  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.
