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Figure 4
Squared standing waves [|E_{\sigma}^{\,2}(\theta,z)|^2] inside a [Ti(3 nm)/Gd(4 nm)]8 multilayer at different grazing angles (bottom part), the rotated reflectivity Iσπ, the asymmetry ratio A = (I+I)/(I+ + I) and the total reflectivity (top graphs). [E_{\sigma}(\theta,z)] is normalized to the amplitude of the incident wave E0 = 1. Calculations for Eph = 7930 eV and with the same parameters of Gd susceptibility as in Fig. 3[link]. Multilayer magnetization is supposed along the beam (L-MOKE geometry). The magnetic contributions to the reflectivity originate only from Gd layers (hatched); therefore the integration in (52)[link] and (53)[link] concerns only this hatched regions. Thin (red) lines show A(θ) and Iσπ(θ) calculated by the exact theory [program pack by Andreeva & Repchenko (2017BB6)], thick dashed (green) lines show the results of A(θ) and Iσπ(θ) calculations obtained by (51)[link], (53)[link] and (52)[link], respectively.

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