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Figure 1
Sketch of the SANS setup and of the two most often employed scattering geometries in magnetic SANS experiments. (a) Applied magnetic field [{\bf H}_{0}] perpendicular to the incident neutron beam ([{\bf k}_{0}\perp{\bf H}_{0}]); (b) [{\bf k}_{0}\parallel{\bf H}_{0}]. 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]. For a given λ, sample-to-detector distance [L_{{\rm SD}}] and distance [r_{{\rm D}}] from the centre of the direct beam to a certain pixel element on the detector, the q value can be obtained using [q\cong k_{0}({r_{{\rm D}}} / {L_{{\rm SD}}})]. The symbols `P', `F' and `A' denote, respectively, the polarizer, spin flipper and analyzer, which are optional neutron optical devices. Note that a second flipper after the sample has been omitted here. In spin-resolved SANS (POLARIS) using a 3He spin filter, the transmission (polarization) direction of the analyzer can be switched by 180° by means of a radiofrequency pulse. 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=0 in (a) and qz=0 in (b)] is neglected. The angle θ may be conveniently used in order to describe the angular anisotropy of the recorded scattering pattern on a two-dimensional position-sensitive detector. Image taken from Michels (2021BB80), reproduced by permission of Oxford University Press.

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