Super-Moiré Spin Textures in Twisted Antiferromagnets

Abstract

Stacking two-dimensional (2D) layered materials offers a powerful platform to engineer electronic and magnetic states. In general, the resulting states, such as Moiré magnetism, have a periodicity at the length scale of the Moiré unit cell. Here, we report a new type of magnetism -- dubbed a super-Moiré magnetic state -- which is characterized by long-range magnetic textures extending beyond the single Moiré unit cell -- in twisted double bilayer chromium triiodide (tDB CrI$_3$). We found that at small twist angles, the size of the spontaneous magnetic texture increases with twist angle, opposite to the underlying Moiré periodicity. The spin-texture size reaches a maximum of about 300 nm in 1.1$°$ twisted devices, an order of magnitude larger than the underlying Moiré wavelength, and vanishes at twist angles above 2$°$. Employing scanning quantum spin magnetometry, the obtained vector field maps suggest the formation of antiferromagnetic Néel-type skyrmions spanning multiple Moiré cells. The twist-angle-dependent study combined with large-scale atomistic simulations suggests that complex magnetic competition between the Dzyaloshinskii--Moriya interaction, magnetic anisotropy, and exchange interactions controlled by the relative rotation of the layers produces the topological textures which arise in the super-Moiré spin orders.

Figures (4)

• Figure 1: a. Schematic of the scanning quantum microscopy technique for the visualization of magnetic textures in tDB CrI$_3$. An NV center (red spin) is located at the apex of a diamond pillar. The NV is initialized by a green laser and controlled by a microwave signal. The sample device consists of two sheets of bilayer CrI$_3$ with a twist angle $\theta$ between them. b. Schematic of Moiré-modulated magnetic interactions at near-zero twist angle, showing FM regions (rhombohedral stacking, shaded red) and AFM regions (monoclinic stacking, shaded blue) are well separated. Thus, the magnetic texture closely follows the underlying Moiré lattice, forming sharp magnetic domain walls. In this regime, $a<a_M$, where $a$ and $a_M$ denote the length scale of magnetic texture and Moiré wavelength respectively. c. Schematic of competing magnetic orders at larger twist angles, where FM- and AFM-favored regions shift toward AA sites. Magnetic competition drives strong noncollinear spin textures, with magnetic domains extending beyond a single Moiré unit cell. In this regime, $a>a_M$. d-f. Atomistic simulated normalized magnetization maps over a 450-nm region for twist angles of 0.5°, 1.1°, and 2°. Only magnetic competition of $J_\perp$ and $J_\parallel$ is considered. A cross-section of the magnetization from a single layer of the tDB CrI$_3$ shows the merging of Moiré cells into larger magnetic textures with increasing twist angle. White dots mark the positions of underlying monoclinic sites for each twist angle. g. Schematic illustration of topological magnetic textures in relation to the underlying Moiré stacking. The arrows indicate the spin configuration in the 2D magnet, while the gray lattice beneath represents the Moiré superlattice. The shaded holes artistically depict regions of distinct stacking. A representative Moiré unit cell is outlined by a blue hexagon. The emergent super-Moiré magnetic textures span multiple Moiré unit cells, with characteristic length scales exceeding 100 nm.
• Figure 2: a, b. 2D magnetization maps of tDB CrI$_3$ at 0.5° and 1.1° twist angles, showing randomly distributed FM and AFM domains. The FM domains have a magnetization of around 30 $\mu_\text{B}/\text{nm}^2$, while other regions are all nearly 0 $\mu_\text{B}/\text{nm}^2$. c. Representative FM domain wall linecuts of 0.5° (red dots) and 1.1° (black dots) of tDB CrI$_3$ samples, fitted with a hyperbolic tangent function (red and black lines). The fitting for 0.5° and 1.1° linecuts showed domain wall widths of 58.5 nm and 118.2 nm. Positions of the linecuts are denoted on (a,b) as white dashed lines. A domain wall linecut from a twisted bilayer CrI$_3$ (dashed grey line) serves as a reference for minimum resolvable domain wall width of around 30 nm. See supplementary section 3 for more statistics and discussion.d. Stray field map of a selected FM area (black dashed rectangle) in (b), after a smooth polynomial background subtraction, showing correlated field variation features within FM domains. e. 2D autocorrelation of the field map of (d), revealing hexagonal textures with correlation length in the long edges around a=340 nm, exceeding the Moiré magnetic periodicity of 36.4 nm at a 1.1° twist angle, giving $a/a_{M}\approx 9.3$. The short edge gives $a/a_{M}\approx 6.2$.
• Figure 3: a. A representative stray field map of 0.5° tDB CrI$_3$ after zero field cooldown, showing stripe-like patterns in an AFM region. b. Autocorrelation of a selected area (dashed black rectangle) in (a), showing a 1D correlation in the diagonal direction, highlighted by the red dashed line. c. Stray field map of the same sample area in (a) after 500 mT-field cooldown, revealing dot-like patterns in the AFM region. d. Autocorrelation of the same area (dashed black rectangle) in (c), showing a hexagonal texture with a spacing of $a/a_M\approx$ 3.5 in the long edge and $a/a_M\approx$ 2.4 in the short edge.e. Stray field map of 1.1° tDB CrI$_3$ after 500 mT-field cooling, showing dot-like patterns. f. Autocorrelation of a selected area (dashed black rectangle) in (e), revealing a similar hexagonal pattern with a spacing of $a/a_M\approx$ 6.7 in the long edge and $a/a_M\approx$ 6.0 in the short edge.
• Figure 4: a. A representative stray field map of a 1.1° tDB CrI$_3$ sample after 500 mT field cooldown, taken at 4K, shows dot-like features in the AFM region. An area (dashed black rectangle) was selected to perform autocorrelation at different temperatures. b-d. 2D autocorrelation of the selected area in (a) at 4K, 25K, and 35K, respectively, demonstrating the robustness of the magnetic textures at elevated temperature. The contrast of higher-order peaks becomes more prominent due to the reduction of the critical field as the critical temperature is approached. The spacing of the hexagonal features yields a ratio of $a/a_{M} \approx 8.1$ in the long edges and $a/a_{M} \approx 6.0$ in the short edge.e. Atomistic simulation of twisted double bilayer CrI$_3$ (tDB CrI$_3$), incorporating interfacial DMI from the hBN/CrI$_3$ interface. Isolated antiferromagnetic (AFM) Néel-type skyrmions emerge in layers 3 and 4. Purple (blue) indicates out-of-plane spins pointing upward (downward), while white denotes in-plane spin orientation. f-h. $B_x$, $B_y$, and $B_z$ stray field reconstruction from fine scan of single dots in (a). The field profile resembles the simulated Néel-type skyrmion shown in (e). From the $B_z$ profile, the feature size is about 60 nm.