Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment

Adams, M.P.; Michels, A.; Kachkachi, H.

doi:10.1107/S1600576722008925

Journal of Applied Crystallography Journal of Applied
Crystallography

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Figure 5
Results for the two-dimensional Fourier components $[|{\widetilde {\cal M}}_{x}|^{2}]$ , $[|{\widetilde {\cal M}}_{y}|^{2}]$ , $[|{\widetilde {\cal M}}_{z}|^{2}]$ , CT = $[-({\widetilde {\cal M}}_{y} {\widetilde {\cal M}}_{z}^{*} + {\widetilde {\cal M}}_{y}^{*} {\widetilde {\cal M}}_{z})]$ and for the total magnetic SANS cross section $[{\cal S}_{\rm M} (\upsilon, \theta_{q})]$ [(48

)] using expression (40

). The upper row shows the results taking into account only the zero-order term in (40

), which corresponds to the case of a homogeneously magnetized particle. The lower row displays the results when the second-order term (ν = 1) in (40

) is taken into account. The parameters are e_A = e_z, b₀ = 0.1e_z (B₀ ≃ 48 mT), k_c = 0.1, k_s = 3 and m₀ = [sinβcosα, sinβsinα, cosβ]. Note that υ_y and υ_z denote the dimensionless components of the scattering vector [compare equation (34)

]. Since the Néel surface anisotropy effectively has a cubic symmetry (see Fig. 1