Altermagnetic XMCD in Hematite Distinct from Weak Ferromagnetic Contributions

Abstract

Altermagnets are compensated collinear magnets that break time-reversal symmetry without net magnetization, enabling unconventional magneto-optical responses. Here, altermagnetic X-ray magnetic circular dichroism (XMCD) is experimentally demonstrated in hematite $α$-Fe$_2$O$_3$. By employing a symmetry-selective geometry in which the x-ray propagation vector is orthogonal to the Dzyaloshinskii-Moriya-induced weak ferromagnetic moment, we isolate a finite XMCD signal that cannot be attributed to conventional weak ferromagnetism. Moreover, we demonstrate that distinct altermagnetic states characterized by different magnetic symmetries can be reversibly switched through the application of an in-plane external magnetic field. Full-multiplet calculations reveal that the signal originates from an anisotropic magnetic dipole moment realized in the $2p^53d^6$ excited states, despite the isotropic $2p^63d^5$ ground state. Our results establish XMCD as a direct probe of excited-state magnetic multipoles and provide a general route for the optical detection of altermagnetic order in compensated magnets.

Figures (5)

• Figure 1: Crystal and magnetic structure of $\alpha$-Fe$_2$O$_3$ for (a) the Néel vector $\mathbf{N}\parallel[1\bar{1}0]$ and (b) $\mathbf{N}\parallel[11\bar{2}]$. The corresponding magnetic point groups are $2^{\prime}/m^{\prime}$ and $2/m$, respectively. The structures is visualized using VESTA Momma_2011. Schematic view along the $[111]$ direction of $\mathbf{N}$, $c$- and $c^{\prime}$-glide planes as well as the twofold rotation axes ($2$ and $2^{\prime}$) for (c) $\mathbf{N}\parallel[1\bar{1}0]$ and (d) $\mathbf{N}\parallel[11\bar{2}]$, respectively.
• Figure 2: (a) X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) spectra at the Fe $L_{2,3}$ edges for $\alpha$-Fe$_2$O$_3$(111). The upper panel shows the polarization-averaged XAS spectrum, $(I_{+} + I_{-})/2$, measured in total electron yield (TEY) mode. The lower panel displays the XMCD signal, defined as $I_{+} - I_{-}$, obtained at 0 T after applying external magnetic fields of $\pm 5$ T applied along the [$1\bar{1}0$] direction. The red and blue curves correspond to measurements after applying $+5$ T and $-5$ T, respectively. The XMCD intensity is magnified by a factor of 10 for clarity. (b) Calculated XAS and XMCD spectra. Red and blue lines correspond to XMCD of $\mathbf{N}~||~[01{\bar{1}}]$ and $\mathbf{N}~||~[0{\bar{1}}1]$. Green line presents XMCD spectrum calculation originating from $\mathbf{M}_{\rm wFM}$ along the [$\bar{2}11$] direction. The intensity is magnified by a factor of 150.
• Figure 3: (a) XMCD spectra measured around Fe $L_{2,3}$-edges under external magnetic field. $\theta$ denotes the tilt angle of the sample respect to the direction of magnetic field and incident X-rays. A dashed vertical line marks $E = 722.3$ eV. (b) Magnetic-field dependence of the XMCD intensity at $L_2$ edge ($E = 722.3$ eV) and $\theta = 30^{\circ}$. The inset illustrates experimental geometry. (c) Time evolution of the XMCD signal at 722.3 eV under a linearly varying magnetic field. (d) Schematic illustration of magnetic structure variation between $\mathbf{N}\parallel[01\bar{1}]$ and $\mathbf{N}\parallel[11\bar{2}]$ in the presence of an in-plane $H_{\parallel}||[1\bar{1}0]$ and out-of-plane $H_{\perp}||[111]$ magnetic field.
• Figure 4: Spin and orbital configurations at two lower Fe sites for (a) $\mathbf{N}\parallel[111]$, (b) $\mathbf{N}\parallel[1\bar{1}0]$, (c) $\mathbf{N}\parallel[11\bar{2}]$. Red, blue, and purple lobes represent orbitals of $\psi_{a,b}$, $e_g^{\pi}$, and $a_{1g}$ electronic states. Green, purple, and red arrows denote antiferromagnetic spin, AMD, and ferromagnetic spin moments (${\bf M}_{\rm wFM}$), respectively. Red and blue boards indicate $c^{\prime}$-glide and $c$-glide planes, respectively.
• Figure 5: Comparison of the weak ferromagnetic dipole, the anisotropic magnetic dipole, and the DM vector in (a) $\alpha$-Fe$_2$O$_3$ and (d) $\alpha$-MnTe. (b) In the cluster of site 1 and 2 in $\alpha$-Fe$_2$O$_3$, the DM vector $\mathbf{D}^{12}_C$ associated with the Fe-O-Fe bonds aligns align parallel to the 3-fold rotational axis and perpendicular to the 2-fold axis of crystal structure. (c) Under magnetoelastic distortion, the crystal symmetry is slightly lowered, leading to a small tilt of the DM vector $\mathbf{D}_M^{12}$ away from the ideal symmetry axis. (e) In MnTe-type systems, in addition to the 3- and 2-fold rotational axis, the mirror symmetry perpendicular to the 3-fold axis makes $\mathbf{D}_C=0$. (f) When magnetoelastic distortion lowers the symmetry, the constraint is lifted and a finite DM vector $\mathbf{D}_M$ emerges, oriented perpendicular to the original 3-fold and 2-fold rotational axes.