  We demonstrate, at room temperature, the strong coupling of the fundamental
and non-uniform magnetostatic modes of an yttrium iron garnet (YIG)
ferrimagnetic sphere to the electromagnetic modes of a co-axial cavity. The
well-defined field profile within the cavity yields a specific coupling
strength for each magnetostatic mode. We experimentally measure the coupling
strength for the different magnetostatic modes and, by calculating the expected
coupling strengths, are able to identify the modes themselves.
