where is the number of magnetic moments, is the Landé g-factor, is the Bohr magneton, is the angular momentum quantum number and is Boltzmann's constant. For a two level system with magnetic moment , the formula reduces to
It comes from Curie's Law, which is the relationship between magnetic susceptibility and temperature of a paramagnetic material
This equation was first derived by Pierre Curie (Marie Curie's husband.)
Because of the relationship between magnetic susceptibility , magnetization and applied magnetic field :
this shows that for a paramagnetic system of non-interacting magnetic moments, magnetization is inversely related to temperature (see Curie's Law).