Small Angle Neutron Scattering Studies of the Vortex Lattice of UPt$_3$

Although a paradigm for unconventional superconductivity, the true nature of the superconducting order parameter in UPt$_3$ is still an open question. We present results from small angle neutron scattering (SANS) studies on the vortex lattice (VL) of UPt$_3$, for fields both perpendicular and parallel to the crystal \textbf{c}-axis, that have implications for the superconducting order parameter. For perpendicular fields, an unconventional temperature dependence of the VL form factor -- and thus penetration depth -- is seen, with different dependences in the A and B-phases. This bulk measurement of the penetration depth indicates the presence of nodes in the superconducting gap. For parallel fields, we report the first measurement of a rocking curve from the VL. This is an encouraging result for the viability of using SANS to detect signatures of time reversal symmetry breaking, as the \textbf{c}-axis is taken as the chiral axis in these order parameter theories.