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Fundamentals and Applications of Magnetic Materials$
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Kannan M. Krishnan

Print publication date: 2016

Print ISBN-13: 9780199570447

Published to Oxford Scholarship Online: December 2016

DOI: 10.1093/acprof:oso/9780199570447.001.0001

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Atomic Origins of Magnetism

Atomic Origins of Magnetism

Chapter:
(p.47) 2 Atomic Origins of Magnetism
Source:
Fundamentals and Applications of Magnetic Materials
Author(s):

Kannan M. Krishnan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199570447.003.0002

A semi-classical formulation to calculate atomic magnetic moments, including some essential concepts of quantum mechanics, is presented. Electrons in orbit are defined by four quantum numbers, to account for the quantization of energy and angular momentum. The latter includes both the orbital and the intrinsic spin contributions, as well as the spin–orbit interactions. Atomic levels in the ground state are then determined using the Pauli exclusion principle and Hund rules to ensure, principally, that the Coulombic interactions between electrons, and secondarily, that the spin–orbit energy, is minimized. We then calculate the total angular momentum of all the electrons in an atom—only the unpaired electrons contribute as the paired ones cancel each other—and establish its relationship to the atomic magnetic moment via the Landé g-factor, based on the Russell–Sanders coupling scheme where the spin–orbit interaction is considered a weak perturbation. The range of validity of this coupling scheme to the calculation of magnetic moments, including the quenching of orbital angular momentum, is established by comparing with measured values, especially for 3d transition metals and the 4f lanthanides.

Keywords:   quantum numbers, quantization, orbital and spin angular momentum, Pauli exclusion principle, Hund rules, Russell–Sanders coupling, atomic magnetic moment, quenching

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