Rayleigh law

The Rayleigh law describes the behaviour 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 [cite journal|last=Rayleigh|first=Lord|title=On the behaviour of iron and steel under the operation of feeble magnetic forces|journal=Phil. Mag.|volume=23|pages=225–248|date=1887|doi=10.1080/14786437108216375] and quantified the magnetization $M$ as a linear and quadratic term in the field:

$M\; =\; chi\_0\; H\; +\; alpha\_R\; mu\_0\; H^2.$

$chi\_0$ is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant $alpha\_R$ describes the irreversible Barkhausen jumps.

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