Configurable antiferromagnetic domains and lateral exchange bias in atomically thin CrPS4

TL;DR

This work uses nanoscale NV magnetometry to visualize and manipulate interfacial exchange bias in atomically thin CrPS$_4$, revealing a tilted odd-layer magnetic moment and antiphase domain walls in even layers. By exploiting a weak surface magnetization, the authors demonstrate deterministic control of AFM domains and reveal how domain walls couple to adjacent layers to generate a tunable, multilevel lateral exchange bias. The combination of high-resolution imaging, micromagnetic/atomistic simulations, and a macrospin exchange-bias model yields a coherent picture of how interfacial exchange, domain-wall energy, and geometry govern reversal processes. The results open avenues for 2D AFM–FM hybrids in spintronic devices, including lateral memory and racetrack-like architectures, and suggest extensions to other A-type 2D AFMs and AFM topological states.

Abstract

Interfacial exchange coupling between antiferromagnets (AFMs) and ferromagnets (FMs) crucially makes it possible to shift the FM hysteresis, known as exchange bias, and to switch AFM states. Two-dimensional magnets unlock opportunities to combine AFM and FM materials; however, the buried AFM-FM interfaces obtained by stacking remains challenging to understand. Here we demonstrate interfacial control via intralayer exchange coupling in the layered AFM CrPS$_4$, where connected even and odd layers realize pristine lateral interfaces between AFM-like and FM-like regions. We distinguish antiphase even-layer states by scanning nitrogen-vacancy centre (NV) magnetometry due to a weak surface magnetization. This surface magnetization enables control over the even-layer state, with different regions switching at distinct fields due to their own lateral couplings. We toggle three AFM domains adjacent to a FM-like region and demonstrate a tunable multilevel exchange bias. Our nanoscale visualization unveils the microscopic origins of exchange bias and advances single two-dimensional crystals for hybrid AFM-FM technologies.

Figures (5)

• Figure 1: Layered AFM in atomically thin $\mathrm{CrPS_4}$. (a) A single NV center inside a diamond probe is scanned over few-layer $\mathrm{CrPS_4}$. The parity ($\ket{+}$ or $\ket{-}$) of an odd layer is determined by the direction of its uncompensated layer of magnetization. Even-layer and odd-layer states with the same parity have aligned layer magnetizations. The direction of the net areal magnetization $\bm{\sigma}$ is specified by a polar angle $\theta_M$ and an in-plane angle $\phi_M$ ($x$-axis). For magnetic imaging, the external field $B_{ext}^{NV}$ is applied at 54.7$^{\circ}$ from normal in the $xz$-plane, parallel to the NV axis. (b) The magnetic moments (red and blue arrows) in bulk $\mathrm{CrPS_4}$ alternate between adjacent layers (A-type AFM) and is tilted in the $ac$-plane. (c) Crystallographic structure in the $ab$-plane, showing two inequivalent Cr atoms within the rectangular unit cell. A row of edge-sharing CrS$_6$ octahedra along the $b$-axis is highlighted in blue. Exfoliated flakes typically form parallelograms bounded by the [110] directions. (d) Optical image of Flake 1 with layer thicknesses labeled. (e) Image of the sample stray field $B_S$ along the NV center axis for the 5-layer corner region in d). The cartoon (inset) shows the layer magnetizations for the $\ket{-4}$, $\ket{-5}$, and $\ket{-6}$ states. (f) Goodness-of-fit parameter $R^2$ for fitting e) using a uniform $\bm{\sigma}$ over the 5L area, oriented along arbitrary directions over the unit sphere. (g) Reconstructed magnetization amplitude $\sigma$ using the best-fit direction, determined to be tilted near the $ac$-plane.
• Figure 2: Antiphase domains in even-layer $\mathrm{CrPS_4}$. (a) Stray field $B_S$ image of Flake 1. The top and bottom 5L regions adopt opposite magnetization states $\ket{+5}$ and $\ket{-5}$, respectively. The weak $B_S$ in the intervening even-layer region reveals an antiphase domain wall between $\ket{+6} =$$\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow$ above and $\ket{-6} =$$\downarrow\uparrow\downarrow\uparrow\downarrow\uparrow$ below. (b) Higher resolution $B_S$ measurement of the 6L antiphase domain wall. The vertical ridge in $B_S$ corresponds to a physical defect (fold) in the sample. (c) Micromagnetic simulation of even-layer domain wall trajectories for a representative geometry. For small positive $B_{ext}^z$, the domain wall takes a minimum length state that touches the odd-layer corner (left). For larger positive $B_{ext}^z$, the domain wall curves to increase the area of the $\ket{-}$ even-layer domain, while avoiding the odd-layer interface (right). (d) $B_S$ image of the transition between 4L and 6L, demonstrating that the even-layer signal is not proportional to thickness. (e) The even-layer $B_S$ plausibly arises from a deviation from perfect compensation between the areal magnetizations $\sigma_{top}$ and $\sigma_{bot}$ of the top and bottom surface layers. The net magnetization $\sigma$, summed over all layers, is shown beneath the wavy line. For Flake 1, the data imply $\sigma_{top} > \sigma_{bot}$. (f) $B_S$ image of $\mathrm{CrPS_4}$ Flake 2 (optical image in inset). (g) Higher resolution $B_S$ image of the domain wall in the bilayer, with $\ket{-2}$ = $\downarrow\uparrow$ on the left and $\ket{+2}$ = $\uparrow\downarrow$ on the right. (h) For Flake 2, the sign of $B_S$ for its even-layer states suggests $\sigma_{bot} > \sigma_{top}$, opposite to Flake 1. (i) Simulation for the bilayer domain wall in Flake 2. The simulations in c) and i) assume uncompensated even-layer magnetizations with the same sign as experiment. All scale bars denote 1 $\mu$m.
• Figure 3: Lateral exchange bias at the even-odd interface. (a) Hysteresis curves for the narrow and wide 3L regions in Flake 2 and the corner 5L in Flake 1 with the surrounding even-layer regions in uniform $\ket{+}$ states. For comparison, the symmetric hysteresis loop for an isolated 3L region is shown as the red background rectangle. (b-e) Stray field $B_S$ images of the narrow and wide 3L at various $B^{NV}_{ext}$ on the hysteresis curve (labeled in a). Domain walls that encircle the wide 3L in the $\ket{-3}$ state begin to depin on the forward sweep prior to $B^{NV}_{ext} = 0$ (see arrow in d). Bwd. - backward sweep; fwd. - forward sweep. (f) Image of the magnetization reversal at $B_{c1}$ for the narrow 3L when all even layers are $\ket{+}$. Barkhausen jumps are thermally activated by scanning (slow scan direction indicated by arrow). Simulations (bottom) reveal that the domain wall between 2L and 3L occurs on the bilayer side (arrow), while that between 3L and 4L is pinned at the interface. (g) Data (top) and simulations (bottom) of the $B_{c1}$ reversal when nearby even layers are in a domain state, as labeled. (h) $B_S$ linecut across the narrow 3L when domain walls exist along both edges (e.g. panel c). (i) $B_S$ linecut when no domain walls exist (e.g., panel e). The green trace (residual) in h) or i) presents the deviation of the data from a fit assuming no domain walls. For clarity, residuals are multiplied by three and zero residual is offset differently for $x < 0$ and $x > 0$.
• Figure 4: Controlled nucleation and translation of AFM domain walls. (a) Hysteresis loop for a bilayer region in a third $\mathrm{CrPS_4}$ flake (Flake 3, optical image in inset). The bilayer hysteresis is driven by its uncompensated surface magnetization and is asymmetric due to interfacial coupling to the 4L region on its right. (b,c,d) $B_S$ images of Flake 3 at various points on the bilayer hysteresis loop, as labeled in a). Large negative $B^{NV}_{ext}$ flips the bilayer from $\ket{+2}$ (with $+\sigma$) to $\ket{-2}$ (with $-\sigma$), while a small positive field reverses $\ket{-2}$ to $\ket{+2}$ by domain wall translation. (e) $B_S$ image of a fourth $\mathrm{CrPS_4}$ flake (Flake 4) with all regions in $\ket{+}$ states. A narrow 6L stripe is partially connected to a wider 4L region (inset). (f) Image after ramping $B^z_{ext}$ to 0.35 T and back. The connected 4L and 6L areas switch from $\ket{+}$ to $\ket{-}$. (g) Image after ramping $B^z_{ext}$ to 1 T and back. The remaining $\ket{+6}$ domain on the left switches to $\ket{-6}$. (h) Image after ramping $B^z_{ext}$ to $-0.3$ T and back. The connected 4L and 6L areas now reverse from $\ket{-}$ to $\ket{+}$. (i) Field-driven motion of even-layer domain walls in Flake 1. The initial domain state (center) is formed from a uniform $\ket{+}$ state (inset) by ramping $B^{z}_{ext}$ to +0.6 T. The domain wall can then be driven left or right by negative or positive field pulses, respectively.
• Figure 5: Multilevel exchange bias through digital control of AFM domains. (a) Outline of the area surrounding the narrow 3L in Flake 2. Three independent even-layer domains can be defined: bilayer ($\ket{2}$), bottom 4L ($\ket{4_B}$), and right 4L ($\ket{4_R}$), forming a composite three-bit state $\ket{2\!\cdot\!4_B\!\cdot\!4_R}$. (b) Pulse sequence for generating different configurations of the three even-layer domains, starting from $\ket{2\!\cdot\!4_B\!\cdot\!4_R} = \ket{-\!-\!-}$. The horizontal colored lines denote the critical fields for the transition labeled in the same color. For example, a pulse to $-0.8$ T exceeds all three negative critical fields and generates the state $\ket{-\!+\!+}$, regardless of the initial state. (c) $B_S$ images of the even-layer domains in various states. Imaged regions depicted by boxes in a). The sign and strength of the stray field on the 4L edge is incompatible with a termination of the interior magnetization and suggests different magnetic uncompensation at the edge. (d) Hysteresis loops displaying a tunable $B^{NV}_{c2}$ for the narrow 3L when the even-layer domains are initialized as $\ket{-\!-\!-}$, $\ket{-\!+\!+}$, $\ket{+\!-\!+}$, and $\ket{-\!-\!+}$ from top to bottom.