X-Ray Magnetic Circular Dichroism in Altermagnetic $\alpha$-MnTe

Altermagnetism is a recently identified magnetic symmetry class combining characteristics of conventional collinear ferromagnets and antiferromagnets, that were regarded as mutually exclusive, and enabling phenomena and functionalities unparalleled in either of the two traditional elementary magnetic classes. In this work we use symmetry, ab initio theory, and experiments to explore x-ray magnetic circular dichroism (XMCD) in the altermagnetic class. As a representative material for our XMCD study we choose $\alpha$-MnTe with compensated antiparallel magnetic order in which an anomalous Hall effect has been already demonstrated. We predict and experimentally confirm a characteristic XMCD line shape for compensated moments lying in a plane perpendicular to the light propagation vector. Our results highlight the distinct phenomenology in altermagnets of this time-reversal symmetry breaking response, and its potential utility for element-specific spectroscopy and microscopy.

Figure 1

Mn moments ${\mathbf{m}}_A$ and ${\mathbf{m}}_B$ in $\alpha$-MnTe structure (with Te octahedra) for the studied Néel vector $\mathbf{L}$ orientations. The mirror plane $\mathcal{M}$ discussed in the text is marked in blue. While in the right panel $\mathcal{M}$ is an element of the magnetic symmetry group, in the left panel it is $\mathcal{MT}$ which leaves the system invariant.

Figure 2

(a) Mn $L_{2,3}$-edge spectra in theory (black) and experiment (red dotted) for light propagating along the $c$ axis. Top: XAS. Middle: XMCD in zero field after cooling in 6 T. Bottom: measured XMCD in the applied field of 6 T (red dotted), calculated XMCD for $\mathbf{k}$ parallel to the magnetic moment scaled by $m_{6\mathrm{T}}/m_{\mathrm{sat}}\approx 1/50$ (black). (b) XMCD after cooling in the opposite fields.

Figure 3

The Mn site-resolved contributions to XMCD calculated by the $\mathrm{LDA}+\mathrm{DMFT}$ AIM for the Néel vector $\mathbf{L}\parallel [1\overline{1}00]$ and the light propagation vector $\mathbf{k}\perp \mathbf{L}$ (a) and $\mathbf{k}\parallel \mathbf{L}$ (b). (c) A cartoon view along the $c$ axis of the possible domain structure with the six easy-axis orientations of $\mathbf{L}$. The domains with even labels (red) contribute $\mathrm{\Delta }F(\omega )$ with positive prefactor, the odd ones (blue) with negative prefactor. The red and blue dots indicate the positive and negative orientation of the out-of-plane magnetization $\mathbf{m}$. (d) The out-of-plane canting of the moments in 6 T applied field does not strongly depend on the domain’s $\mathbf{L}$. (The domain sizes and shapes were chosen randomly and are not intended to have physical meaning).

Figure 4

The single-site XMCD for $\mathbf{k}\parallel \mathbf{L}$ (left) and $\mathbf{k}\perp \mathbf{L}$ (right) for models (i)–(iv) described in the text. The XMCD intensities are magnified by a factor indicated in panels.