The response of magnetization to external stimuli has drawn attention for more than a century, providing fundamental insights into the physical mechanisms behind magnetization dynamics. The Stoner–Wohlfarth model, proposed in 1948, describes the magnetization reversal in the form of coherent rotation of a single-domain ferromagnetic nanoparticle1 (Fig. 1a). Beyond its fundamental importance as a type of hydrogen model for ferromagnetism2, it provides guidance for the design of magnetic devices for data computing and information storage8,9. However, the simplicity of the model makes it arduous for explaining the magnetic behaviour of other ferromagnetic systems, which usually have multidomain structures associated with unavoidable defects. In this regard, vdW magnets exhibit a natural advantage, as their defect-free vdW interfaces allow them to be considered single-domain, at least in the vertical dimension. Such 2D FMs with strong interlayer coupling can be called the Stoner–Wohlfarth FMs, such as Fe 3 GeTe 2 , whose magnetic reversal behaviours are well described by the Stoner–Wohlfarth model below a certain thickness10.
Fig. 1: Classification of various types of magnetism and evolution of the magnetic order. a, Binary switching of magnetization controlled by the magnetic field in FMs. b, Magnetic-field-insensitive Néel vector in conventional 3D AFMs. c, Interlayer-free 2D A-type AFMs (2D A-AFMs). Left, the evolution of magnetization with the magnetic field (taking 4L as an example). The corresponding magnetization is marked on each plateau. Right, schematic of interlayer-free flipping from M = 0 to M = +2. The red or blue quadrilaterals represent a ferromagnetic layer with opposite magnetization, +1 or −1, respectively. d, SHG hysteresis loop on 4L CrSBr with the in-plane magnetic field between ±0.6 T sweeping along the easy axis of CrSBr. The assignment of magnetic states during transitions is discussed in ref. 12. e, Interlayer-locked 2D A-AFMs. Left, FM-like binary switching of Néel vector controlled by the magnetic field. Right, schematic of interlayer-locked flipping between +L and −L. f, SHG hysteresis loop on 4L CrPS 4 with the out-of-plane magnetic field between ±2 T. a.u., arbitrary units. Full size image
As an extension, is there a Stoner–Wohlfarth AFM—a single-domain AFM whose antiferromagnetic order (Néel vector L) can be coherently switched 180° by the magnetic field? From an application perspective, seeking such AFMs is crucial for improving the data-storage density and information-processing efficiency attributed to their zero stray field and ultrafast dynamics3,4. For the conventional three-dimensional (3D) collinear AFM, however, a 180° switching of the Néel vector is unavailable owing to the vanishing Zeeman energy (Fig. 1b). Although recently a new type of collinear AFM known as altermagnets has been demonstrated to exhibit 180° switching of the Néel vector, they are not the Stoner–Wohlfarth AFMs, as the incomplete switching ratio revealed by the anomalous Hall effect suggests the existence of microscopic multidomain structures5,6,7. Of particular interest are the 2D vdW A-type AFMs, in which spins within each layer order ferromagnetically and adjacent layers couple antiferromagnetically. The weak interlayer magnetic coupling leads to their controllable antiferromagnetism. The magnetic evolution of some representative 2D A-type AFMs, such as CrSBr (refs. 11,12) and CrI 3 (refs. 13,14), has been extensively studied in the past, following a behaviour of layer-by-layer flipping with the magnetic field, as sketched in Fig. 1c and illustrated in Fig. 1d for 4L CrSBr and Extended Data Fig. 1 for 4L CrI 3 . Such AFMs are also not the expected Stoner–Wohlfarth AFMs because the Néel vector is not coherently switched to its antiphase state at once (L to −L) but tends to a metastable state by an interlayer-free flipping (Fig. 1c).
Here we report a new type of 2D vdW A-type AFM, CrPS 4 as a representative, whose antiferromagnetic order undergoes an interlayer-locked antiferromagnetic switching (Fig. 1e). The magnetic evolution manifests as a FM-like binary switching (Fig. 1f) rather than the layer-by-layer flipping observed in interlayer-free AFMs. CrPS 4 is an air-stable vdW semiconductor and crystallizes into a non-centrosymmetric monoclinic structure with space group C 2 (refs. 15,16). As shown in Fig. 2a, the material forms an A-type antiferromagnetic order along the c-axis below the Néel temperature 38 K (refs. 16,17,18). Transport measurements in CrPS 4 indicate that its magnetic behaviour undergoes a spin-flop transition into a canted state at approximately 0.7 T, followed by a spin-flip transition into a ferromagnetic state around 7 T under an out-of-plane magnetic field19,20,21 (schematically shown in Extended Data Fig. 2). Besides, recent reflective magnetic circular dichroism (RMCD) studies show a clear hysteresis loop below the spin-flop field in odd-layer CrPS 4 , suggesting the existence of further magnetic transitions16. However, RMCD is only sensitive to the net magnetization, so it fails to uncover the layer-resolved magnetization reversal for this transition and, more importantly, it is incompetent to investigate the magnetic evolution of even-layer CrPS 4 whose net magnetization is zero.
Fig. 2: FM-like binary switching in odd-layer and even-layer AFM CrPS 4 . a, Crystallographic and magnetic structure of CrPS 4 . The magnetic moments denoted by the red and blue arrows on Cr3+ alternate oppositely between adjacent layers. b, Optical microscopic image of a CrPS 4 flake (sample 1) with the labelled layer thicknesses. Scale bar, 5 μm. c–h, SHG and RMCD hysteresis loops on 2L (c,f), 3L (d,g) and 4L (e,h) CrPS 4 with the out-of-plane field between ±0.1 T. i, Symmetry transformation of the non-centrosymmetric antiferromagnetic state in even-layer CrPS 4 under the spatial-inversion operation i. The spatial-inversion operation converts one antiferromagnetic state to the other but not to itself. j, Symmetry transformation of the centrosymmetric antiferromagnetic state in odd-layer CrPS 4 . a.u., arbitrary units. Full size image
To reveal the barely detectable antiferromagnetic order and its potential evolution, we use the second-harmonic generation (SHG) microscopic technique because the nonlinear optical signal is no longer restricted by the net magnetization but is sensitive to the symmetry changes12,14,22,23. The SHG process typically originates from the dominant electric-dipole mechanism and the prerequisite for this process is the broken spatial-inversion symmetry. The layered antiferromagnetic order such as even-layer CrPS 4 simultaneously breaks both the spatial-inversion and time-reversal symmetries, thus contributing time-noninvariant (c-type) electric-dipole SHG and permitting SHG to detect the antiferromagnetic order and symmetry-related phenomena.
Figure 1f shows a typical magnetic-field-dependent SHG loop on tetralayer CrPS 4 at 6.5 K, in which the field is perpendicular to the sample and sweeps forward and backward between ±2 T. At high magnetic fields beyond ±0.7 T, the loop exhibits a smooth trajectory, originating from the gradual canted states associated with spin-flop transition (Extended Data Fig. 2). Notably, a clear FM-like hysteresis loop appears at much lower fields (±0.01 T), indicating the existence of further magnetic transitions in CrPS 4 .
We further focus on this FM-like loop and examine its layer-dependent evolution. Figure 2b shows the optical microscopic image of few-layer CrPS 4 with thicknesses of 2L–4L. As well as the tetralayer, this FM-like switching also exists in the bilayer but is absent in the trilayer (Fig. 2c–e). Without loss of generality, similar odd–even-layer contrast is shown for other thicknesses in Extended Data Fig. 3. Notably, when the polar RMCD is used for the same sample, the features are exactly opposite to that of SHG. Only the odd layers show the hysteresis loop, whereas all of the even layers do not (Fig. 2f–h). As the temperature increases, the hysteresis loops observed in both SHG and RMCD shrink and eventually vanish at the critical temperature of around 34 K, at which the antiferromagnetic order disappears (Supplementary Text 1 and Extended Data Fig. 4).
For even-layer CrPS 4 , the single FM-like loop present in SHG but absent in RMCD suggests that the magnetic transition near 0 T originates from the antiferromagnetic binary switching. That means, when applying a magnetic field along the out-of-plane direction of CrPS 4 , all layers are antiferromagnetically locked and simultaneously flipped to their time-reversal counterpart, that is, switching from the +L state to the −L state. Because the layered antiferromagnetic order of even-layer CrPS 4 breaks the spatial-inversion symmetry (Fig. 2i), c-type SHG χ(c) emerges and couples linearly to the Néel vector, which is expressed by χ(c)(−L) = −χ(c)(L). Besides, the crystallographic structure of CrPS 4 is non-centrosymmetric, resulting in the extra time-invariant (i-type) SHG χ(i). Therefore, when the switching between the time-reversal antiferromagnetic counterparts occurs, the self-interference |χ(i) ± χ(c)|2 leads to the intensity contrast in SHG loops24,25,26. The antiferromagnetic switching is further supported by the helicity-reversed SHG loops (Extended Data Fig. 5), in which the helicity of excitation is equivalent to exerting a time-reversal operation to the system (see details in Supplementary Text 2). However, the switching is invisible in RMCD signals as the magnetization of even layers is completely compensated.
For odd-layer CrPS 4 , owing to the uncompensated magnetization, a hysteresis loop emerges in RMCD signals, verifying that the antiferromagnetic switching also exists in odd-layer samples. To understand the absence of SHG loop in odd layers, we noted that the layered antiferromagnetic order alone for odd layers is centrosymmetric, as illustrated in Fig. 2j. Yet, because of the broken spatial-inversion symmetry in crystallographic lattice, both χ(i) and χ(c) can be non-zero. The centrosymmetric antiferromagnetic order substantially alleviates the degree of symmetry breaking—leading to negligible χ(c). As a result, the SHG signals of odd-layer samples remain constant during the antiferromagnetic switching.
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