  Metals composed of weakly-coupled, stacked layers possess a Fermi surface
that slightly varies in size along the stacking direction. This appears in de
Haas-van Alphen (dHvA) oscillations of the magnetisation with magnetic field as
two close frequencies, corresponding to the two extremal Fermi surface
cross-sectional areas. We show that, for layered materials of sufficiently high
mobility, Coulomb interactions can have a dramatic effect on the form of the
dHvA oscillations: there is also generically an oscillation at the small
difference of the two large frequencies. We determine the size and form of this
effect, and show that it probes the short-range part of the Coulomb
interactions within the layered material. We argue that this interaction effect
may explain recent experimental observations of anomalous low-frequency dHvA
oscillations in the ultrapure delafossites.
