Magnetic scattering

Coppens, P.

doi:10.1107/97809553602060000550

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

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International Tables for Crystallography (2006). Vol. B. ch. 1.2, p. 11 | 1 | 2 |

Section 1.2.5.2. Magnetic scattering

P. Coppens^a ^*

^aDepartment of Chemistry, Natural Sciences & Mathematics Complex, State University of New York at Buffalo, Buffalo, New York 14260-3000, USA
Correspondence e-mail: coppens@acsu.buffalo.edu

1.2.5.2. Magnetic scattering

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The interaction between the magnetic moments of the neutron and the unpaired electrons in solids leads to magnetic scattering. The total elastic scattering including both the nuclear and magnetic contributions is given by $[|F({\bf H}){|^{2}_{\rm total}} = |F_{N} ({\bf H}) + {\bf Q}({\bf H})\cdot {\hat\boldlambda}|^{2}, \eqno(1.2.5.1a)]$ where the unit vector $[\hat{{\boldlambda}}]$ describes the polarization vector for the neutron spin, $[F_{N}({\bf H})]$ is given by (1.2.4.2b) and Q is defined by $[{\bf Q} = {mc \over eh} {\int} {\bf \widehat{H}} \times [{\bf M}({\bf r}) \times {\bf \widehat{H}}] \exp (2\pi i{\bf H}\cdot {\bf r})\ \hbox{d}{\bf r}. \eqno(1.2.5.2a)]$ $[{\bf M}({\bf r})]$ is the vector field describing the electron-magnetization distribution and $[\widehat{{\bf H}}]$ is a unit vector parallel to H.

Q is thus proportional to the projection of M onto a direction orthogonal to H in the plane containing M and H. The magnitude of this projection depends on $[\sin \alpha]$ , where α is the angle between Q and H, which prevents magnetic scattering from being a truly three-dimensional probe. If all moments $[{\bf M}({\bf r})]$ are collinear, as may be achieved in paramagnetic materials by applying an external field, and for the maximum signal (H orthogonal to M), (1.2.5.2a) becomes $[{\bf Q} = {\bf M}({\bf H}) = {mc \over eh} {\int} {\bf M}({\bf r}) \exp (2\pi i{\bf H}\cdot {\bf r})\ \hbox{d}{\bf r} \eqno(1.2.5.2b)]$ and (1.2.5.1a) gives $[{|F|^{2}}_{\!\!\!\rm total} = |F_{N}({\bf H}) - M({\bf H})|^{2} \eqno(1.2.5.1b)]$ and $[|F{|^{2}_{\rm total}} = |F_{N} ({\bf H}) + M({\bf H})|^{2}]$ for neutrons parallel and antiparallel to $[{\bf M} ({\bf H})]$ , respectively.

References

International Tables for Crystallography (2006). Vol. B. ch. 1.2, p. 11