X-ray Faraday effect at the L_2,3 edges of Fe, Co, and Ni: Theory and experiment

The x-ray Faraday effect at the L_2,3 edges of the 3d ferromagnets Fe, Co, Ni and of Fe_0.5Ni_0.5 alloy is studied both theoretically and experimentally. We perform ab initio calculations of the x-ray Faraday effect on the basis of the local spin-density approximation and we adopt the linear-response formalism to describe the material’s response to the incident light. Experimental x-ray Faraday rotation and ellipticity spectra are measured with linearly polarized soft-x-ray synchrotron radiation at BESSY, Berlin. The measured x-ray Faraday rotations are remarkably large, up to 2.8×10⁵ deg/mm, which is more than one order of magnitude larger than those observed in the visible range. From the measured Faraday spectra we determine the intrinsic dichroic contributions to the dispersive and absorptive parts of the refractive index, and compare these to ab initio calculated counterparts. The theoretical dichroic spectra are in good qualitative agreement with the experimental data. The inclusion of the spin polarization of the core states leads to a small, yet non-negligible, improvement of the theoretical dichroic spectra. Our results illustrate that the many-particle x-ray excitation spectrum can be sufficiently well approximated by the Kohn-Sham single-particle spectrum. From the computed magneto-x-ray spectra we determine, using the sum rules, the orbital moments, which we compare to the exact orbital moments.