Where μ μ M J is the z -component of the magnetic moment for each Zeeman level, so μ μ M J = M J g J μ μ B − − μ μ B 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. (in this treatment, we assume that the x - and y -components of the magnetization, averaged over all molecules, cancel out because the field applied along the z -axis leave them randomly oriented.) The energy of each Zeeman level is E M J = − − M J g J μ μ B H . For temperatures over a few K, M J g J μ μ B H / k B T ≪ ≪ 1 , and we can apply the approximation e M J g J μ μ B H / k B T ≃ ≃ 1 + M J g J μ μ B H / k B T : m ¯ ¯ = ∑ ∑ M J = − − J J M J g J μ μ B e M J g J μ μ B H / k B T ∑ ∑ M J = − − J J e M J g J μ μ B H / k B T ≃ ≃ g J μ μ B ∑ ∑ M J = − − J J M J ( 1 + M J g J μ μ B H / k B T ) ∑ ∑ M J = − − J J ( 1 + M J g J μ μ B H / k B T ) = g J 2 μ μ B 2 H k B T ∑ ∑ − − J J M J 2 ∑ ∑ M J = − − J J ( 1 ) , which yields: m ¯ ¯ = g J 2 μ μ B 2 H 3 k B T J ( J + 1 ) . The bulk magnetization is then M = n m ¯ ¯ = n 3 k B T [ g J 2 J ( J + 1 ) μ μ B 2 ] H , and the susceptibility is given by χ χ = ∂ ∂ M m ∂ ∂ H = n 3 k B T μ μ e f f 2 ; and μ μ e f f = g J J ( J + 1 ) μ μ B .