Theory of magnetic neutron small-angle scattering using the dynamical theory of diffraction instead of the Born approximation. I. Determination of the scattering angle

Two ways are given for solving the problem of the dependence of the refraction on the direction of magnetization on both sides of the refractive boundary, one applying the Halpern magnetic scattering vector, the other applying the dynamical theory of diffraction. They lead to different results. Experimental investigation of refraction by magnetic boundaries shows no dependence of the angle of deflection on the relative angles of magnetization in adjacent domains. This behaviour is only described correctly by the dynamical theory, which far from Laue reflections leads to a treatment by the Schrödinger equation with a spin-dependent potential dependent on the average continuous homogenous magnetic induction, both for the law of refraction and for the precession of the spin. The results of this treatment are discussed as a consequence of the behaviour of the spin of the neutrons. This gives some insight about how and why, with refraction, the intensities of the direct and deflected beams depend on the magnetization directions in adjacent domains. The dynamical theory also shows that the Halpern magnetic scattering vector applies only with Laue or Bragg reflections and not with transmission far from those reflections.