Electric Field Control Of Moire Skyrmion Phases\nin Twisted Multiferroic NiI<sub>2</sub> Bilayers

Twisted magnetic van der Waals materials provide a flexible platform\nto engineer unconventional magnetism. Here we demonstrate the emergence\nof electrically tunable topological moiré magnetism in twisted\nbilayers of the spin-spiral multiferroic NiI<sub>2</sub>. We establish\na rich phase diagram featuring uniform spiral phases, a variety of <i>kπ</i>-skyrmion lattices, and nematic spin textures ordered\nat the moiré scale. The emergence of these phases is driven\nby the local stacking and the resulting moiré modulated frustration.\nNotably, when the spin-spiral wavelength is commensurate with the\nmoiré length scale by an integer <i>k</i>, multiwalled\nskyrmions become pinned to the moiré pattern. We show that\nthe strong magnetoelectric coupling displayed by the moiré\nmultiferroic allows electric control of the <i>kπ</i>-skyrmion lattices by an out-of-plane electric field. Our results\nestablish a highly tunable platform for skyrmionics based on twisted\nvan der Waals multiferroics, potentially enabling a new generation\nof ultrathin topologically protected spintronic devices.