Curie constant

In magnetism, 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 in kelvins (K),^[1] by

C={\frac {\mu _{0}\mu _{\rm {B}}^{2}}{3k_{\rm {B}}}}ng^{2}J(J+1)

,^[2]

where $n$ is the number of magnetic atoms (or molecules) per unit volume, $g$ is the Landé g-factor, $\mu _{\rm {B}}$ is the Bohr magneton, $J$ is the angular momentum quantum number and $k_{\rm B}$ is Boltzmann's constant. For a two-level system with magnetic moment $\mu$ , the formula reduces to

C={\frac {1}{k_{\rm {B}}}}n\mu _{0}\mu ^{2}

,

while the corresponding expressions in Gaussian units are

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

,

C={\frac {1}{k_{\rm {B}}}}n\mu ^{2}

.

The constant is used in Curie's Law, which states that for a fixed value of an applied magnetic field $\scriptstyle {\mathbf {H}}$ , the magnetization of a material is (approximately) inversely proportional to temperature.

M={\frac {C}{T}}H

.

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} M}{\mathrm {d} H}}\approx {\frac {M}{H}}

,

this shows that for a paramagnetic system of non-interacting magnetic moments, magnetization $\scriptstyle \mathbf {M}$ is inversely related to temperature $T$ .

References

^ Coey, J. M. D.; Coey, J. M. D. (2010-03-25). Magnetism and Magnetic Materials. Cambridge University Press. ISBN 978-0-521-81614-4.
^ Kittel, Charles (11 November 2004). Introduction to Solid State Physics, 8th Edition. Wiley. pp. 304. ISBN 0-471-41526-X.

[1] Coey, J. M. D.; Coey, J. M. D. (2010-03-25). Magnetism and Magnetic Materials. Cambridge University Press. ISBN 978-0-521-81614-4.

[2] Kittel, Charles (11 November 2004). Introduction to Solid State Physics, 8th Edition. Wiley. pp. 304. ISBN 0-471-41526-X.

[1]

[2]

Curie constant

See also

References