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Figure 1
Sketch of the two most often employed scattering geometries in magnetic SANS experiments. (a) [{\bf k}_{0}\perp{\bf H}_{0}]; (b) [{\bf k}_{0}\parallel{\bf H}_{0}]. We emphasize that in both geometries the applied-field direction [{\bf H}_{0}] defines the [{\bf e}_{z}] direction of a Cartesian laboratory coordinate system. The momentum transfer or scattering vector [{\bf q}] corresponds to the difference between the wavevectors of the incident ([{\bf k}_{0}]) and the scattered ([{\bf k}_{1}]) neutrons, i.e. [{\bf q} = {\bf k}_{0}-{\bf k}_{1}]. Its magnitude for elastic scattering, [q = |{\bf q}| = (4\pi/\lambda)\sin(\psi)], depends on the mean wavelength λ of the neutrons and on the scattering angle [2\psi]. SANS is usually implemented as elastic scattering ([k_{0} = k_{1} = 2\pi/\lambda]), and the component of [{\bf q}] along the incident neutron beam [i.e. qx in (a) and qz in (b)] is neglected. The angle θ specifies the orientation of the scattering vector on the two-dimensional detector; θ is measured between [{\bf H}_{0}\parallel{\bf e}_{z}] and [{\bf q}\cong\{0,q_{y},q_{z}\}] (a) and between [{\bf e}_{x}] and [{\bf q}\cong\{q_{x},q_{y},0\}] (b). Note that in many SANS publications the scattering angle is denoted by the symbol [2\theta]. However, in order to comply with our previous notation (see e.g. the publications in the reference list), we prefer to denote this quantity by [2\psi].

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
Volume 55| Part 4| August 2022| Pages 1055-1062
https://doi.org/10.1107/S1600576722005349
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