Demagnetization factors for cylindrical shells and related shapes

• Published in: Journal of magnetism and magnetic materials Vol. 321; no. 9; pp. 1306 - 1315
• Main Authors: Beleggia, M., Vokoun, D., De Graef, M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-05-2009; Elsevier
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Core-shell; Critical-point effects, specific heats, short-range order; Demagnetization factor; Dipolar interaction; Exact sciences and technology; Magnetic properties and materials; Magnetostatic energy; Nano-ring; Numerical simulation studies; Physics; Shape anisotropy; Dipolar interaction; 41.20.Gz; Magnetostatic energy; Demagnetization factor; 02.30.Nw; 75.60.−d; Nano-ring; Core-shell; Shape anisotropy; 75.30.Gw; Geometrical shape; 75.60.-d; Magnetic hysteresis; Cylindrical shape; Dipole interactions; Analytical method; High field; Series expansion; Demagnetization
• ISSN: 0304-8853
• DOI: 10.1016/j.jmmm.2008.11.046

Magnetostatic self and interaction energies can be computed via demagnetization factors whenever the magnetic state is close to a uniform state, e.g. in the presence of a strong applied field, or when the dimensions involved are within the single-domain limit. We derive analytical expressions for the demagnetization factors of cylindrical shells and rings with rectangular and square cross-sections. The factors are given either as a combination of elliptic integrals or as a series expansion in powers of the dimensionless ratio between inner and outer radii. Limiting cases are analysed for particular ranges of the shape parameters. We also investigate the ring with a square cross-section, and the elliptic ring, where analytical expressions are provided only for small eccentricity. Finally, we introduce the dipolar coupling integral encoding magnetostatic interactions between a magnetized cylinder and a thin coating on its lateral surface.