Electric field control of moiré skyrmion phases in twisted multiferroic NiI$_2$ bilayers

Twisted magnetic van der Waals materials provide a flexible platform to engineer new forms of unconventional magnetism. Here we demonstrate the emergence of electrically tunable topological moiré magnetism in twisted bilayers of the spin-spiral multiferroic NiI$_2$. We establish a rich phase diagram featuring uniform spiral phases, a variety of $kπ$-skyrmion lattices, and nematic spin textures ordered at the moiré scale. The emergence of these phases is driven by the local stacking and the resulting modulated frustration in the spin spiral stemming from the moiré pattern. Notably, when the spin-spiral wavelength is commensurate with the moiré length scale by an integer $k$, multi-walled skyrmions become pinned to the moiré pattern. We show that the strong magnetoelectric coupling displayed by the moiré multiferroic allows the electric control of the $kπ$-skyrmion lattices by an out-of-plane electric field, which couples to the moiré-induced electric polarization. While adiabatic changes in the electric field preserve the topology of the spin configurations, abrupt variations can trigger transitions between different skyrmion lattice ground states. Our results establish a highly tunable platform for skyrmionics based on twisted van der Waals multiferroics, potentially enabling a new generation of ultrathin topologically-protected spintronic devices.