The Rayleigh law describes the behavior of ferromagnetic materials at low fields.

Ferromagnetic materials consist of magnetic domains. When a small external field ${\displaystyle H}$ 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 ${\displaystyle M}$ as a linear and quadratic term in the field:

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

Here ${\displaystyle \chi _{0}}$ is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant ${\displaystyle \alpha _{R}}$ 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

• 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.