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Magnetic dipole

About: Magnetic dipole is a research topic. Over the lifetime, 15730 publications have been published within this topic receiving 324730 citations.


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TL;DR: In this paper, a thermodynamic theory of weak ferromagnetism of α-Fe 2 O 3, MnCO 3 and CoCO 3 is developed on the basis of landau's theory of phase transitions of the second kind.

4,730 citations

Journal ArticleDOI
Hans A. Bethe1
TL;DR: In this paper, the diffraction of electromagnetic radiation by a hole small compared with the wave-length is treated theoretically, and a complete solution is found satisfying Maxwell's equations and the boundary conditions everywhere.
Abstract: The diffraction of electromagnetic radiation by a hole small compared with the wave-length is treated theoretically. A complete solution is found satisfying Maxwell's equations and the boundary conditions everywhere (Section 4). The solution holds for a circular hole in a perfectly conducting plane screen, but it is believed that the method will be applicable to much more general problems (Section 8). The method is based on the use of fictitious magnetic charges and currents in the diffracting hole which has the advantage of automatically satisfying the boundary conditions on the conducting screen. The charges and currents are adjusted so as to give the correct tangential magnetic, and normal electric, field in the hole. The result (Section 5) is completely different from that of Kirchhoff's method, giving for the diffracted electric and magnetic field values which are smaller in the ratio (radius of the hole/wave-length) (Section 6). The diffracted field can be considered as caused by a magnetic moment in the plane of the hole, and an electric moment perpendicular to it (Section 6). The theory is applied to the problem of mutual excitation of cavities coupled by small holes (Section 9). This leads to equations very similar to those for ordinary coupled circuits. The phase and amplitude relations of two coupled cavities are not uniquely determined, but there are two modes of oscillation, of slightly different frequency, for which these relations are opposite (Section 10). The problem of stepping up the excitation from one cavity to another is treated (Section 11).

2,562 citations

Journal ArticleDOI
TL;DR: In this article, the second moment of the frequency deviation of the absorption line of the electron was calculated and the fourth moment was also computed to examine how good an approximation is the conventional assumption of a Gaussian shape.
Abstract: In regular crystals, the width of the absorption lines arising from the magnetic moment of the electron or nucleus is caused primarily by the interaction between the magnetic dipoles. It is prohibitively difficult to determine the precise shape of the absorption line theoretically, but the invariance of the diagonal sum in quantum mechanics permits the calculation of the second moment of the frequency deviation, and hence the r.m.s. line breadth. The latter agrees excellently with the observations of Pake and Purcell on the magnetic absorption of the F nucleus in Ca${\mathrm{F}}_{2}$, both in absolute magnitude, and in the dependence on the direction between the magnetic field and the principal cubic axes. The fourth moment was also computed to examine how good an approximation is the conventional assumption of a Gaussian shape. As long as no exchange is present (the nuclear case) the Gaussian model is moderately good. For the 100 direction in a cubic crystal, the theoretical ratio of root mean fourth to root mean square breadth is 1.25. Pake and Purcell's measurements yield 1.24. A Gaussian model would require 1.32. The theory is extended to include crystals with two kinds of spin moments (two types of nuclei, or simultaneous nuclear and electronic spin). Coupling between unlike moments is less effective (by a factor ⅔ in the r.m.s. width) than that between like in broadening the lines.In the paramagnetic absorption caused by electronic spin, it is imperative to include the effect of exchange coupling. This interaction does not contribute to the second moment, but greatly increases the fourth. As a result, the lines are peaked much more sharply than one would compute from the second moment with the Gaussian model for line shape. This "exchange narrowing" explains why microwave paramagnetic absorption lines are much narrower than one first conjectures from the amount of dipolar coupling.The theoretical calculations are given in Sections II-IV. The final sections V-VI give the comparison with the experiments of Pake and Purcell, and with the model of Bloembergen, Purcell, and Pound, for r-f absorption in liquids.

2,139 citations

Journal ArticleDOI
TL;DR: Sum rules are derived for the circular dichroic response of a core line (CMXD) that relate the intensity of the CMXD signal to the ground-state expectation value of the magnetic field operators (orbital, spin, and magnetic dipole) of the valence electrons.
Abstract: Sum rules are derived for the circular dichroic response of a core line (CMXD). They relate the intensity of the CMXD signal to the ground-state expectation value of the magnetic field operators (orbital, spin, and magnetic dipole) of the valence electrons. The results obtained are discussed and tested for transition metals and rare earths.

1,828 citations

01 Jan 2013
TL;DR: In this paper, the ab initio quasirelativistic Hartree-Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions is used to derive transition data for a multicharged tungsten ion.
Abstract: a b s t r a c t The ab initio quasirelativistic Hartree–Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions is used to derive transition data for a multicharged tungsten ion. The configuration interaction method is applied to include electron correlation effects. The relativistic effects are taken into account in the Breit–Pauli approximation for quasirelativistic Hartree–Fock radial orbitals. The energy level spectra, radiative lifetimes and Lande gfactors are calculated for the 4p 6 4d 2 , 4p 6 4d4f, and 4p 5 4d 3 configurations of the ion W 36+ . The transition wavelengths, spontaneous transition probabilities, oscillator strengths, and line strengths for the electric dipole, electric quadrupole, electric octupole, and magnetic dipole transitions among the levels of these configurations are tabulated.

1,704 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023121
2022263
2021327
2020369
2019405
2018380