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 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 and quantified the magnetization as a linear and quadratic term in the field:

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