Route towards stable homochiral topological textures in $A$-type antiferromagnets

Topologically protected whirling magnetic textures could emerge as data carriers in next-generation post-Moore computing. Such textures are abundantly observed in ferromagnets (FMs); however, their antiferromagnetic (AFM) counterparts are expected to be even more relevant for device applications, as they promise ultrafast, deflection-free dynamics while being robust against external fields. Unfortunately, such textures have remained elusive; hence identifying materials hosting them is key to developing this technology. Here, we present comprehensive micromagnetic and analytical models investigating topological textures in the broad material class of $A$-type antiferromagnets, specifically focusing on the prototypical case of $\alpha {\text{-Fe}}_2{\text{O}}_3$—an emerging candidate for AFM spintronics. By exploiting a symmetry-breaking interfacial Dzyaloshinskii-Moriya interaction (iDMI), it is possible to stabilize a wide topological family, including AFM (anti)merons, bimerons, and the hitherto undiscovered AFM skyrmions. While iDMI enforces homochirality and improves the stability of these textures, the widely tunable anisotropy and exchange interactions enable precise control of their core dimensions. We then present a unifying framework to model the scaling of texture sizes based on a simple dimensional analysis. As the parameters required to host and tune homochiral AFM textures may be obtained by rational materials design of $\alpha {\text{-Fe}}_2{\text{O}}_3$, it could emerge as a promising platform to initiate AFM topological spintronics.

Figure 1

(a) The crystal and magnetic structures of AFM $\alpha {\text{-Fe}}_2{\text{O}}_3$, showing a sequence of antiparallel FM layers that we model in our simulations. The light red and dark blue arrows show the orientation of the magnetic moments in the two sublattices above $T_{\text{M}}$. The gray planes separate the two sublattices and host the O atoms. (b) The simulation configuration, where cells belonging to the two antiparallel sublattices are shown in red and blue and the arrows show the magnetic moment orientation in a given cell for $T>T_{\text{M}}$. The curved arrows show the AFM coupling between adjacent layers ($A_{\text{OOP}}$) and the FM coupling between cells in the same layer ($A$).

Figure 2

(a)–(d) A gallery of topological textures in $\alpha {\text{-Fe}}_2{\text{O}}_3$, based on our micromagnetic simulations. In all cases only a single magnetic layer is shown. The black arrows represent the in-plane spin directions, and the color contrast corresponds to the $z$ component of magnetization. The green scale bar in the bottom-right corner of each panel is 100 nm.

Figure 3

Radius $R$ of meron textures, based on micromagnetic simulations (black squares) and analytical calculations (blue curves). The iDMI was included in all cases. $A, |K_{\text{eff}}|$, and $D$ were varied in (a), (b), and (c), respectively, with the rest of the parameters kept constant.

Figure 4

Radius $R$ of antimeron textures, based on micromagnetic simulations (black squares) and analytical calculations (blue curves). The iDMI was included in all cases. $A, |K_{\text{eff}}|$, and $D$ were varied in (a), (b), and (c), respectively, with the rest of the parameters kept constant.

Figure 5

(a) Relaxed Néel bimeron intercore distance $s_{\text{eq}}$ as a function of $A$ and $K_{\text{eff}}$ for $D=2$ $\mathrm{mJ}/{\mathrm{m}}^2$. The simulation points are given by solid black circles. (b)–(e) Snapshots of the relaxed configuration in one of the layers for several points in the diagram, where the arrows represent the IP spin direction and the color contrast represents the $z$ component of the magnetization as in Fig. 2. The green scale bar in the bottom-right corner of (b)–(e) is 100 nm. The images correspond to the following values: (b) $A=14 \mathrm{pJ}/\mathrm{m}, K_{\text{eff}}=-17 \mathrm{kJ}/{\mathrm{m}}^3$; (c) $A=19 \mathrm{pJ}/\mathrm{m}, K_{\text{eff}}=-17 \mathrm{kJ}/{\mathrm{m}}^3$; (d) $A=14 \mathrm{pJ}/\mathrm{m}, K_{\text{eff}}=-10 \mathrm{kJ}/{\mathrm{m}}^3$; and (e) $A=19 \mathrm{pJ}/\mathrm{m}, K_{\text{eff}}=-10 \mathrm{kJ}/{\mathrm{m}}^3$.

Figure 6

(a) Néel skyrmion stability window as a function of $A$ and $K_{\text{eff}}$ for $D=1 \mathrm{mJ}/{\mathrm{m}}^2$. The color scale represents the relaxed FWHM of the skyrmions, and the black area shows the region where the skyrmion was found to radially collapse and therefore was unstable. The $A$ and $K_{\text{eff}}$ values for which simulations were performed are shown by solid black circles. (b) $K_{\text{eff}}$-vs-$A$ curves at constant skyrmion radius, calculated for the smallest size for which a skyrmion can be stabilized in our simulations (given by the $F_{\text{av}}$ value next to each curve). Symbols and colors correspond to different iDMI strengths.

Figure 7

(a) Rescaled radii of simulated merons (black squares) and antimerons (red circles) as a function of ${\kappa }^{\prime }=D_{\text{eff}}/\sqrt{A{K}_{\text{eff}}}$ compared with the corresponding linear meron (antimeron) ansatz, Eq. (1) [Eq. (2)]. (b) Rescaled radii of skyrmions (black squares) and bimerons (red circles). In each case the solid symbols show the smaller textures in the approximately linear scaling regime, and open symbols show larger textures where the energy landscape is very flat. An analytical linear bimeron model and two different types of skyrmion ansatz [42, 43] are shown for comparison. The blue line is a linear fit to the small radii bimerons. The vertical green dashed line shows the well-known upper stability threshold for skyrmions at ${\kappa }^{\prime }=4/\pi$, demonstrating that our skyrmions do not reach this threshold for any material parameters considered herein.