Neutron Scattering

1) If no magnetic induction B (which is determined by the external field H and the
magnetization of the sample) is present one yields R++ = R__ and R +_ = R_+ = 0 . Thus, there is
no dependence of the scattering on the spin orientation of the incoming neutrons .
2) If B = B- (magnetic induction perpendicular to the surface) no magnetic scattering is
expected either. The reason are the Maxwell equations which do not allow a change of the
mean value of B in field direction (V - B = 0) . This means that B does not change at the
sample surfaces . Therefore, R++ = R__ and R+ _ = R_+ = 0 .
3) If B = Bil only non-spin-flip processes appear (s = s') . The reason is the vanishing cross
product between s and B . This means that no interaction between the spins and the
induction is present so that the spins cannot flip. However, a magnetic contribution to the
refraction index has to be added for R++ and subtracted for R__ . Thus, R++ # R__ but still R +- _
R-+ = 0 .
4) IfB = B the spins can flip during the scattering process . Therefore, non-spin-flip processes
appear with R+ _ # 0 and R_ + # 0 . In contrast to point 3) the non-spin-flip reflectivities are
identical (R ++ = R--) .
In summary, from all reflectivities R ++ , R__ , R+_ and R_+ the exact magnitude and orientation of
the magnetization profile of the sample can be determined with polarized neutron reflectivity .
References
[1] J . Als-Nielsen, Topics in Current Physics. Structure and Dynamics of Surfaces
(Springer, Berlin, 1986) .
[2] P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough
Surfaces (Pergamon, New York, 1963) .
[3] L . Névot, P . Croce, Revue de Physique appliqué 15, 761 (1980) .
[4] S.K . Sinha, E.B . Sirota, S. Garoff. H.B . Stanley, Phys . Rev . B 38, 2297 (1988) .
[5] A.L. Barabâsi, H .E . Stanley, Fractal Concepts in Surface Growth (Cambridge
University Press, Cambridge, 1995) .
[6] V . Holt', J. Kubena,1. Ohlidal, K . Lischka,W. Plotz, Phys . Rev. B 47, 15 896 (1993) .
[7] J . Lekner, Theory of Reflection (Martinus Nijhoff, Dordrecht, Boston, 1987) .
[8] S . Dietrich, A . Haase, Phys . Rep . 260, 1 (1995) .
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