Demagnetizing factors for rectangular prisms

Chen, D.-X.; Pardo, Enric; Sanchez, Alvaro

doi:10.1109/tmag.2005.847634

Cited by 157 publications

(111 citation statements)

References 10 publications

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“…The pyrochlore lattice with tilt angle cos θ = 1/ √ 3 yields a smaller N than the bcc lattice with cos θ = 1/ √ 2 for χ int > 0. The spin ice pyrochlore lattice and the dipolar model with Heisenberg spins yield the same result as the continuum method of Chen et al [19], and we conjecture that models with isotropic χ will generally follow this behavior [19].…”

Section: Discussionsupporting

confidence: 72%

“…These highly cited papers bear witness to the importance of accurately computable and easily accessible demagnetizing factors. Given that (i) it was realized already in the 1920s that N for a nonellipsoidal sample is a function not only of the sample shape but also of χ int itself [14,15], and that (ii) many experiments are routinely performed not on ellipsoids but on cuboids [16,17], it is perhaps remarkable that it was only very recently that the χ dependence of N was calculated for cuboids away from the χ int → 0 limit [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Microscopic aspects of magnetic lattice demagnetizing factors

Twengström

Bovo

Gingras

et al. 2017

Phys. Rev. Materials

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The demagnetizing factor N is of both conceptual interest and practical importance. Considering localized magnetic moments on a lattice, we show that for nonellipsoidal samples, N depends on the spin dimensionality (Ising, XY, or Heisenberg) and orientation, as well as the sample shape and susceptibility. The generality of this result is demonstrated by means of a recursive analytic calculation as well as detailed Monte Carlo simulations of realistic model spin Hamiltonians. As an important check and application, we also make an accurate experimental determination of N for a representative collective paramagnet (i.e., the Dy 2 Ti 2 O 7 spin ice compound) and show that the temperature dependence of the experimentally determined N agrees closely with our theoretical calculations. Our conclusion is that the well-established practice of approximating the true sample shape with "corresponding ellipsoids" for systems with long-range interactions will in many cases overlook important effects stemming from the microscopic aspects of the system under consideration.

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Section: Discussionsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Microscopic aspects of magnetic lattice demagnetizing factors

Twengström

Bovo

Gingras

et al. 2017

Phys. Rev. Materials

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“…This mapping naturally depends on the geometry of the sample, and can be expressed in terms of a demagnetization factor. These have been tabulated 12 for rectangular prisms with isotropic permeability, but our samples are highly anisotropic and new calculations are therefore required. When the permeability is isotropic, the divergence of the magnetization is zero everywhere within the sample, and one need only consider the surfaces in order to calculate the demagnetizing field.…”

Section: mentioning

confidence: 99%

A d.c. magnetic metamaterial

et al. 2008

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Electromagnetic metamaterials 1 are a class of materials which have been artificially structured on a subwavelength scale. They are currently the focus of a great deal of interest because they allow access to previously unrealisable properties like a negative refractive index 2 . Most metamaterial designs have so far been based on resonant elements, like split rings 3 , and research has concentrated on microwave frequencies and above. In this work, we present the first experimental realisation of a non-resonant metamaterial designed to operate at zero frequency. Our samples are based on a recently-proposed template 4 for an anisotropic magnetic metamaterial consisting of an array of superconducting plates. Magnetometry experiments show a strong, adjustable diamagnetic response when a field is applied perpendicular to the plates. We have calculated the corresponding effective permeability, which agrees well with theoretical predictions. Applications for this metamaterial may include non-intrusive screening of weak DC magnetic fields. The first metamaterials 3,5 were designed to operate at microwave frequencies. Since then, while there has been some research on radio-frequency metamaterials 6 , most of the research effort has been focused on higher frequencies: technologically-important microwaves or visible light 7 . The low-frequency end of the spectrum has remained relatively unexplored. In addition, the majority of metamaterials devised to date consist of an arrangement of resonant components. There is a good reason for this: the response of a resonator varies greatly as a function of the frequency at which it is being driven. Close to the resonant frequency, the amplitude of the response can be very large, while the phase changes. The range of available values of the response function, or susceptibility, is therefore very wide. One of the crowning achievements of (and driving forces behind) metamaterials research is the realization of a negative refractive index 2,8 , and a simple argument shows that this cannot be achieved without relying on resonant structures. However, the price of working close to the resonant frequency is that losses and frequency dispersion are greatest here. When a negative response is not required then a non-resonant structure is advantageous. Another recent development means that there is new demand for metamaterials with nonnegative anisotropic parameters. Transformation optics 9 is a design paradigm that allows a new level of control over electromagnetic fields. For a given design, it provides a recipe for the material parameters as a function of position. The parameters generated in this way are always non-negative and anisotropic. A spectacular demonstration of the technique was provided by the construction of an electromagnetic cloak 10 using metamaterials. The interior of the cloak is shielded from microwaves with minimal disruption to the exterior fields.

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“…As a summary, such calculations with accuracy about 0.1% have been carried out for the magnetometric demagnetizing factor of cylinders, square bars, and rectangular prisms, 16,17,22,46,47 for the ac susceptibility of conducting cylinders and magnetic conducting spheres, 14,18 and for the perpendicular susceptibility of completely shielded rectangular films. 20,21 Using well calibrated ac susceptometers to study superconducting materials, model calculations ͑with lower accuracy͒ for the properties of the samples are important.…”

Section: F Model Calculationsmentioning

confidence: 99%

Calibration of low-temperature ac susceptometers with a copper cylinder standard

Chen

Skumryev

2010

Review of Scientific Instruments

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A high-quality low-temperature ac susceptometer is calibrated by comparing the measured ac susceptibility of a copper cylinder with its eddy-current ac susceptibility accurately calculated. Different from conventional calibration techniques that compare the measured results with the known property of a standard sample at certain fixed temperature T, field amplitude H m , and frequency f, to get a magnitude correction factor, here, the electromagnetic properties of the copper cylinder are unknown and are determined during the calibration of the ac susceptometer in the entire T, H m , and f range. It is shown that the maximum magnitude error and the maximum phase error of the susceptometer are less than 0.7% and 0.3°, respectively, in the region T = 5 -300 K and f = 111-1111 Hz at H m = 800 A / m, after a magnitude correction by a constant factor as done in a conventional calibration. However, the magnitude and phase errors can reach 2% and 4.3°at 10 000 and 11 Hz, respectively. Since the errors are reproducible, a large portion of them may be further corrected after a calibration, the procedure for which is given. Conceptual discussions concerning the error sources, comparison with other calibration methods, and applications of ac susceptibility techniques are presented.

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Demagnetizing factors for rectangular prisms

Cited by 157 publications

References 10 publications

Microscopic aspects of magnetic lattice demagnetizing factors

Microscopic aspects of magnetic lattice demagnetizing factors

A d.c. magnetic metamaterial

Calibration of low-temperature ac susceptometers with a copper cylinder standard

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