Demagnetizing factors for completely shielded rectangular prisms

Pardo, Enric; Chen, Du-Xing; Sanchez, Alvaro

doi:10.1063/1.1787134

Cited by 34 publications

(28 citation statements)

References 12 publications

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“…2) for which demagnetizing factors can be calculated analytically [1,2]. In general, however, magnetic field is highly non-uniform inside and outside of finite samples of arbitrary (non-ellipsoidal) shapes and various approaches were used to handle the problem [3][4][5][6][7][8][9]. As discussed below, the major obstacle has been that so far the total magnetic moment of arbitrary shaped samples could not be calculated and approximations and assumptions had to be made.…”

Section: Introductionmentioning

confidence: 99%

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

2018

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Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various nonellipsoidal shapes. The procedure is based on calculating the total magnetic moment by integrating the magnetic induction obtained from a full three-dimensional (3D) solution of the Maxwell equations using an adaptive mesh. The results are relevant for superconductors (and conductors in ac fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse fields, as well as infinite rectangular and elliptical cross-section strips. Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various nonellipsoidal shapes. The procedure is based on calculating the total magnetic moment by integrating the magnetic induction obtained from a full three-dimensional (3D) solution of the Maxwell equations using an adaptive mesh. The results are relevant for superconductors (and conductors in ac fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse fields, as well as infinite rectangular and elliptical cross-section strips. Disciplines Condensed Matter Physics | Metallurgy | Physics

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Section: Introductionmentioning

confidence: 99%

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

2018

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“…In addition, an alternative way to determine the demagnetization factor is from a rectangular prism approximation based on the dimensions of the crystal, giving us N ≈ 0.9688. 40 The corrected values of H c1 obtained by following the two methods described above are illustrated in Fig. 3 for H c. Even though both procedures yield different values of H c1 , the ratio of both methods is just a constant factor with no change in the shape or the dependence (see the inset of Fig.…”

Section: B Experimental Determination Of the Lower Critical Fieldmentioning

confidence: 99%

Temperature dependence of lower critical fieldHc1(T)shows nodeless superconductivity in FeSe

et al. 2013

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We investigate the temperature dependence of the lower critical field H c1 (T ) of a high-quality FeSe single crystal under static magnetic fields H parallel to the c axis. The temperature dependence of the first vortex penetration field has been experimentally obtained by two independent methods and the corresponding H c1 (T ) was deduced by taking into account demagnetization factors. A pronounced change in the H c1 (T) curvature is observed, which is attributed to anisotopic s-wave or multiband superconductivity. The London penetration depth λ ab (T ) calculated from the lower critical field does not follow an exponential behavior at low temperatures, as it would be expected for a fully gapped clean s-wave superconductor. Using either a two-band model with s-wave-like gaps of magnitudes 1 = 0.41 ± 0.1 meV and 2 = 3.33 ± 0.25 meV or a single anisotropic s-wave order parameter, the temperature dependence of the lower critical field H c1 (T ) can be well described. These observations clearly show that the superconducting energy gap in FeSe is nodeless.

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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 completely shielded rectangular prisms

Cited by 34 publications

References 12 publications

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

Temperature dependence of lower critical fieldHc1(T)shows nodeless superconductivity in FeSe

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

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