International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 2.9, p. 127

Reflectivity measurements with polarized neutrons can reveal the inplane magnetizationvector depth profile in magnetic thin films and multilayers. The interaction between the neutron and atomic magnetic moments is dependent upon their relative orientations. Two important yet simple selection rules apply in the case where the neutron polarization axis (defined by an applied magnetic field at the sample position) is perpendicular to Q. Any component of the inplane magnetization parallel to this quantization axis gives rise to nonspinflip (NSF) neutron scattering, which interferes with scattering due to the nuclear potential: any perpendicular magnetic component creates spinflip (SF) scattering, which is purely magnetic. Consequently, the atomic magnetic moment's direction can be inferred by measuring the two NSF (++, −−) and two SF (+−, −+) reflectivities (where +− refers to a reflection measurement in which the incident neutron magnetic moment is parallel to the applied field and only neutrons with their magnetic moment antiparallel to the applied field are measured, etc.), in addition to its absolute magnitude (which is proportional to a magnetic scattering density ρ_{M} = Np, where p is a magnetic scattering length). The matrix formalism described earlier to obtain the reflectivity in the nonpolarizedbeam case can be extended to treat polarized beams as well. The resulting transfer matrix is, however, in the latter instance a 4 × 4 matrix relating two spindependent reflectivities and transmissions for each of two possible incidentneutron spin states. The matrix elements are given in Felcher, Hilleke, Crawford, Haumann, Kleb & Ostrowski (1987), and more detailed discussions of the method of polarized neutron reflectometry can be found in Majkrzak (1991) and Majkrzak, Ankner, Berk & Gibbs (1994).
References
Felcher, G. P., Hilleke, R. O., Crawford, R. K., Haumann, J., Kleb, R. & Ostrowski, G. (1987). Polarized neutron reflectometer: a new instrument to measure magnetic depth profiles. Rev. Sci. Instrum. 58, 609–619.Majkrzak, C. F. (1991). Polarized neutron reflectometry. Physica (Utrecht), B173, 75–88.
Majkrzak, C. F., Ankner, J. F., Berk, N. F. & Gibbs, D. (1994). Magnetic multilayers, edited by L. H. Bennett & R. E. Watson, pp. 299–354. Singapore: World Scientific.