# X-ray Magnetic and Natural Circular Dichroism from first principles: Calculation of K- and L1-edge spectra

## TL;DR

This paper presents a first-principles computational method for calculating X-ray magnetic and natural circular dichroism spectra at K- and L1-edges in solids, incorporating relativistic effects and a new spin-position coupling term.

## Contribution

The authors develop an efficient relativistic first-principles approach that includes a novel spin-position operator for accurate XMCD and XNCD spectra calculations, applied to magnetic metals and a non-centrosymmetric compound.

## Key findings

- Electric quadrupole contributions are significant in XMCD spectra.
- The spin-position coupling term accounts for 28% of the XMCD amplitude in iron.
- The method accurately reproduces angular dependence of XNCD spectra.

## Abstract

An efficient first principles approach to calculate X-ray magnetic circular dichroism (XMCD) and X-ray natural circular dichroism (XNCD) is developed and applied in the near edge region at the K-and L1-edges in solids. Computation of circular dichroism requires precise calculations of X-ray absorption spectra (XAS) for circularly polarized light. For the derivation of the XAS cross section, we used a relativistic description of the photon-electron interaction that results in an additional term in the cross-section that couples the electric dipole operator with an operator $\mathbf{\sigma}\cdot (\mathbf{\epsilon} \times \mathbf{r})$ that we name spin-position. The numerical method relies on pseudopotentials, on the gauge including projected augmented wave method and on a collinear spin relativistic description of the electronic structure. We apply the method to the calculations of K-edge XMCD spectra of ferromagnetic iron, cobalt and nickel and of I L1-edge XNCD spectra of $\alpha$-LiIO3, a compound with broken inversion symmetry. For XMCD spectra we find that, even if the electric dipole term is the dominant one, the electric quadrupole term is not negligible (8% in amplitude in the case of iron). The term coupling the electric dipole operator with the spin-position operator is significant (28% in amplitude in the case of iron). We obtain a sum-rule relating this new term to the spin magnetic moment of the p-states. In $\alpha$-LiIO3 we recover the expected angular dependence of the XNCD spectra.