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 $H$ 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 $M$ as a linear and quadratic term in the field:

M=\chi _{0}H+\alpha _{R}\mu _{0}H^{2}.

Here $\chi _{0}$ is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant $\alpha _{R}$ 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.
^ 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" (PDF). Adv. Phys. 4 (14): 191–243. Bibcode:1955AdPhy...4..191N. doi:10.1080/00018735500101204.
^ 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. Bibcode:1997JAP....82.1788D. doi:10.1063/1.365981.
^ 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. Bibcode:1999Fer...224..299T. doi:10.1080/00150199908210580.

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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[1] 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.

[2] Néel, Louis (1942). "Théories des lois d'aimantation de Lord Rayleigh". Cahiers Phys. 12: 1–20.

[3] Néel, Louis (1955). "Some theoretical aspects of rock-magnetism" (PDF). Adv. Phys. 4 (14): 191–243. Bibcode:1955AdPhy...4..191N. doi:10.1080/00018735500101204.

[4] Turik, A.V. (1963). "Theory of polarization and hysteresis of ferroelectrics". Soviet Physics - Solid State. 5 (4): 885–887.

[5] Damjanovic, D. (1997). "Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics". J. Appl. Phys. 82 (4): 1788–1797. Bibcode:1997JAP....82.1788D. doi:10.1063/1.365981.

[6] 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. Bibcode:1999Fer...224..299T. doi:10.1080/00150199908210580.

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