197,259 research outputs found

    General magnetostatic shape-shape interactions

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    The magnetostatic interaction energy between two magnetic elements of arbitrary,7 Shape is presented as a convolution between the cross-correlation of the particle shapes and the dipolar tensor field. A generalized dipole-dipole interaction is derived, where the magnetic moments associated with the two particles interact through a magnetometric tensor field. carrying all the shape information. Example computations are given in order to verify the correctness of the formalism The well-known result of the interaction between prisms, employed in most micromagnetic simulations. is correctly retrieved. The numerical accuracy of the method is also compared to a simple analytical result. Finally, one additional example computation, two interlaced interacting rings, is presented to show the generality of the formalism. (C) 2004 Elsevier B.V. All rights reserved

    On the computation of the demagnetization tensor field for an arbitrary particle shape using a Fourier space approach

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    A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given. (C) 2003 Elsevier Science B.V. All rights reserved

    The fluxgate ring-core demagnetization field

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    The local demagnetization factor for the ring-core flux gate is derived analytically, based on a tangential magnetization model. The results are in good agreement with experimental data for a wide range of ring shape parameters. Approximate expressions in the limit of a narrow, thin ring are obtained, and indicate that the local demagnetization factor scales with the ratio of the cross-sectional area to the total area of the ring. Analytical modeling of the demagnetization factors for a uniform magnetization state results in an underestimate of the local cross-section averaged demagnetization factors by 50% or more. (C) 2006 Elsevier B.V. All rights reserved

    General magnetostatic shape-shape interaction forces and torques

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    Expressions for the magnetostatic interaction force and torque between two magnetic objects of arbitrary shape are derived within the shape amplitude formalism. A generalized force is derived as the gradient of the magnetometric tensor field, which is the convolution of the cross-correlation of the object shapes with the dipolar tensor fields. Expressions for the mechanical and magnetic torques are also derived in terms of the magnetometric tensor field. Expressions suitable for numerical evaluation are given as finite Fourier summations. Example computations are given for the interactions between pairs of uniformly magnetized spheres (for which analytical results are compared to numerical results), cubes, octahedra, tetrahedra, and cuboctahedra. The accuracy of the derived numerical relations for energy, force, and torques is of the order of 0.1% for object spacings smaller than the object dimensions. (C) 2009 Elsevier B.V. All rights reserved

    Demagnetization factors for cylindrical shells and related shapes

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    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. (C) 2008 Elsevier B.V. All rights reserved

    Vector field electron tomography of magnetic materials: Theoretical development

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    The theory of vector field electron tomography, the reconstruction of the three-dimensional magnetic induction around a magnetized object, is derived within the framework of Lorentz transmission electron microscopy. The tomographic reconstruction method uses as input two orthogonal tilt series of magnetic phase maps and is based on the vector slice theorem. An analytical reconstruction of the magnetic induction of a single magnetic dipole is presented as a proof-of-concept. The method is compared to two previously reported approaches: a reconstruction starting from the gradient of the magnetic phase maps, and a direct reconstruction of the magnetic vector potential. Numerical examples as well as estimates of the reconstruction errors for a range of magnetic particle shapes are reported. (c) 2007 Elsevier B.V. All rights reserved

    Demagnetization factors of the general ellipsoid: An alternative to the Maxwell approach

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    A transparent, exhaustive, and self-contained method for the calculation of the demagnetization tensor of the uniformly magnetized ellipsoid is presented. The method is an alternative to the established Maxwell derivation and is based on a Fourier-space approach to the micromagnetics of magnetized bodies. The key to the success of the procedure lies in the convenient treatment of shape effects through the Fourier representation. The scaled form of the demagnetization factors which depends on two dimensionless aspect ratios is argued to be their natural integral representation. Amongst other advantages, it allows for the immediate implementation of symmetry arguments such that only one of the principal factors needs to be computed. The oblate and prolate ellipsoids of revolution are examined from the same general point of view. The demagnetization factors for these distinct types of spheroid are seen to be related by analytic continuation of well-known Gaussian hypergeometric functions

    The equivalent ellipsoid of a magnetized body

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    The equivalent ellipsoid for magnetized bodies of arbitrary shape can be determined by imposing the equality between the demagnetization factors of the two shapes of equal volume. It is shown that the 'commonsense' criterion for mapping two different shapes by imposing the equality of the demagnetization factors for equal aspect ratios often results in large errors. We propose a general method for the rigorous determination of the equivalent ellipsoid. The cases of the exact equivalent ellipsoids for discs, cylinders with elliptical cross section and prisms are worked out and discussed
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