Our vector mapping includes the local real-space detection of the orientation of the altermagnetic order vector, L = M1 − M2, with respect to the MnTe crystal axes in the (0001)-plane by X-ray magnetic linear dichroism (XMLD)-PEEM, and of the sign of L for a given crystal orientation by including X-ray magnetic circular dichroism (XMCD)-PEEM. In antiferromagnets with opposite spin sublattices connected by translation or inversion, the \({\mathcal{T}}\)-odd XMCD is excluded by symmetry. In such cases, only the L axis can be detected by the \({\mathcal{T}}\)-even XMLD-PEEM, but the sign of L remains unresolved25,26,27,28,29,30. Contrary to this, the recent theoretical and experimental spectroscopic study of altermagnetic MnTe has demonstrated the presence of a sizable XMCD, reflecting the \({\mathcal{T}}\)-symmetry breaking in the electronic structure by the altermagnetic g-wave spin polarization12. Furthermore, the XMCD spectral shape owing to L pointing in the (0001) plane is qualitatively distinct from the XMCD spectral shape owing to a net magnetization M = M1 + M2 along the [0001] axis12. This was demonstrated in ref. 12 by comparing the measured XMCD spectral shapes at a zero magnetic field and at a 6-T field applied along the [0001] axis. In the former case, M is weak and the measured spectral shape agrees with the predicted spectral shape due to L. In the latter case, M is sizable and qualitatively modifies the spectral shape, again in agreement with theory. We performed normal incidence X-ray PEEM, which is the optimum geometry for measuring both the in-plane Néel axis in the XMLD, and the altermagnetic XMCD. Images are taken at zero external field, where the XMCD signal owing to the weak relativistic remnant M is negligible compared with the altermagnetic XMCD owing to \({\bf{L}}\parallel \langle 1\bar{1}00\rangle \) directions in the (0001) plane12. The latter gives rise to our measured XMCD-PEEM contrast as confirmed by its spectral dependence (Methods and Extended Data Fig. 1). In analogy to the d.c. anomalous Hall effect, the XMCD can be described by the Hall vector, \({\bf{h}}=({\sigma }_{zy}^{a},{\sigma }_{xz}^{a},{\sigma }_{yx}^{a})\), where σij = −σji are the antisymmetric components of the frequency-dependent conductivity tensor. For L in the (0001) plane of MnTe, h points along the [0001] axis, that is, \({\sigma }_{zy}^{a}={\sigma }_{xz}^{a}=0\) and \({\sigma }_{yx}^{a}\ne 0\), with the exception of \({\bf{L}}\parallel \langle 2\bar{1}\bar{1}0\rangle \) axes where \({\sigma }_{yx}^{a}=0\) by symmetry.
The method of combining the XMCD-PEEM and XMLD-PEEM images into the vector map of L is illustrated in Fig. 1b. As the L vector subtends the angle, ϕ, in the MnTe (0001) plane relative to the \([1\bar{1}00]\) axis, the XMCD is proportional to cos(3ϕ), with maximum magnitude for \({\bf{L}}\parallel \langle 1\bar{1}00\rangle \) -axes and vanishing for \({\bf{L}}\parallel \langle 2\bar{1}\bar{1}0\rangle \) axes12. An XMCD-PEEM image of a 25–μm2 unpatterned area of MnTe is shown in Fig. 1c, where positive and negative XMCD appear as light and dark contrast, respectively. The corresponding three-colour XMLD-PEEM map, shown in Fig. 1d, was obtained from a set of PEEM images taken with the X-ray linear polarization rotated, within the MnTe (0001) plane, in 10° steps from −90° to +90° relative to the horizontal [\(1\bar{1}00\)] axis. In this image, the local L-vector axis is distinguished (by red–green–blue colours), but the absolute direction remains unresolved. This information is included by combining the XMCD-PEEM and XMLD-PEEM in a six-colour vector map, shown in Fig. 1e,f, where positive XMCD regions change the colour (red–green–blue to orange–yellow–purple) of the XMLD-PEEM map and negative XMCD regions leave it unchanged. The Mn L2,3 X-ray absorption and altermagnetic XMCD spectra are shown in Fig. 1g. The XMCD-PEEM images are obtained at fixed energy corresponding to the peak in the altermagnetic XMCD at the L2 edge. The XMCD contrast reverses between positive and negative peaks of the XMCD spectrum, as shown in Extended Data Fig. 1, and vanishes at elevated temperatures where the spontaneous anomalous Hall effect is absent, as shown in Extended Data Fig. 2.
The characteristic vector mapping of L in our unpatterned MnTe film, shown in Fig. 1e,f, shows a rich landscape of (meta)stable textures akin to earlier reports in compensated magnets26,27,28,29,30. There exist 60° and 120° domain walls separating domains with L aligned along the different easy axes, as well as vortex-like textures. Highlighted in Fig. 1f is an example of an altermagnetic vortex–antivortex pair, analogous to magnetic textures previously detected in antiferromagnets such as CuMnAs (ref. 30). However, only the XMLD-PEEM was available in the antiferromagnet30, that is, only the spatially varying Néel-vector axis could be identified, similar to our XMLD-PEEM image in Fig. 1d. In our altermagnetic case, we can add the information from the measured XMCD-PEEM (Fig. 1c). This allows us to plot the vector map of L, as shown in Fig. 1e,f. We directly experimentally determine that the L vector makes a clockwise rotation by 360° around the first vortex nanotexture, indicated by the magenta–white circle, whereas the other nanotexture is an antivortex with an opposite winding of the L vector, indicated by the cyan–white circle.
