We propose that X-ray absorption and emission magnetic circular dichroism (XAS-MCD and XES-MCD) are promising measurements to directly detect ferroic higher-rank multipoles as candidate order parameters in altermagnets. Using the sum rules for XES-MCD and connecting them to multipole language, we demonstrate that the expectation value of the magnetic octupole moment is finite in the d-wave altermagnetic candidate rutile-type compounds TF2 (T=transition metal). We also perform spectral calculations of XAS-MCD and XES-MCD based on an effective model with a full multiplet approach. While the intensity of the XAS-MCD spectra vanishes, the XES-MCD spectra exhibit finite intensity, whose spectrum becomes opposite by inverting the N\`eel vector. These results clearly indicate ferroic magnetic octupole order in these compounds.
@article{arxiv.2509.14716,
title = {Detection of ferroic octupole ordering in $d$-wave altermagnetic rutile-type compounds},
author = {Masaichiro Mizumaki and Norimasa Sasabe and Takayuki Uozumi and Rikuto Oiwa and Hiroaki Kusunose},
journal= {arXiv preprint arXiv:2509.14716},
year = {2025}
}