We perform an extensive experimental spectroscopic study of the collective spin-wave dynamics occurring in a pair of magnetic nano-disks coupled by the magneto-dipolar interaction. For this, we take advantage of the stray field gradient produced by the magnetic tip of a ferromagnetic resonance force microscope (f-MRFM) to continuously tune and detune the relative resonance frequencies between two adjacent nano-objects. This reveals the anti-crossing and hybridization of the spin-wave modes in the pair of disks. At the exact tuning, the measured frequency splitting between the binding and anti-binding modes precisely corresponds to the strength of the dynamical dipolar coupling $Omega$. This accurate f-MRFM determination of $Omega$ is measured as a function of the separation between the nano-disks. It agrees quantitatively with calculations of the expected dynamical magneto-dipolar interaction in our sample.
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