Magnetic circular dichroism in core-level x-ray photoelectron spectroscopy of altermagnetic RuO$_2$ films

While ferromagnetism and antiferromagnetism are well-established classes of magnetic order, a third class of collinear magnetic order, termed altermagnetism, has recently attracted scientific interest. We measured magnetic circular dichroism (MCD) in core-level photoemission (XPS) at the Ru 2⁢𝑝$_{3/2}$ and 2⁢𝑝$_{1/2}$ core levels in epitaxial RuO$_2$⁢(110)/TiO$_2$⁢(110)films using circularly polarized x rays at 6 keV, as well as x-ray magnetic circular dichroism (XMCD) in resonant x-ray absorption at the Ru M$_{3/2}$(3⁢𝑝$_{3/2}$ and 3⁢𝑝 $_{1/2}$) edges. Charge transfer multiplet calculations show that the MCD-XPS and the XMCD can be explained by an altermagnetic locking of Ru magnetic moments and a distorted crystal field orientation. The distortion is caused by the epitaxial strain. The collinear magnetic moments in RuO$_2$occupy sublattice sites with distorted octahedral crystal fields that are rotated by 90∘with respect to each other. A change in the sign of the MCD-XPS at different sample positions indicates the presence of altermagnetic domains with the size of around hundreds of micrometers.