Spectral Indicators of Piezomagnetically Induced Symmetry Breaking in Altermagnets

Abstract: Recent developments in the multipole reformulation of X-ray absorption spectroscopy (XAS) have provided a unified framework to describe magnetic and orbital responses in terms of ferroic multipole order parameters. X-ray magnetic circular dichroism (XMCD) is known to probe spin, orbital, and anisotropic magnetic dipole (AMD) moments. Its applications to altermagnets and noncollinear antiferromagnets have revealed that the XMCD response is often governed by the ferroic states of the AMD in the photo-excited states rather than by conventional magnetic dipoles in the ground states. In this work, we extend the multipole-based analysis to X-ray magnetic linear dichroism (XMLD) and demonstrate that XMLD in altermagnets can be understood as a manifestation of piezomagnetic effects: linear couplings between magnetic dipole and electric quadrupole moments. Using symmetry analysis combined with exact diagonalization calculations of $L_{2,3}$-edge XAS, we systematically investigate representative altermagnets, including $α$-MnTe, MnF$_2$, and CrSb. We show that the ferroic ordering of higher-rank magnetic multipoles, particularly spinful magnetic octupoles, gives rise to characteristic field-odd XMLD signals that directly reflect the underlying piezomagnetic response tensors allowed by magnetic point-group symmetry. Furthermore, we discuss XMCD signals induced by piezomagnetic effects, in which strain generates magnetic dipole moments. Our results establish XMLD and XMCD as element-specific probes of magnetoelastic multipole order in altermagnets and provide a general symmetry-based pathway to identify hidden ferroic multipoles and strain-controllable spin phenomena beyond conventional ferromagnetism.