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The calculation of the amplitude of X-rays scattered by a magnetically ordered substance, carried out in the relativistic quantum theory (i.e. taking the spin into account), is detailed. The effect of the orbital momentum is described in an appendix. The practical formulae dealing with the polarization of the beams are given both in a simple form for the usual experiments and in a complete form, using the Stokes vectors, for the most general case. The experiments show a change in the intensity of the X-rays diffracted by a ferromagnetic (pure iron) or a ferrimagnetic (zinc-substituted magnetite) powder when the magnetization, perpendicular to the diffraction plane, is reversed. The relative values of these intensity changes range from 10-4 to 5 x 10-3 and agree in sign and magnitude with the predictions. They are proportional to the spin-density structure factor multiplied by the imaginary part of the charge- density structure factor; the large anomalous scattering of the Cu radiation in the iron-containing samples is used in the present experiments.
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