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The Curie constant is a material-dependent property that relates a material's magnetic susceptibility to its temperature.

The Curie constant, when expressed in SI units, is given by

$C=\frac{{\mu }_B^2}{3k_B}N{g}^{2}J(J+1)$

where $N$ is the number of magnetic atoms (or molecules) per unit volume, $g$ is the Landé g-factor, ${\mu }_B$ (9.27400915e-24 J/T or A·m²) is the Bohr magneton, $J$ is the angular momentum quantum number and $k_B$ is Boltzmann's constant. For a two-level system with magnetic moment $\mu$, the formula reduces to

$C=\frac{1}{k_B}N{\mu }^2$

The constant is used in Curie's Law, which states that for a fixed value of a magnetic field, the magnetization of a material is (approximately) inversely proportional to temperature.

$\mathbf{M}=\frac{C}{T}\mathbf{B}$

This equation was first derived by Pierre Curie.

Because of the relationship between magnetic susceptibility $\chi$, magnetization $\mathbf{M}$ and applied magnetic field $\mathbf{H}$:

$\chi =\frac{\mathbf{M}}{\mathbf{H}}$

this shows that for a paramagnetic system of non-interacting magnetic moments, magnetization $\mathbf{M}$ is inversely related to temperature $T$ (see Curie's Law).

See also

• Paramagnetism

References

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