Nanoscale imaging of spin textures with locally varying altermagnetic response in $α$-Fe$_2$O$_3$

Abstract

Altermagnetism is a recently identified magnetic state in which time-reversal symmetry is broken despite a collinear compensated spin structure. The response of altermagnets is determined not only by their $d$-, $g$-, or $i$-wave spin order, but also the orientation of their Néel vector $\mathbf{L}$. Therefore, accessing a response that fundamentally depends on the orientation of $\mathbf{L}$, such as the anomalous Hall effect, remains experimentally challenging in particular at the nanoscale. Here, we harness nano-spectroscopic X-ray magnetic circular dichroism (XMCD) to investigate nanoscale modulated altermagnetic responses in $α$-Fe$_2$O$_3$ (Hematite). By performing spectroscopy across the temperature-induced $\mathbf{L}$-reorientation Morin transition, we observe the on-and-off switching of XMCD, in agreement with our theoretical calculations. Although the bulk XMCD vanishes below the Morin temperature, we confirm the reorientation of $\mathbf{L}$ by harnessing polarization-independent X-ray absorption spectroscopy. Moreover, we observe a finite XMCD signal in nanoscale domain walls with locally modulated Néel vectors, while the surrounding domains exhibit no XMCD. At room temperature, we instead identify altermagnetic meron spin textures that exhibit XMCD in their planar regions but no XMCD in their nanoscopic cores. Our results establish a pathway to harness complex spin textures with nanoscale functionalities in a broader class of altermagnets with various $\mathbf{L}$-orientations and using light, earth-abundant elements.

Figures (6)

• Figure 1: a Magnetic structure of $\alpha$-Fe$_2$O$_3$ in a rhombohedral unit cell. The hexagonal crystallographic axes are also indicated in the figure. b Altermagnetic spin-polarization calculated in momentum space for the $k_z=0$ plane and an energy of 198.5 meV below the valence band maximum. c Temperature dependence of the magnetization of Sample #1 measured under a magnetic field of 0.01 T along the hexagonal $m$-axis. Néel vectors in a hexagonal setting below and above $T_\mathrm{M}$ are schematically illustrated in the inset. Magnetic moments (orange arrows) above $T_\mathrm{M}$ are slightly canted within the $c$-plane, resulting in a small uncompensated moment (gray arrow). The uncompensated magnetic moment is oriented by the magnetic field, resulting in the Néel vector becoming perpendicular to the magnetic field. Below $T_\mathrm{M}$, the magnetic moments (green arrows) align parallel to the $c$-axis without canting. d,e Magnetic structure of $\alpha$-Fe$_2$O$_3$ in a rhombohedral unit cell below and above $T_\mathrm{M}$. Under time-reversal symmetry operation $\mathcal{T}$, the Néel vector $\bf{L}$ reverses its orientation. Expected X-ray magnetic circular dichroic (XMCD) contrast for normal-incidence X-rays $\mathbf{k} \parallel c$-axis for each spin configuration is schematically illustrated in the bottom.
• Figure 1: Overview absorption images from the STXM experiments. The metallic conductor regions are highlighted in yellow as a guide to the eye.
• Figure 2: X-ray magnetic circular and linear dichroism (XMCD and XMLD) of $\alpha$-Fe$_2$O$_3$ across Fe $L_{2,3}$-edges and corresponding calculations. a,b X-ray absorption spectra acquired with circular right/linearly horizontal (red line) and circular left/linearly vertical (blue line) polarizations were measured by integral TEY measurements (Sample #1) above $T_{\mathrm{M}}$. A magnetic field of approximately $100~\mathrm{mT}$ was applied within the $c$-plane. c,d Corresponding experimental XMCD and XMLD spectra. e,f Calculated XMCD and XMLD spectra. g,h STXM images of $\alpha$-Fe$_2$O$_3$ (Sample #2) were recorded at the Fe $L_2$-edge, 724.25 eV for circular polarizations and 724.5 eV for linear polarization (nominal values) indicated by red and blue arrows in c and d. XMCD and XMLD images at room temperature show altermagnetic domains and Néel vector, respectively. i,j Zoomed XMCD and XMLD images of the regions indicated by magenta boxes in g and h exhibit different contrast modulation, consistent with a 180$^\circ$ domain wall. Dependence of XMCD and XMLD contrasts on the in-plane $\textbf{L}$-orientation as indicated by the contrast wheels. At 50 K, all contrast vanished in the k XMCD and l XMLD images corresponding to g and h.
• Figure 2: XMLD image at 724.5 eV. The lines used for the line profiles in Fig. \ref{['fig_4']}d and e are indicated.
• Figure 3: Comparison between in-plane and out-of-plane $\bf{L}$-configurations. a Unpolarized experimental spectral data ($L_2$ edge) acquired from sum of linear polarization images (LH+LV) above and below $T_\mathrm{M}$ and b correspondingly calculated X-ray absorption spectra ($L_3$ and $L_2$ edges). c Overview image using a single polarization (LV) at 724.5 eV (indicated by red arrows in a) and corresponding magnified views of the region enclosed by the white box in c. The domain wall with in-plane $\bf{L}$-orientation is visible in d an absorption image obtained from the sum of linear horizontal and vertical polarization data. Here, the nonmagnetic absorption contrast was removed to emphasize the domain wall contrast (see Supplementary Figure 4 for details). e XMCD image recorded at 724.25 eV and f XMLD image at 724.5 eV of the same region show dichroic signals only for the area covered by the in-plane domain wall.