Twist-tuned exchange and hysteresis in a bilayer van der Waals magnet

Abstract

Moiré superlattices in twisted bilayers enable profound reconstructions of the electronic bandstructure, giving rise to correlated states with remarkable tunability. Extending this paradigm to van der Waals magnets, twisting creates spatially varying interlayer exchange interactions that stabilize emergent spin textures and the coexistence of ferromagnetic and antiferromagnetic domains. Here, we demonstrate the emergence of robust magnetic hysteresis in bilayer CrSBr upon twisting by an angle of ~ 3°. This is observed as the corresponding hysteretic evolution of the exciton energy, that directly correlates with the bilayer magnetic state, in magnetic field dependent photoluminescence measurements. A two-sublattice model captures this behavior, attributing it to the twist-induced reduction of interlayer exchange that stabilizes both parallel and antiparallel spin configurations across a broad field range. Comparison with experiment enables quantitative extraction of the effective exchange strength. Remarkably, the system exhibits coherent averaging across the moiré supercell, yielding an effective monodomain response characterized by switching into the antiferromagnetic state, rather than forming spin textures or fragmented domains. Spatially resolved measurements further uncover local variations in hysteresis loops, consistent with position-dependent modulation of the average exchange interaction. Our results establish twist engineering as a powerful route to programmable magnetic memories in two-dimensional magnets, harnessing the robustness of antiferromagnetic order.

Figures (16)

• Figure 1: Twist engineering and magnetic hysteresis in bilayer CrSBr.a. Schematic of the moiré superlattice formed in twisted bilayer CrSBr at a twist angle of $\theta \approx 3^\circ$, with the moiré unit cell outlined by a red dashed box. b. Side view along the $a$-axis showing two representative atomic registries—A and M—with distinct stacking configurations. These registries modulate the interlayer exchange interaction. c. Schematic of pristine bilayer CrSBr exhibiting spatially uniform interlayer exchange interaction $J_{\text{inter}}$. The corresponding exciton energy $E_x$, that depends on the angle between the two layer magnetisationswilson2021interlayer, displays negligible hysteresis under an external magnetic field $B$ applied along the $b$-axis. Red and blue arrows denote the upward and downward field sweep directions, respectively. d. In contrast, twisted bilayer CrSBr with spatially averaged interlayer exchange interaction $J^*_{\text{inter}}$ exhibits pronounced magnetic hysteresis in the $E_x$–$B$ curves. Orange and purple arrows indicate the layer magnetisations of the bilayers.
• Figure 2: Magnetic field dependent exciton energy measured via photoluminescence (PL) spectra in twisted and pristine bilayer CrSBr. a. PL peak energy A-exciton at T=4.7 K of the pristine bilayer under a magnetic field applied along the in-plane $b$-axis. b. same as a but for out-of-plane $c$-axis (full symbols) and $a$-axis (hollow symbols). c. PL peak energy A-exciton of the twisted bilayer under a magnetic field applied along the in-plane $b$-axis. d. same as c but for out-of-plane $c$-axis (full symbols) and $a$-axis (hollow symbols). In all panels, red squares represent the magnetic field sweep from negative to positive values, while blue triangles indicate the reverse sweep (positive to negative). The measured exciton energy provides direct access to the magnetic configurations (see Fig. \ref{['fig:3']}c) due to the former's dependence on the angle between the two layer magnetisations. Switching fields are indicated by grey lines.
• Figure 3: Theoretical analysis of magnetic ground state and hysteresis in a twisted bilayer antiferromagnet.a. Due to the strong intralayer ferromagnetic exchange, the description of position-dependent interlayer exchange (left) arising from a moiré superlattice can be effectively reduced to a simplified two-sublattice model (right) with a spatially averaged effective interlayer exchange. b. Analytically evaluated magnetisation curves $M/M_s$ as a function of applied magnetic field along the principal crystal axes: magnetic easy axis $b$ (left), intermediate axis $a$ (center), and hard axis $c$ (right) respectively. The red solid and blue dotted curves represent forward and reverse magnetic field sweeps, respectively. Here, hysteresis emerges for magnetic field applied along $b$ because both parallel and antiparallel states are stable in the indicated field range. Switching field values are indicated (see main text) c. The corresponding exciton energy shift $\Delta E_{X}$ evaluated using the relation $\Delta E_{X} \propto \cos^2 \left(\theta/2\right)$ with $\theta$ being the angle between the two sublattice magnetisations wilson2021interlayerheissenbuttel2025quadratic.
• Figure 4: Spatially resolved magneto-optical response of a twisted bilayer magnet.a, Optical microscope image of the fabricated twisted bilayer sample. The black box indicates the region of interest, with three marked positions (1–3) corresponding to the spatial locations where magneto-optical measurements were performed. b–d, Magnetic field-dependent exciton energy measured at positions 1 (b), 2 (c), and 3 (d), under a magnetic field applied along the magnetic easy axis $b$. Red squares represent field sweeps from negative to positive , and blue triangles represent sweeps from positive to negative. The observed hysteresis and energy shifts reflect position-dependent magnetic switching behavior and interlayer exchange coupling in the twisted bilayer. The switching fields $h_{P-}$ and $h_{AP+}$ are indicated by grey lines. While spot 1 manifests only parallel and antiparallel magnetic configurations, spot 2 and spot 3 present evidence for canted state as well, consistent with our theoretical analysis (Supplementary Note 1).
• Figure S1: Schematic depiction of the two sublattice magnetizations' configuration. The different values of angles $\beta$ and $\phi$ allow capturing all possible states from antiparallel, parallel, to canted. The schematic depicted adequately captures the cases when the applied field is along the easy ($\hat{z}$) or intermediate ($\hat{x}$) axis. When consider applied field along the hard ($\hat{y}$) axis, the same parametrization of the magnetic configuration works with the x axis replaced by the y axis.