Demagnetization factors for cylindrical shells and related shapes

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 th...

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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
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Abstract	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.
AbstractList	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.
Author	Beleggia, M. De Graef, M. Vokoun, D.
Author_xml	– sequence: 1 givenname: M. surname: Beleggia fullname: Beleggia, M. organization: Institute for Materials Research, University of Leeds, Leeds LS2 9JT, UK – sequence: 2 givenname: D. surname: Vokoun fullname: Vokoun, D. organization: Institute of Physics, Academy of Science of the Czech Republic, Prague, Czech Republic – sequence: 3 givenname: M. surname: De Graef fullname: De Graef, M. email: degraef@cmu.edu organization: Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA
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Keywords	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
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SubjectTerms	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
Title	Demagnetization factors for cylindrical shells and related shapes
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