Bayesian spectroscopy of synthesized soft X-ray absorption spectra showing magnetic circular dichroism at the Ni-L3, -L2 edges

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We proposed a data-driven science study by Bayesian spectroscopy to analyze an X-ray magnetic circular dichroism (XMCD) spectrum and magnetic moments. In Bayesian spectroscopy, model selection becomes available to estimate the number of spectral components by using Bayes free energy. To demonstrate such advantage, we decomposed synthesized X-ray absorption (XA) and XMCD spectra at the L3,2-absorption edge of the Ni ion in NiFe 2O 4. In the synthesized ∓helicity XA spectra, random noise was superimposed and a finite spectral width was convolved to mimic measured spectra. From these XA spectra, spectral components having intensity beyond the noise level were successfully extracted without excess or deficiency although transition components in close proximity within the spectral width were merged. From the XMCD spectrum, we also succeeded in extracting separately the original ∓helicity components although an additional −helicity component comparing with the case of XA spectra was extracted in the model selection. This additional component was extracted to explain an asymmetric XMCD spectral structure at the L3 edge, and this result demonstrates that Bayesian spectroscopy can fully exploit the advantage of XMCD measurements being superior for detecting close transition components of opposite helicities. In addition, we proposed to use posterior probability distributions obtained by Bayesian spectroscopy for estimating magnetic moments through samplings of the spectral intensities for the separately decomposed ∓helicity components on the L3,2-absorption edge.