We present an inelastic neutron scattering study of phonon lineshapes in thevortex state of the type-II superconductor YNi$_2$B$_2$C. In a previous study[Phys. Rev. Lett. \textbf{101}, 237002 (2008)] it was shown that certainphonons exhibit a clear signature of the superconducting gap $2\Delta$ onentering the superconducting state. Our interest was to find out whether or notthe lineshape of such phonons reflects the inhomogeneous nature of the vortexstate induced by a magnetic field smaller than the upper critical field$B_{c2}$ .We found that this is indeed the case because the observed phononlineshapes can be well described by a model considering the phonon as a localprobe of the spatial variation of the superconducting gap. We found that evenat $B=3\,\rm{T}$, where the inter-vortex distance is less than $300\,$\AA, thephonon lineshape still shows evidence for a variation of the gap.
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