The temperature dependence of free electron susceptibility

One of the earliest applications of the Fermic-Dirac statistics was that of pauli to the treatment of the paramagnetism, due to the electron spin, of an electron gas. The result he obtained, for low temperatures, may be put in the form M p = 3/2 Nμ 2 H/ε 0 , where M p is the total magnetic moment due to the spin effect, N the number of electrons, μ the Bohr magneton, and ε 0 the maximum electron energy in the completely degenerate state. It was later shown by Landau that electrons, apart from the spin effect, gave a diamagnetic contribution to the susceptibility. The diamagnetic effect (which is zero on a classical basis) arises from the discreteness of the energy states of an electron in a magnetic field. For low temperatures the result obtained is M D = -½ Nμ 2 H/ε 0 , where M D is the diamagnetic contribution to the moment. The spin effect was further considered by Bloch, who gave, as a higher approximation at low temperatures, M P = 3/2 Nμ 2 H/ε 0 {1-π 2 /12( k T/ε 0 ) 2 }.