Anisotropy of the Vortex Magnetic Field Distribution in LuNi$_2$B$_2$

It is well known that the vortex lattice (VL) symmetry and orientation in type-II superconductors is very sensitive to any anisotropy within the screening current plane. A classic example is the sequence of transitions from hexagonal to rhombic to square symmetry, which was first observed in the borocarbide superconductors and explained by a Fermi surface anisotropy coupled with the non-local electrodynamics responsible for vortex-vortex interactions. Recently, however, this is mounting experimental evidence for a strong gap anisotropy and possible point nodes in the basal plane of these materials. Here we report on small-angle neutron scattering studies of the VL in a carefully annealed, high quality LuNi$_2$B$_2$C single crystal, which permitted us to measure the VL form factor for a large number of reflections. These measurements allow a reconstruction of the real space profile of the magnetic field around the vortices, reflecting the basal plane anisotropy of the screening currents in LuNi$_2$B$_2$C. The results will be compared to predictions for both Fermi surface and gap anisotropies, and will serve as a valuable reference for more complicated compounds as e.g. Sr$_2$RuO$_4$, heavy fermions and high-$T_c$'s.