodot array, we demonstrate that the intermodal coupling can
approach the strong coupling regime with coupling strength up to 0.82 GHz and
cooperativity of 2.51. Micromagnetic simulations reveal that the intermodal
coupling is mediated by the exchange field inside each nanodot. The coupling
strength could be continuously tuned by varying the bias field strength and
orientation, opening routes for external control over hybrid magnonic systems.
These findings could greatly enrich the rapidly evolving field of quantum
magnonics.
