  We investigated the depth dependence of current-induced magnetic fields in a
bilayer of a normal metal (Au) and a ferrimagnetic insulator (Yttrium Iron
Garnet - YIG) by using low energy muon spectroscopy (LE-muSR). This allows us
to explore how these fields vary from the Au surface down to the buried Au|YIG
interface, which is relevant to study physics like the spin-Hall effect. We
observed a maximum shift of 0.4 G in the internal field of muons at the surface
of Au film which is in close agreement to the value expected for Oersted
fields. As muons are implanted closer to the Au|YIG interface the shift is
strongly suppressed, which we attribute to the dipolar fields present at the
Au|YIG interface. Combining our measurements with modelling, we show that
dipolar fields caused by the finite roughness of the Au|YIG interface
consistently explains our observations. Our results, therefore, gauge the
limits on the spatial resolution and the sensitivity of LE-muSR to the
roughness of the buried magnetic interfaces, a prerequisite for future studies
addressing current induced fields caused by the spin-Hall effect.
