X-ray magnetic circular dichroism in altermagnets: insights from symmetry

Abstract

Altermagnets are a unique subset of antiferromagnets possessing ferromagnet-like responses that are odd in the Néel vector, making X-ray magnetic circular dichroism (XMCD) a natural probe of ground state altermagnetic order. Because the relativistic ingredient of XMCD at the $L$-edge is supplied predominantly by core-level spin--orbit coupling (SOC), the dichroic signal can reflect the non-relativistic order of the valence electrons. Here we develop a complete symmetry framework for XMCD in altermagnets (AMs) preserving the crystalline unit cell. We tabulate the symmetry-allowed optical Hall vector, anisotropic magnetic dipole (AMD), and underlying octupolar components for all magnetic point groups, thereby identifying the experimental geometries that maximize the XMCD signal. We show that only twelve magnetic point groups, none with a rotation axis of order three or higher, are compatible with both altermagnetism and finite XMCD. By extending the Landau theory of collinear AMs, we connect these relativistic constraints to the spin--orbit-free order. We show that the AMD is forced to vanish at zero valence SOC in conventional antiferromagnets, and that every AM sublattice structure allows the Hall vector and AMD at linear or cubic order in the Néel vector; whether the resulting XMCD is nonzero depends on the Néel vector orientation at finite SOC. The Landau theory thus fixes the Néel-vector dependence of the XMCD for all AM candidates, and separates $d$-wave AMs, whose signal is inherited from a non-relativistic AMD, from $g$- and $i$-wave AMs, whose signal requires valence SOC or core--valence multiplet effects. We illustrate these predictions with first-principles Bethe--Salpeter calculations of $L$-edge XMCD for five representative altermagnetic materials and one conventional antiferromagnet.