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 ^[1] and quantified the magnetization $M$ as a linear and quadratic term in the field:

$M = \chi_0 H %2B \alpha_R \mu_0 H^2.$

Here $\chi_0$ is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant $\alpha_R$ describes the irreversible Barkhausen jumps.

References

^ Rayleigh, Lord (1887). "On the behaviour of iron and steel under the operation of feeble magnetic forces". Phil. Mag.. 1 23: 225–248.

Kronmüller, Helmut; Fähnle, Manfred (2003). Micromagnetism and the microstructure of ferromagnetic solids. Cambridge University Press. ISBN 0521331358.
Cullity (1972). Introduction to magnetic materials. Addison-Wesley.