Curie's law

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For many paramagnetic materials, the magnetization of the material is directly proportional to an applied magnetic field, for sufficiently high temperatures and small fields. However, if the material is heated, this proportionality is reduced. For a fixed value of the field, the magnetic susceptibility is inversely proportional to temperature, that is

${\displaystyle M=\chi H,\quad \chi ={\frac {C}{T}},}$

where

${\displaystyle \chi >0}$ is the (volume) magnetic susceptibility,

${\displaystyle M}$ is the magnitude of the resulting magnetization (A/m),

${\displaystyle H}$ is the magnitude of the applied magnetic field (A/m),

${\displaystyle T}$ is absolute temperature (K),

${\displaystyle C}$ is a material-specific Curie constant (K).

Pierre Curie discovered this relation, now known as Curie's law, by fitting data from experiment. It only holds for high temperatures and weak magnetic fields. As the derivations below show, the magnetization saturates in the opposite limit of low temperatures and strong fields. If the Curie constant is null, other magnetic effects dominate, like Langevin diamagnetism or Van Vleck paramagnetism.