What is the Magnetization of a Material?

by Alexander FufaeV

The magnetization $ \boldsymbol{M} $ describes the magnetic properties of a material. It is formed by the sum of all atomic magnetic moments $ \boldsymbol{\mu} $ per volume $ V $:

Definition of magnetization

$$ \begin{align} \boldsymbol{M} ~=~ \frac{1}{V} \, \underset{i}{\boxed{+}} ~ \boldsymbol{\mu}_i \end{align} $$

If you apply an external magnetic field $\boldsymbol{H}$ (or equivalently $\class{violet}{\boldsymbol{B}}$) and place a material into this magnetic field, the material will behave differently depending on the magnitude of the magnetization:

Magnetization depends on the external magnetic field

$$ \begin{align} \boldsymbol{M} ~=~ \chi \, \boldsymbol{H} \end{align} $$

Here $\chi$ is the magnetic susceptibility, which determines how good a material can be magnetized.

If the magnetic susceptibility is negative: $ -1 \lt \chi \lt 0 $, then the material is diamagnetic. (Note that $\chi$ cannot be less than -1. A superconductor has $\chi = -1 $ and is a perfect diamagnet).

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The magnetization of the material weakens the external magnetic field $B$ in the material (diamagnetism).
If the magnetic susceptibility is positive: $ \chi \gt 0 $, then the material is paramagnetic.

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The magnetization of the material slightly amplifies the external magnetic field $B$ in the material (paramagnetism).
If the magnetic susceptibility is much greater than zero: $ \chi \gg 0 $, then the material is ferromagnetic.