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- Curie's Law can be derived by considering a substance with noninteracting magnetic moments with angular momentum J. If orbital contributions to the magnetic moment are negligible , then in what follows J = S. If we apply a magnetic field along what we choose to call the z-axis, the energy levels of each paramagnetic center will experience Zeeman splitting of its energy levels, each with a z-component labeled by MJ . Applying semiclassical Boltzmann statistics, the magnetization of such a substance is
Where is the z-component of the magnetic moment for each Zeeman level, so is called the Bohr magneton and g'J is the Landé g-factor, which reduces to the free-electron g-factor, g'S when J = S. The energy of each Zeeman level is . For temperatures over a few K, , and we can apply the approximation :
which yields:
The bulk magnetization is then and the susceptibility is given by (en)
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