  We have imaged the excitation of small-amplitude spin-wave eigenmodes,
localized within $\sim$ 100 nm of the vertices of nanoscale Ni$_{81}$Fe$_{19}$
ellipses, using time-resolved scanning transmission x-ray microscopy (STXM) at
2 GHz and resolution of 70 nm. Taking advantage of the buried-layer sensitivity
of STXM, we find that the magnetization precession at the two vertices changes
from predominantly in-phase to out-of-phase in samples with and without a
conductive layer deposited over the ellipses. As a plausible interpretation for
the reversal in phase, we propose that unexpectedly strong Oersted fields are
generated in the discontinuous overlayer, although effects of edge roughness
cannot be fully excluded. The results demonstrate the capabilities of STXM to
image small-amplitude, GHz magnetization dynamics with the potential to map rf
magnetic fields on the nanoscale.
