Abstract
Magnetic fields are understood by classical electromagnetism as resulting from macroscopic currents circulating in conductors. However, this description does not help us to understand the existence of magnetic fields spontaneously induced by materials like iron or cobalt when there are no macroscopic currents imposed by external sources. Only quantum mechanics can explain electronic states corresponding to permanent currents at the microscopic scale. We have just seen an example in the case of superconductors. Likewise, the electron orbital angular momentum and spin are the purely quantum entities which underlie the magnetism of materials.
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- 1.
Note that atomic nuclei also carry spins, and have magnetic moments that give rise to Curie magnetism. However, the nuclear magnetic moments are very small compared with that of the electron and make an altogether negligible contribution to the magnetic properties of the solid, which are thus entirely electronic in origin. The nuclear magnetism can only be directly detected by a magnetometer in quite exceptional circumstances (materials with weak electronic magnetism at very low temperatures), but is easier to observe using resonance methods (see Chap. 11).
- 2.
In practice, these considerations need to be treated cautiously. In a solid, there are usually magnetic anisotropies, to be discussed in the next chapter, stemming from the dipole interaction between spins and/or the spin–orbit interaction. These terms tend to orient M with respect to the crystal axes. However, the operation \(\textbf{S}\rightarrow-\textbf{S}\) remains a symmetry of the Hamiltonian even in this case. A ferromagnetic state will thus always break at least one symmetry.
- 3.
The magnetic susceptibility of an antiferromagnetic compound has specific features that often allow one to establish the existence of the antiferromagnetic state (see Problem 18: Properties of an Antiferromagnetic Solid).
- 4.
See Problem 17: Electronic Properties of La 2CuO4.
- 5.
See Problem 7: Insulator–Metal Transition.
References
Becker, R., Döring, W.: Ferromagnetismus. Springer, Berlin (1939)
Rougé, A.: Introduction à ła Physique Subatomique. Editions de l’Ecole Polytechnique, Palaiseau, France
Basdevant, J.L., Dalibard, J.: Quantum Mechanics. Springer-Verlag, Berlin, Heidelberg (2002)
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Alloul, H. (2011). Magnetism of Insulators. In: Introduction to the Physics of Electrons in Solids. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13565-1_8
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DOI: https://doi.org/10.1007/978-3-642-13565-1_8
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