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}}{3k_{B}}}ng^{2}J(J+1)

^[1]

where $n$ is the number of magnetic atoms (or molecules) per unit volume, $g$ is the Landé g-factor, $\mu _{B}$ 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 _{0}\mu ^{2}

while the corresponding expressions in Gaussian units are

C={\frac {\mu _{B}^{2}}{3k_{B}}}ng^{2}J(J+1)

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 $\scriptstyle \mathbf {M}$ and applied magnetic field $\scriptstyle {\mathbf {H}}$ is almost linear at low fields, then

\chi ={\frac {\mathrm {d} \mathbf {M} }{\mathrm {d} \mathbf {H} }}\approx {\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).

References

↑ Kittel, Charles. Introduction to Solid State Physics, 8th Edition. Wiley. p. 304. ISBN 0-471-41526-X.

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[1] Kittel, Charles. Introduction to Solid State Physics, 8th Edition. Wiley. p. 304. ISBN 0-471-41526-X.

Curie constant

See also

References