  Layered van der Waals materials have risen as powerful platforms to
artificially engineer correlated states of matter. Here we show the emergence
of a multiferroic order in a twisted dichalcogenide bilayer superlattice at
quarter-filling. We show that the competition between Coulomb interactions
leads to the simultaneous emergence of ferrimagnetic and ferroelectric orders.
We derive the magnetoelectric coupling for this system, which leads to a direct
strong coupling between the charge and spin orders. We show that, due to
intrinsic spin-orbit coupling effects, the electronic structure shows a
non-zero Chern number, thus displaying a topological multiferroic order. We
show that this topological state gives rise to interface modes at the different
magnetic and ferroelectric domains of the multiferroic. We demonstrate that
these topological modes can be tuned with external electric fields as well as
triggered by supermoire effects generated by a substrate. Our results put
forward twisted van der Waals materials as a potential platform to explore
multiferroic symmetry breaking orders and, ultimately, controllable topological
excitations in magnetoelectric domains.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Materials Science