X-ray magnetic circular dichroism of altermagnet $\alpha$-Fe$_2$O$_3$ based on multiplet ligand-field theory using Wannier orbitals

Abstract

Hematite $\alpha$-Fe$_2$O$_3$ is a $g$-wave altermagnetic material, which has an easy-axis phase and easy-plane weak ferromagnetic phase below and above Morin transition temperature, respectively. The presence of these phases renders it a good candidate to study the characteristic spin splitting in altermagnets under the impacts of relativistic effect and finite temperature. In this regard, we have calculated the band structure of $\alpha$-Fe$_2$O$_3$ based on density functional theory (DFT) which also considers the Hubbard-U correction and spin-orbit coupling (SOC) effects. Additionally, the charge self-consistent DFT + dynamical mean-field theory (DMFT) calculations have been performed at finite temperatures. It is found that the altermagnetic spin splitting in $\alpha$-Fe$_2$O$_3$ preserves with either SOC or temperature effect taken into account. Furthermore, we present a numerical simulation of the x-ray magnetic circular dichroism (XMCD) of the L$_{2,3}$ edge of Fe using a combination of DFT with multiplet ligand-field theory (MLFT). In terms of the different N\'eel vectors present in $\alpha$-Fe$_2$O$_3$, we calculate the x-ray absorption spectroscopy (XAS) of the L$_{2,3}$ edge of Fe in the form of conductivity tensor and analyze the XMCD response from a perspective of symmetry. A characteristic XMCD line shape is expected when the N\'eel vector is along [010] direction (magnetic point group $2^\prime/m^\prime$) and the light propagation vector is perpendicular to the N\'eel vector, which can be further distinguished from the XMCD response originated from weak ferromagnetism with the light propagation vector parallel to the N\'eel vector.