X-ray magnetic and natural circular dichroism from first principles: Calculation of K - And L1 -edge spectra

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 σ·(ϵ×r) that we call the spin position operator. 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 calculations of K-edge XMCD spectra of ferromagnetic iron, cobalt, and nickel and of I L1-edge XNCD spectra of α-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 term to the spin magnetic moment of the p states. In α-LiIO3 we recover the expected angular dependence of the XNCD spectra.