  We present measurements on ultra clean single crystals of the bilayered
ruthenate metal Sr3Ru2O7, which has a magnetic-field-tuned quantum critical
point. Quantum oscillations of differing frequencies can be seen in the
resistivity both below and above its metamagnetic transition. This frequency
shift corresponds to a small change in the Fermi surface volume that is
qualitatively consistent with the small moment change in the magnetisation
across the metamagnetic transition. Very near the metamagnetic field, unusual
behaviour is seen. There is a strong enhancement of the resistivity in a narrow
field window, with a minimum in the resistivity as a function of temperature
below 1 K that becomes more pronounced as the disorder level decreases. The
region of anomalous behaviour is bounded at low temperatures by two first-order
phase transitions. The implications of the results are discussed. PACS:
68.35.Rh, 71.27.+a, 72.15.-v, 74.70.Pq
