  Magnetostatic modes of Yttrium Iron Garnet (YIG) films are investigated by
ferromagnetic resonance force microscopy (FMRFM). A thin film ``probe'' magnet
at the tip of a compliant cantilever introduces a local inhomogeneity in the
internal field of the YIG sample. This influences the shape of the sample's
magnetostatic modes, thereby measurably perturbing the strength of the force
coupled to the cantilever. We present a theoretical model that explains these
observations; it shows that tip-induced variation of the internal field creates
either a local ``potential barrier'' or ``potential well'' for the
magnetostatic waves. The data and model together indicate that local magnetic
imaging of ferromagnets is possible, even in the presence of long-range spin
coupling, through the induction of localized magnetostatic modes predicted to
arise from sufficiently strong tip fields.
