Néel vector dependence of x-ray magnetic circular dichroism in altermagnets

Dependence of x-ray magnetic circular dichroism on the experimental geometry is described by a frequency-dependent Hall vector. Using group theory, we derive a general relationship between the Hall vector and the orientation of the N\'eel vector $\mathbf{L}$ in altermagnets within the free valence spin (FVS) approximation, where the spin-orbit coupling of the valence electrons and their exchange interaction with the core electrons are neglected. For a given spin point group, the full $\mathbf{L}$ dependence of the Hall vector can be expressed in terms of several irreducible spectral functions. This derivation generalizes earlier results for the special cases of MnTe and ${\mathrm{MnF}}_{2}$. Depending on the system symmetry, x-ray magnetic circular dichroism may be present within the FVS approximation, emerge only when the FVS-neglected terms are included, or be completely forbidden.