Curie constant

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

$C = \frac{\mu_0 \mu_B^2}{3 k_B}N g^2 J(J+1)$

where θ₀ is the permeability constant, N is the number of magnetic atoms (or molecules) per unit volume, (according to Cullity, N is the Avogadro's number; Kittel does not talk about the meaning), g is the Landé g-factor, μ_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 μ, 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 χ, magnetization $\scriptstyle\mathbf{M}$ and applied magnetic field $\scriptstyle\mathbf{H}$:

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

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

See also

• Paramagnetism