Bayes-Turchin analysis of x-ray absorption data above the FeL2,3-edges

Abstract

Extended x-ray absorption fine structure ͑EXAFS͒ data and magnetic EXAFS ͑MEXAFS͒ data were measured at two temperatures ͑180 and 296 K͒ in the energy region of the overlapping L-edges of bcc Fe grown on a V͑110͒ crystal surface. In combination with a Bayes-Turchin data analysis procedure these measurements enable the exploration of local crystallographic and magnetic structures. The analysis determined the atomiclike background together with the EXAFS parameters which consisted of ten shell radii, the Debye-Waller parameters, separated into structural and vibrational components, and the third cumulant of the first scattering path. The vibrational components for 97 different scattering paths were determined by a two parameter forcefield model using a priori values adjusted to Born-von Karman parameters of inelastic neutron scattering data. The investigations of the system Fe/ V͑110͒ demonstrate that the simultaneous fitting of atomic background parameters and EXAFS parameters can be performed reliably. Using the L 2 -and L 3 -components extracted from the EXAFS analysis and the rigid-band model, the MEXAFS oscillations can only be described when the sign of the exchange energy is changed compared to the predictions of the Hedin Lundquist exchange and correlation functional.

Correlation of magnetism and structure for ultra thin Au/Co/Au films: Evidence for magnetoelastic effects

“…From the results of further EXAFS analysis of a few more cases which will be described in a forthcoming article [13], we find that there exists a rather small range of the values of the magnetoelastic constants which reproduce the magnetization easy axis in figure 1 assuming K ME to be linear in the strains. That is, we obtain that B 1 +2B 3 must be negative with a value of about -1 to -4x10 7 Jm -3 , and B 2 must be positive, in the range of 0 to 5x10 7 Jm -3 in order to reproduce the observed magnetic anisotropy. To illustrate this result, we simulate K eff , assuming B 1 +2B 3 =-3.0x10 7 Jm -3 and B 2 =1.3 x10 7 Jm -3 .…”

“…That is, we obtain that B 1 +2B 3 must be negative with a value of about -1 to -4x10 7 Jm -3 , and B 2 must be positive, in the range of 0 to 5x10 7 Jm -3 in order to reproduce the observed magnetic anisotropy. To illustrate this result, we simulate K eff , assuming B 1 +2B 3 =-3.0x10 7 Jm -3 and B 2 =1.3 x10 7 Jm -3 . This is shown in figure 4, as a function of the Co thickness, t. Several lines are shown in figure 4, assuming constant strains for the case of uncapped, capped with 0.5 ML Au, capped with >1ML Au.…”

“…The total number of parameters in the fitting procedure is 24 for Co/Cu(111) and 32 for the Co/Au thin films. These are the background spline-parameters μ 0 (n=1,…, 15), the shell radii R i (n=16,…, 23), the structural disorder Note that the values of parameters which stay at the a priori values after the fit do not imply that those values are determined by the experiment; instead, this means that nothing new is learned from the experiment concerning those parameters and the a posteriori error in this case is mostly determined by the width of the a priori probability distribution [6,7]. In the present case the nearest two shell radii R 1 and R 2 are well determined by the data.…”

“…It also provides a precise way of treating the atomic background μ 0 (k) together with a careful treatment of the errors which come both from the experiment and the model. Readers are referred to references [6,7] for a complete description of the method. In this report we present a selection of results obtained for an uncapped 5Å Co film and the 5 Å Co film capped with a 3.5 Å Au overlayer, where the magnetic easy axis is in-plane and out-ofplane, respectively, see figure 1.…”

“…In the EXAFS analysis of overlapping L-edges we apply the Bayes-Turchin approach [6,7]. This method is based on a Bayesian approach originally proposed by Turchin and Nozik [12].…”