Fig. 2: Integrated XAS and XMCD for both Co and Gd elements applied in the sum rules.

In a, d are shown the X-ray magnetic circular dichroism (XMCD) for both Co and Gd, and the calculated p and q parameters. The parameter q is not represented in (d) due to its small value. X-ray absorption spectra (XAS) acquired for right (μ⁺) and left (μ⁻) circularly polarized X-ray are summed (μ⁺ + μ⁻) for Co and Gd and displayed in b, e, correspondingly. The integrals taken over the spectra are used to estimate the amount r. The discussion on the extracted parameters is detailed in the Supplementary Note 1. Quantities p, q, and r are used to extract orbital and spin magnetic moments in the sum rules equation and hence the averaged (orbital + spin) moments. The averaged moments are strictly constant as a function of the magnetic field, as shown in (c). For the Gd, in module, the averaged moments are constant from 1 to 5 T, and then reduces drastically for fields between 8 and 9 T as observed in (f). The error bars were estimated by the values of the parameters p, q and r extracted along with the XMCD and XAS.