  In recent years it has become understood that quantum oscillations of the
magnetization as a function of magnetic field, long recognized as phenomena
intrinsic to metals, can also manifest in insulating systems. Theory has shown
that in certain simple band insulators, quantum oscillations can appear with a
frequency set by the area traced by the minimum gap in momentum space, and are
suppressed for weak fields by an intrinsic "Dingle damping" factor reflecting
the size of the bandgap. Here we examine quantum oscillations of the
magnetization in excitonic and Kondo insulators, for which interactions play a
crucial role. In models of these systems, self-consistent parameters themselves
oscillate with changing magnetic field, generating additional contributions to
quantum oscillations. In the low-temperature, weak-field regime, we find that
the lowest harmonic of quantum oscillations of the magnetization are
unaffected, so that the zero-field bandgap can still be extracted by measuring
the Dingle damping factor of this harmonic. However, these contributions
dominate quantum oscillations at all higher harmonics, thereby providing a
route to measure this interaction effect.
