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Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment
The magnetization profile and the related magnetic small-angle neutron scattering cross section of a single spherical nanoparticle with Néel surface anisotropy are analytically investigated. A Hamiltonian is employed that comprises the isotropic exchange interaction, an external magnetic field, a un...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
International Union of Crystallography
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9721331/ https://www.ncbi.nlm.nih.gov/pubmed/36570665 http://dx.doi.org/10.1107/S1600576722008925 |
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author | Adams, Michael P. Michels, Andreas Kachkachi, Hamid |
author_facet | Adams, Michael P. Michels, Andreas Kachkachi, Hamid |
author_sort | Adams, Michael P. |
collection | PubMed |
description | The magnetization profile and the related magnetic small-angle neutron scattering cross section of a single spherical nanoparticle with Néel surface anisotropy are analytically investigated. A Hamiltonian is employed that comprises the isotropic exchange interaction, an external magnetic field, a uniaxial magnetocrystalline anisotropy in the core of the particle and the Néel anisotropy at the surface. Using a perturbation approach, the determination of the magnetization profile can be reduced to a Helmholtz equation with Neumann boundary condition, whose solution is represented by an infinite series in terms of spherical harmonics and spherical Bessel functions. From the resulting infinite series expansion, the Fourier transform, which is algebraically related to the magnetic small-angle neutron scattering cross section, is analytically calculated. The approximate analytical solution for the spin structure is compared with the numerical solution using the Landau–Lifshitz equation, which accounts for the full nonlinearity of the problem. The signature of the Néel surface anisotropy can be identified in the magnetic neutron scattering observables, but its effect is relatively small, even for large values of the surface anisotropy constant. |
format | Online Article Text |
id | pubmed-9721331 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | International Union of Crystallography |
record_format | MEDLINE/PubMed |
spelling | pubmed-97213312022-12-22 Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment Adams, Michael P. Michels, Andreas Kachkachi, Hamid J Appl Crystallogr Research Papers The magnetization profile and the related magnetic small-angle neutron scattering cross section of a single spherical nanoparticle with Néel surface anisotropy are analytically investigated. A Hamiltonian is employed that comprises the isotropic exchange interaction, an external magnetic field, a uniaxial magnetocrystalline anisotropy in the core of the particle and the Néel anisotropy at the surface. Using a perturbation approach, the determination of the magnetization profile can be reduced to a Helmholtz equation with Neumann boundary condition, whose solution is represented by an infinite series in terms of spherical harmonics and spherical Bessel functions. From the resulting infinite series expansion, the Fourier transform, which is algebraically related to the magnetic small-angle neutron scattering cross section, is analytically calculated. The approximate analytical solution for the spin structure is compared with the numerical solution using the Landau–Lifshitz equation, which accounts for the full nonlinearity of the problem. The signature of the Néel surface anisotropy can be identified in the magnetic neutron scattering observables, but its effect is relatively small, even for large values of the surface anisotropy constant. International Union of Crystallography 2022-11-04 /pmc/articles/PMC9721331/ /pubmed/36570665 http://dx.doi.org/10.1107/S1600576722008925 Text en © Michael P. Adams et al. 2022 https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited. |
spellingShingle | Research Papers Adams, Michael P. Michels, Andreas Kachkachi, Hamid Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment |
title | Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment |
title_full | Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment |
title_fullStr | Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment |
title_full_unstemmed | Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment |
title_short | Magnetic neutron scattering from spherical nanoparticles with Néel surface anisotropy: analytical treatment |
title_sort | magnetic neutron scattering from spherical nanoparticles with néel surface anisotropy: analytical treatment |
topic | Research Papers |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9721331/ https://www.ncbi.nlm.nih.gov/pubmed/36570665 http://dx.doi.org/10.1107/S1600576722008925 |
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