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

Abstract

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.

Figures (4)

• Figure 1: (a) Schematic of the spin-spiral of monolayer NiI$_2$ with wavelength $2\pi/q$.(b) Exchange interactions $J_1$ and $J_3$ of the Ni triangular lattice leading to the non-collinear spin-spiral state. (c) Schematic of a NiI$_2$ twisted bilayer, with Ni atoms represented in blue, and I atoms in grey. (d) Magnitude of the propagation vector $q$ as a function of the interlayer exchanges $J_\perp/J_1$ and $J_3/J_1$. (e) Moiré pattern of twisted bilayer NiI$_2$, showing the moiré unit cell (red), and the spatial patches with $C_2$ symmetric rhombohedral stacking along different directions (yellow). (f) Schematic of the domains of $q$ originated by the local broken symmetry.
• Figure 2: (a) Spin $\boldsymbol{S}$, (b) propagation vector $\boldsymbol{q}$, and (c) polarization $\boldsymbol{P}$ of a skyrmion and skyrmionium lattice in twisted bilayer NiI$_2$. These occur for twist angles $\theta\approx3.89^\circ$ and $\theta\approx2.13^\circ$, left and right panels respectively. The panels show the top layer of a twisted bilayer, with the bottom one featuring an analogous profile.
• Figure 3: (a) Phase diagram of twisted bilayer NiI$_2$ as a function of normalized interlayer exchange $AJ_\perp/J_1$ and $qL_m/2\pi$. The factor $A=L_m^2/a^2$ introduces the relative area between the moiré and the single unit cells, ensuring that the same ground states are represented along vertical lines in the phase diagram. The red line represents NiI$_2$ as $L_m$ increases or, equivalently, as the twist angle becomes smaller. (b-g) Representative ground state solutions in the phase diagram of the panel (a): (b) uniform spin spiral, (c), (e), and (g) display the simple, $2\pi-$ and $3\pi-$skyrmion lattices respectively., and (d) and (f) show intermediate phases with nematic order between commensurate solutions. Only the top layer of the twisted bilayer is shown for clarity.
• Figure 4: (a) Adiabatic evolution of the skyrmion lattice ground state of twisted NiI$_2$. The polarization along $z$ for the top layer undergoes a hysteresis loop as the field magnitude $\lambda E_\text{ext}/J_1$ is changed along the loop $0\to0.15\to-0.15\to0$ (b) Non-adiabatic evolution of the ground state, resulting in a transition from a skyrmion to a skyrmionium lattice.