Bayesian spectroscopy with designed prior probabilities for high-precision estimation of magnetic moments in X-ray magnetic circular dichroism spectra

X-ray magnetic circular dichroism (MCD) spectra are the difference spectra of X-ray absorption (XA) measured in magnetic materials with left and right circular polarizations ([Formula: see text]helicity) under a magnetic field. We propose a Bayesian spectroscopy (BS) method to estimate magnetic moments with high accuracy utilizing the [Formula: see text]helicity XA and the MCD spectra. The method employs designed prior probabilities as follows: (a) First, the [Formula: see text]helicity XA spectra are analyzed using BS to obtain the multivariate posterior probability density distribution; (b) From the sampling history, the highest multivariate posterior density intervals (HMPDI) are obtained for the respective parameters, where the multivariate posterior density exceeds an appropriate threshold; (c) For the BS of MCD, we design the prior probabilities as uniform distributions based on the HMPDIs. This method can reproduce [Formula: see text]helicity XA and MCD spectra simultaneously with high accuracy, even in MCD spectra with a low signal-to-noise ratio. Furthermore, the posterior probability distributions of the magnetic moments become narrower, and the estimation accuracy is remarkably improved, demonstrating the high noise tolerance of this analytical method.