2019-Sustainable Industrial Processing Summit
SIPS2019 Volume 13: Composite, Ceramic, Nanomaterials, Polymers, and Mathematics
| Editors: | F. Kongoli, M. de Campos, S. Lewis, S. Miller, S. Thomas |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2019 |
| Pages: | 171 pages |
| ISBN: | 978-1-989820-12-4 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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How to Handle the Exchange Energy Term in Micromagnetic Models
Marcos de Campos1;1UFF - FEDERAL FLUMINENSE UNIVERSITY, Volta Redonda, Brazil;
Type of Paper: Regular
Id Paper: 204
Topic: 16
Abstract:
In the modelling of magnetic properties of magnetic materials, four energy terms need to be considered: (i) the Zeeman term, due the applied field, (ii) the term due to the magnetostic energy, (iii) the term due to the magnetocrystalline anisotorpy, and (iv) the term due to exchange energy. These four terms are considered in micromagnetic models.
In the present study, different formulations for the exchange energy terms are compared [1].
The Heisenberg exchange interaction is usually described by a scalar product, which results in a term depending on the cosine function. The approximation of the 1- cosine function by a Taylor series gives a polynomial of order two, since other terms of the Taylor series expansion are neglected.
Replacing a cosine funstion by a polynomial of order two, however, overestimates the exchange energy contribution significantly.
It is shown that existence of antiferromagnetism can reduce the energy of system.
Thus, the exchange energy term needs to consider all other neighbours because they can reduce the energy of the system.
Thus, the exchange energy is more properly described by a Fourier series than by a polynomial of order two.