Theory of circular dichroism in resonant inelastic x-ray scattering

We analyze circular dichroism (CD) in resonant inelastic x-ray scattering (RIXS) in magnetic materials. We define RIXS-CD as the difference between scattering amplitudes for the right- and left-circularly polarized incoming photons and unpolarized (total) outgoing photons. We employ the impurity approximation, in which the interference between scattering events on different atoms is neglected. We perform a symmetry analysis of several common antiferromagnetic and altermagnetic structures and outline a general approach. This analysis is supported by numerical calculations using an atomic model with realistic crystal fields obtained from first principles. We show that RIXS-CD is distinguished from first-order spectroscopies such as x-ray magnetic circular dichroism by its insensitivity to the time-reversal symmetry breaking. As a result we find that RIXS-CD is present in the paramagnetic state of materials with lower symmetry. In antiferromagnets the RIXS-CD is invariant under N\'eel vector reversal. In altermagnets and ferromagnets the RIXS-CD spectra for time-reversed states are, in general, independent, except for the special case when there is a unitary symmetry of the Hamiltonian connecting the two states.