History Dependence of the Vortex Lattice Rotation in the B-phase of UPt$_3$ with ${\bf H} \parallel {\bf c}$*

The unconventional superconductor UPt$_3$ is widely believed to be a triplet superconductor, where the low temperature superconducting B-phase is a chiral state. We have performed small angle neutron scattering (SANS) from the vortex lattice (VL) in UPt$_3$ at the Paul Scherrer Institute with the magnetic field parallel to the hexagonal $c$-axis in the 0.5 T to 0.9 T range. The diffraction pattern of the VL rotates away from a high symmetry direction producing two domains of different orientation. Our field dependent measurements show a subtle magnetic field history dependence of this orientation; VLs prepared with the magnetic field parallel or anti-parallel with respect to the angular momentum from the circulating screening currents show different field-history dependence. These results suggest a coupling of a chiral superconducting order parameter with the applied magnetic field.