The Rayleigh law describes the behaviour of ferromagnetic materials at low fields

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

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Ferromagnetic materials consist of magnetic domains

Magnetic domains

A magnetic domain describes a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction...

. When a small external field is applied, domains parallel to the external field start to grow. In this region, domain wall

Domain wall

A domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...

s 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

Magnetic susceptibility

In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...

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

Barkhausen effect

The Barkhausen effect is a name given to the noise in the magnetic output of a ferromagnet when the magnetizing force applied to it is changed...

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