Indications of a Field Dependent Vortex Core Size in CeCoIn$_5$

Using Small-Angle Neutron Scattering, we have imaged the flux- line lattice (FLL) in the {\em d}-wave, heavy fermion superconductor CeCoIn$_5$. At low fields, a hexagonal FLL is observed which undergoes a first order transition to a rhombic (distorted square) symmetry as the field is increased above 0.55 T. As the field is increased futher, the FLL approaches a square symmetry. Measurements of the FLL reflectivity yields a constant form factor independent of the applied magnetic field, in stark contrast to the exponential decrease usually observed. The field-independent form factor may indicate a field dependent vortex core size, $\xi$ $\propto$ $H^{-1/2}$, in qualitative agreement with recent theoretical predictions for ultra-clean, high-$\kappa$ superconductors [V.G. Kogan and N.V. Zhelezina, PRB {\bf 71}, 134505 (2005)].