Physics:Rayleigh law
The Rayleigh law describes the behavior of ferromagnetic materials at low fields.
Ferromagnetic materials consist of magnetic domains. When a small external field [math]\displaystyle{ H }[/math] is applied, domains parallel to the external field start to grow. In this region, domain walls are moving. They are hindered by material defects. Lord Rayleigh investigated this first [1] and quantified the magnetization [math]\displaystyle{ M }[/math] as a linear and quadratic term in the field:
- [math]\displaystyle{ M = \chi_0 H + \alpha_R \mu_0 H^2. }[/math]
Here [math]\displaystyle{ \chi_0 }[/math] is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant [math]\displaystyle{ \alpha_R }[/math] describes the irreversible Barkhausen jumps.
The Rayleigh law was derived theoretically by Louis Néel.,[2][3]
The same law describes polarization[4] and direct[5] and converse[6] piezoelectric response of some ferroelectric and ferroelectric-ferroelastic materials. The common feature for ferromagnetic, ferroelectric and ferroelastic materials (i.e., ferroic materials) are domains whose boundaries (domain walls) can be moved by magnetic, electric or mechanical fields.
References
- ↑ Rayleigh, Lord (1887). "On the behaviour of iron and steel under the operation of feeble magnetic forces". Philosophical Magazine 23 (142): 225–248. doi:10.1080/14786448708628000. ISSN 1941-5982. https://zenodo.org/record/1431175.
- ↑ Néel, Louis (1942). "Théories des lois d'aimantation de Lord Rayleigh". Cahiers Phys. 12: 1–20.
- ↑ Néel, Louis (1955). "Some theoretical aspects of rock-magnetism". Adv. Phys. 4 (14): 191–243. doi:10.1080/00018735500101204. Bibcode: 1955AdPhy...4..191N. https://hal.archives-ouvertes.fr/hal-02888358/file/N%C3%A9el%20-%201955%20-%20Some%20theoretical%20aspects%20of%20rock-magnetism.pdf.
- ↑ Turik, A.V. (1963). "Theory of polarization and hysteresis of ferroelectrics". Soviet Physics - Solid State 5 (4): 885–887.
- ↑ Damjanovic, D. (1997). "Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics". J. Appl. Phys. 82 (4): 1788–1797. doi:10.1063/1.365981. Bibcode: 1997JAP....82.1788D.
- ↑ Taylor, D.V.; Damjanovic, D.; Setter, N. (1999). "Nonlinear contributions to dielectric and piezoelectric properties in lead zirconate titanate thin films". Ferroelectrics 224 (4): 299–306. doi:10.1080/00150199908210580. Bibcode: 1999Fer...224..299T.
- Kronmüller, Helmut; Fähnle, Manfred (2003). Micromagnetism and the microstructure of ferromagnetic solids. Cambridge University Press. p. 148. ISBN 0-521-33135-8.
- Cullity (1972). Introduction to magnetic materials. Addison-Wesley. p. 342.
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