Rayleigh law
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The Rayleigh law (sometimes called Rayleigh law on low-field magnetization) describes the behaviour of ferromagnetic materials at low fields.
Ferromagnetic materials consist of magnetic domains. When a small external field <math>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 <ref>Template:Cite journal</ref> and quantified the magnetization <math>M</math> as a linear and quadratic term in the field:
- <math>M = \chi_0 H + \alpha_\text{R} \mu_0 H^2.</math>
Here <math>\chi_0</math> is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant <math>\alpha_\text{R} </math> describes the irreversible Barkhausen jumps.
The Rayleigh law was derived theoretically by Louis Néel.,<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>
The same law describes polarization<ref>Template:Cite journal</ref> and direct<ref>Template:Cite journal</ref> and converse<ref>Template:Cite journal</ref> 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.