Magnetization curves of an Fe/Gd multilayer film calculated from Gd magnetization depth profiles determined by resonant x-ray magnetic scattering

Magnetization-versus-applied-field curves M(H) are calculated for an [Fe(3.48 nm)/Gd(5.43 nm)](15) multilayer film using the Gd magnetization depth profiles derived from the resonant x-ray magnetic scattering data collected with an applied field of 2.4 kOe. Stable magnetic structures for other field strengths are calculated by minimizing the sum of the Fe-Fe, Gd-Gd and Gd-Fe exchange energies and the Zeeman energy in a temperature range of 140-240 K. The calculated curves fit very well the slowly rising M(H) curves observed at temperatures between 140 and 200 K, where the Gd layers are ferromagnetic, over a wide field range up to 50 kOe on adjusting a molecular-field constant for the Fe-Gd interfaces, the only one free parameter used. The concave magnetization depth profiles in the Gd layers are essential to reproduce the observed M(H) curves. The discrepancies between the observed and calculated curves in, low-field regions represent the limitation of the single-magnetic-domain model used in the calculation.