Detection of ferroic octupole ordering in $d$-wave altermagnetic rutile-type compounds

Abstract

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 TF${}_2$ (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 Nèel vector. These results clearly indicate ferroic magnetic octupole order in these compounds.

References in corpus (21)

• Crystal Hall effect in Collinear Antiferromagnets
• Giant momentum-dependent spin splitting in centrosymmetric low Z antiferromagnets
• Spin current generation in organic antiferromagnets
• Antiferromagnetism in RuO${}_2$ as $d$-wave Pomeranchuk instability
• Observation of Giant Band Splitting in Altermagnetic MnTe
• Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors
• X-ray Magnetic Circular Dichroism in Altermagnetic $\alpha$-MnTe
• Magnetic octupoles as the order parameter for unconventional antiferromagnetism
• Multipole classification in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena
• Complete Multipole Basis Set for Single-Centered Electron Systems
• Unified description of electronic orderings and cross correlations by complete multipole representation
• Essential role of anisotropic magnetic dipole in anomalous Hall effect
• Evidence for Octupole Order in Ce${}_{0.7}$La${}_{0.3}$B${}_6$ from Resonant X-ray Scattering
• Weakly spin-dependent band structures of antiferromagnetic perovskite LaMO${}_3$ (M = Cr, Mn, Fe)
• Magnetic-Field-Induced 4f-Octupole in CeB6 Probed by Resonant X-ray Diffraction
• Augmented Magnetic Octupole in Kagome Antiferromagnets Detectable via X-ray Magnetic Circular Dichroism
• Presence of x-ray magnetic circular dichroism effect for zero-magnetization state in antiferromagnetism
• Observation of spontaneous x-ray magnetic circular dichroism in a chiral antiferromagnet
• Circular Dichroism in Resonant Inelastic X-ray Scattering: Probing Altermagnetic Domains in MnTe
• Sum rules for x-ray circular and linear dichroism based on complete magnetic multipole basis
• X-ray magnetic circular dichroism originating from the $T_z$ term in collinear altermagnets under trigonal crystal field