A low energy radioactive beam of polarized $^8$Li has been used to observe the vortex lattice near the surface of superconducting NbSe$_2$. The inhomogeneous magnetic field distribution associated with the vortex lattice was measured using depth-resolved $beta$-detected NMR. Below $T_c$ one observes the characteristic lineshape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with magnetic field. In particular in a low field of 10.8 mT the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.
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