  Flat band moir\'e superlattices have recently emerged as unique platforms for
investigating the interplay between strong electronic correlations, nontrivial
band topology, and multiple isospin 'flavor' symmetries. Twisted
monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low
crystal symmetry and the tunability of its bandwidth and topology with an
external electric field. Here, we find that orbital magnetism is abundant
within the correlated phase diagram of tMBG, giving rise to the anomalous Hall
effect (AHE) in correlated metallic states nearby most odd integer fillings of
the flat conduction band, as well as correlated Chern insulator states
stabilized in an external magnetic field. The behavior of the states at zero
field appears to be inconsistent with simple spin and valley polarization for
the specific range of twist angles we investigate, and instead may plausibly
result from an intervalley coherent (IVC) state with an order parameter that
breaks time reversal symmetry. The application of a magnetic field further
tunes the competition between correlated states, in some cases driving
first-order topological phase transitions. Our results underscore the rich
interplay between closely competing correlated ground states in tMBG, with
possible implications for probing exotic IVC ordering.
