Standing wave approach in the theory of X-ray magnetic reflectivity

Abstract

Edited by M. Yabashi, Japan An extension of the exact X-ray resonant magnetic reflectivity theory has been developed, taking into account the small value of the magnetic terms in the X-ray susceptibility tensor. It is shown that squared standing waves (fourth power of the total electric field) determine the output of the magnetic addition to the total reflectivity from a magnetic multilayer. The obtained generalized kinematical approach essentially speeds up the calculation of the asymmetry ratio in the magnetic reflectivity. The developed approach easily explains the peculiarities of the angular dependence of the reflectivity with the rotated polarization (such as the peak at the critical angle of the total external reflection). The revealed dependence of the magnetic part of the total reflectivity on the squared standing waves means that the selection of the reflectivity with the rotated polarization ensures higher sensitivity to the depth profiles of magnetization than the secondary radiation at the specular reflection condition.

Evolution of the magnetic hyperfine field profiles in an ion-irradiated Fe60Al40 film measured by nuclear resonant reflectivity

“…The nuclear resonant scattering in the studied Fe 60 Al 40 film is essentially smaller than the electronic scattering because the sample is not enriched by 57 Fe. In such a case the NRR amplitude can be described by the generalized kinematic approximation (Andreeva et al, 2019). Assuming polarization of the synchrotron beam, the frequency-dependent part of the (Left) NRR time spectra measured at several grazing angles in the vicinity of the critical one for selected positions on the Fe 60 Al 40 gradient sample (symbols are the experimental counts and lines are the fit).…”

Reflectivity spectra as absorption resonant spectra: is it correct?

“…Mitsui et al, 2012aMitsui et al, ,b, 2020Ro ¨hlsberger et al, 2012;Haber et al, 2017;Cini et al, 2018Cini et al, , 2020Okabayashi et al, 2021a). It has been shown that the reflectivity amplitude from an ultrathin resonant layer placed under a reflecting medium R tot ð!Þ can be described by the formula (Andreeva & Lindgren, 2002;Andreeva et al, 2019)…”

Interface resolved magnetism at metal–organic (Fe/Alq3) interfaces under x-ray standing wave condition

“…It may be noted that, as compared to the square dependence influence on secondary radiation such as x-ray fluorescence, the intensity of the nuclear resonance part from the thin layer is proportional to the fourth power of the standing wave amplitude and hence has more sensitivity compared to the XSW based conventional techniques. 32 Figure 2(d) shows the GI-NRS delay spectrum calculated using REFTIM 33 software at q 1 ¼ 0.054 Å À1 and q 2 ¼ 0.060 Å À1 by assuming (i) different magnitudes of the hyperfine field of 57 Fe bulk $ 33 T and 57 Fe diffused $ 20 T and (ii) the same hyperfine field (33 T) in both layers but with different spin orientations as shown in Figs. 2(d-i) and 2(d-ii), respectively.…”