Magneto Acoustic Quantum Oscillations in High Fields and the Fermi Surface of UPt$_3$

We report magneto-acoustic quantum oscillations (MAQO) in the heavy fermion system UPt$_3$ in magnetic fields B, upto 33 T. For B in the ab-plane of the hexagonal crystal MAQO in the sound velocity commence at $\approx$ 12 T and grow with field. However, in contrast to typical Lifshitz-Kosevich behaviour the frequency corresponding to the dominant oscillation increases continuously as the metamagnetic transition (MMT) at 20 T is reached. This dominant MAQO arises from the $\delta$ orbit of band 1 with a large effective mass of 33 m$_e$, for B $<$ 20 T and disappears after the MMT. Thus, the MMT involves a significant change of the Fermi surface, primarily in band 1. For B $\parallel$ ab-plane and $<$ 20 T we reproduce successfully orbits established through previous de Haas-van Alphen and Shubnikov de Haas measurements. We also observe several new orbits, some that can be identified with existing band theory and others not seen previously with completely new frequencies. For B $\parallel$ c-axis we observe MAQOs which also commence at $\approx$ 12 T and grow gradually but break suddenly into a large amplitude and change in frequency at 24.8 T. These enhanced oscillations get weaker again at 30 T. These abrupt changes at 24.8 T and 30 T are signatures of Lifshitz transitions and coincide with the newly discovered spin density wave states for this orientation reported by us recently.