X-ray magnetic circular dichroism evidence of intrinsic $d$-wave altermagnetism in rutile-structure NiF$_2$

Abstract

We present the x-ray magnetic circular dichroism (XMCD) at the Ni $L_{2,3}$-edge as an evidence of the $d$-wave altermagnetism in rutile-structure NiF$_2$. Sizable XMCD signal is observed in excellent agreement with theoretical simulations. Owing to a considerable net magnetization due to spin canting, the XMCD spectrum consists of an altermagnetic signal as well as a non-negligible ferromagnetic contribution. We verify experimentally that the XMCD spectrum can be written as a sum of contributions from altermagnetism and weak ferromagnetism. Two experimental methods to isolate the ferromagnetic contribution are shown to yield essentially the same result. These are dependence of XMCD on applied magnetic fields below the N\'eel temperature and the XMCD measured in applied field above the N\'eel temperature. Our results demonstrate the utility of XMCD as a probe for altermagnetic materials with the coexisting weak ferromagnetism induced by the relativistic spin-orbit coupling.