On the Néel Vector Dependence of X-ray Magnetic Circular Dichroism in Altermagnets

TL;DR

This work develops a group-theoretical framework to relate the x-ray Hall vector $\mathbf{h}(\omega)$ to the Néel vector $\mathbf{L}$ in altermagnets under the free valence spin (FVS) approximation. The authors show that $\mathbf{h}(\omega)$ depends linearly on $\mathbf{L}$ through symmetry-determined spectral functions, yielding the general form $\mathbf{h}(\omega)=\tfrac{1}{2}\big(\boldsymbol{\Omega}(\omega)-\mathbf{g}\boldsymbol{\Omega}(\omega)\mathbf{g}^T\big)\hat{\mathbf{L}}$, where $\boldsymbol{\Omega}$ encodes site- and edge-specific invariants and $\mathbf{g}$ maps between magnetic sublattices. Applying this to rutile and NiAs structures shows that XMCD can be allowed or forbidden purely by symmetry in FVS, with rutile yielding a single spectral function linking $\mathbf{h}$ to $\mathbf{L}$ (and enabling in-plane domain imaging), while NiAs generally suppresses XMCD unless symmetry is lowered by core-valence exchange or valence SOC. Across representative altermagnets, including MnTe and CrSb, the framework clarifies when core-valence effects are essential to observe XMCD and provides a compact, symmetry-based route to interpret XMCD data as a probe of Néel-vector orientation and domain structure.

Abstract

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 Néel vector $\bL$ 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 $\bL$-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 MnF$_2$. Depending on the system symmetry, XMCD in the FVS approximation may be present, emerge only when the neglected terms are included, or be completely forbidden.