Moiré spintronics: Emergent phenomena, material realization and machine learning accelerating discovery

TL;DR

This review surveys moiré spintronics in twisted van der Waals magnets, emphasizing stacking-dependent magnetism, non-collinear spin textures, moiré magnetic exchange interactions, moiré skyrmions, and moiré magnons. It details how twist-angle and registry modulate interlayer exchanges and topological excitations, with CrI$_3$-family systems as primary platforms, and discusses theoretical frameworks for MMIE and topological magnons. A central focus is the role of machine learning in accelerating discovery: ML force fields (DPmoire), deep learning Hamiltonians (xDeepH), and generalized transformations (twist operator/deep Wannier) enable large-scale simulations and material-agnostic screening, complemented by ML-based interpretation of experiments and autonomous design. The review also outlines challenges, including lattice relaxation, disorder, and the need for closed-loop AI-driven discovery platforms to translate moiré spintronics from fundamental science to practical devices, and it highlights opportunities in high-$T_c$ moiré magnets and moiré multiferroics.

Abstract

Twisted van der Waals (vdW) materials have emerged as a promising platform for exploring exotic quantum phenomena and engineering novel material properties in two dimensions, potentially revolutionizing developments in spintronics. This Review provides an overview of recent progress on emerging moiré spintronics in twisted vdW materials, with a particular focus on two-dimensional magnetic materials. Following a brief introduction to the general features of twisted vdW materials, we discuss recent theoretical and experimental studies on stacking-dependent interlayer magnetism, non-collinear spin textures, moiré magnetic exchange interactions, moiré skyrmions and moiré magnons. We further highlight the potential of machine learning to accelerate the discovery and design of multifunctional materials for moiré spintronics. Finally, we conclude by addressing the most pressing challenges and potential opportunities in this rapidly expanding field.

Figures (8)

• Figure 1: Overview of moiré spintronics with emergent phenomena.
• Figure 2: Schematic illustration of the moiré pattern of graphene (red) on hBN (blue) with a relative rotation angle between the crystals of (a) $0^{\circ}$ and (b) $3^{\circ}$. Black hexagons mark the moiré plaquette. (c) Schematic of TBG and its superlattice unit cell. $\lambda_{\mathrm{SL}}$ is the moiré period and $A_{\mathrm{SL}}$ is the unit cell area. (d) A false-colored TEM image of graphene quasicrystal in TBG rotated exactly 30$^{\circ}$, mapped with 12-fold Stampfli-inflation tiling. Magneto-optical Kerr effect for (e) monolayer (1L), (f) bilayer (2L) and (g) trilayer (3L) of CrI$_{3}$. By measuring the Kerr rotation angle $\theta_{\mathrm{K}}$, the evolution of magnetization with the application of an external magnetic field in the out-of-plane configuration are traced. (h) and (i) Schematic of rhombohedral (monoclinic) stacking with top (left) and side view (right) indicating the ferromagnetic (antiferromagnetic) interlayer coupling. The green (purple) atoms represent the Cr atoms in the top (bottom) layer while the brown ones represent the I atoms. (j) and (k) Magnetic field dependence of MCD at 3.5K for two 2L and two 5-layer (5L) regions of the CrI$_{3}$ flake before (j) and after (k) applying a pressure of 1.8Gpa, indicating stacking order transition, as the rhombohedral (monoclinic) phase prefers ferromagnetic (antiferromagnetic) interlayer coupling. Panels (a) and (b) reproduced with permission from Woods et al., Nat. Phys. 10, 451 (2014). Copyright 2014 Springer Nature. Woodsc2014 Panel (c) reproduced with permission from Cao et al., Phys. Rev. Lett. 117, 116804 (2016). Copyright 2016 American Physical Society. Caoy2016 Panel (d) reproduced with permission from Ahn et al., Science 361, 782 (2018). Copyright 2018 American Association for the Advancement of Science. Ahn2018 Panels (e)-(g) reproduced with permission from Huang et al., Nature 546, 270 (2017). Copyright 2017 Springer Nature. Huangb2017 Panels (h) and (i) reproduced with permission from Song et al., Nat. Mater. 18, 1298 (2019). Copyright 2019 Springer Nature. Songt2019 Panels (j) and (k) reproduced with permission from Li et al., Nat. Mater. 18, 1303 (2019). Copyright 2019 Springer Nature. Lit2019
• Figure 3: Moiré superlattice structure and moiré magnetism in twisted bilayer CrI$_{3}$. (a) Schematics of a moireé superlattice structure in bilayer CrI$_{3}$ with a small-twist-angle. R, M and AA represent rhombohedral, monoclinic and AA stacking, respectively. (b) Schematic illustration of a magnetic domain wall between the R- and M-stacking domain regions. (c)-(f) Magnetic-field dependence of MCD of a bilayer CrI$_{3}$ by natural stacking (c) and twisted stacking with twist angle 1.2$^{\circ}$ (d), 4$^{\circ}$ (e) and 15$^{\circ}$ (f), respectively. (g) MCD as a function of magnetic field at selective temperatures for a bilayer CrI$_{3}$ with twist angle 1.2$^{\circ}$. (h) Polar reflective MCD and MOKE signals as a function of magnetic field for the monolayer (top panel), the twisted bilayer (middle panel), and a pristine bilayer (bottom panel) CrI$_{3}$, respectively. (i) Scanning NV magnetometry magnetization map of twisted bilayer CrI$_{3}$ at 0.21T. Nanoscale antiferromagnetic and ferromagnetic domains are clearly resolved. Panels (a)-(g) reproduced with permission from Xu et al., Nat. Nanotechnol. 17, 143 (2022). Copyright 2022 Springer Nature. Xuy2022 Panels (h) and (i) reproduced with permission from Song et al., Science 374, 1140 (2021). Copyright 2021 American Association for the Advancement of Science. Songt2021
• Figure 4: Schematics of generating MMEIs via Sliding-mapping Approach. (a) Moiré superlattice of the tBL-CrI$_3$. Insets are four domain regions with different stacking orders: AA, AB, AB' and BA stacking. Blue frame indicates the local site in (b). Dashed-yellow line represents the unit cell of moiré superlattice. (b) Examples of one-to-one correspondence between $J_{\mathrm{inter}}$ in tBL-CrI$_3$ and $\mathcal{J}_{\mathrm{inter}}(\textbf{r})$ in sliding BL-CrI$_3$. (c)-(e) Color mapping of interlayer exchange interaction (left panel in c), intralayer nearest-neighboring exchange interaction (middle panel in c), intralayer next-nearest-neighboring exchange interaction (right panel in c), interlayer DMI (d), and intralayer DMI (e) between two Cr atoms as a function of sliding vector. Here, all the magnetic parameters are in the unit of meV. Panels (a)-(e) reproduced with permission from Yang et al., Nat. Comput. Sci. 3, 314 (2023). Copyright 2023 Springer Nature. Yangb2023
• Figure 5: (a) Phase diagram as a function of the maximum MMEI and the moiré periodicity at zero external magnetic field. $J_{ex}$ denotes the maximum of MMEI in the moiré superlattice. The triangle in the magnetic bubble lattice phase marks parameters for panel (b), and the dot in the skyrmion lattice phase is for panel (c). (b) Spin texture of the magnetic bubble lattice, shown in 2$\times$2 moiré supercells. The arrows show the in-plane orientation at DWs. (c) Energies per supercell of the lowest lying stable magnetic configurations as a function of external magnetic field. Solid curves are four skyrmion lattices of distinct topological skyrmion number C and vorticity $l$. Dashed curves are FM states. Green (orange) arrows indicate the evolution by sweeping the magnetic field up (down), where vorticity and location of skyrmion can switch under the conservation of topological charge. (d) Moiré periodicity $L$ vs maximum interlayer exchange field $B_{\mathrm{max}}$ phase diagram with spiral (Sp) and skyrmion crystal (SkX) phases. (e) Spin texture in tBL-CrI$_3$ at twist angle 1.41$^\circ$. Insets show the SkBs in the top and bottom layers. (f) Helicity $\gamma$ as a function of azimuth angle $\varphi$. (g) Schematic diagram of SkB-SkB interactions in the same layer or different layers. (h) Phase diagram of five distinct topological phases in the $J_{\perp}-J_{D}$ parameter space. $J_{\perp}$ and $J_{D}$ represent the interlayer exchange coupling and DDI, respectively. Red and blue color distinguishes skyrmion number of $\pm$1. (i) Schematic diagram of five distinct spin textures as shown in (h). (i) Steady-state spin textures evolved from a paramagnetic state for a 3$\times$3 moiré supercell in tBL-CrI$_3$. The local topological skyrmion number is indicated at each domain. (k) Schematic diagram of a stable meron-antimeron pair in a twisted magnet. Twist-induced AFM domain array in a FM order background (left panel). Schematic diagram of a stable Meron-antimeron pair (right panel). Red and blue indicate parallel and antiparallel spin alignments between the top and bottom layers respectively. Arrows and circles depict their in-plane winding textures and core positions, respectively. (l) Schematic illustration of a Meron Kekulé lattice in a twisted bilayer antiferromagnet. Yellow dots denote the cores of AFM merons that form a Kekulé lattice structure. Black solid lines denote intracell bonds between meron cores within the same moiré supercell, while white solid lines denote intercell bonds between meron cores across different supercells. The white dashed line depicts a single moiré supercell. Blue color indicates parallel alignment, while red indicates antiparallel alignment between Néel vectors across the top and bottom layers. Arrows represent the in-plane components of Néel vectors (right panel). Panels (a)-(c) reproduced with permission from Tong et al., Nano Lett. 18, 7194 (2018). Copyright 2018 American Chemical Society. Tongq2018 Panel (d) reproduced with permission from Akram et al., Phys. Rev. B 103, L140406 (2021). Copyright 2021 American Physical Society. Akram2021 Panels (e)-(g) reproduced with permission from Yang et al., Nat. Comput. Sci. 3, 314 (2023). Copyright 2023 Springer Nature. Yangb2023 Panels (h) and (i) reproduced with permission from Ray et al., Phys. Rev. B 104, 014410 (2021). Copyright 2021 American Physical Society. Roy2021 Panel (j) reproduced with permission from Xiao et al., Phys. Rev. Research 3, 013027 (2021). Copyright 2021 American Physical Society. Xiaof2021 Panel (k) reproduced with permission from Kim et al., Nano Lett. 24, 74 (2024). Copyright 2024 American Chemical Society. Kim2024 Panel (l) reproduced with permission from Kim et al., npj Quantum Mater. 10, 68 (2025). Copyright 2025 Springer Nature. Kim2025