Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 2.9, p. 127

Section 2.9.3. Polarized neutron reflectivity

G. S. Smitha and C. F. Majkrzakb

aManuel Lujan Jr Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

2.9.3. Polarized neutron reflectivity

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Reflectivity measurements with polarized neutrons can reveal the in-plane magnetization-vector 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 in-plane magnetization parallel to this quantization axis gives rise to non-spin-flip (NSF) neutron scattering, which interferes with scattering due to the nuclear potential: any perpendicular magnetic component creates spin-flip (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 ρM = Np, where p is a magnetic scattering length). The matrix formalism described earlier to obtain the reflectivity in the non-polarized-beam 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 spin-dependent reflectivities and transmissions for each of two possible incident-neutron spin states. The matrix elements are given in Felcher, Hilleke, Crawford, Haumann, Kleb & Ostrowski (1987[link]), and more detailed discussions of the method of polarized neutron reflectometry can be found in Majkrzak (1991[link]) and Majkrzak, Ankner, Berk & Gibbs (1994[link]).


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.

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