All metals exhibit a weak paramagnetism which is temperature independent. This type of magnetism, known as Pauli paramagnetism, can be explained by the above model (see Fig.7.1). When a magnetic field is applied to a metal, the orientation of the magnetic moments of the electrons is constrained to be either parallel or antiparallel to the field direction.

Figure 7.1: Spin-up and spin-down state separation in a metal as per Pauli paramagnetism in the (a) absence of applied field (H = 0) and (b) in the presence of field (H > 0).

Since the energy of the electron in either of the orientations is different, this leads to the splitting of the parallel and antiparallel energy states. Electrons with magnetic moment m parallel to the field direction have energies reduced by (where – μ_B is the Bohr magnetron), while those in antiparallel orientation will have energies increased by . Some of these antiparallel electrons can reduce the energy of the system by occupying parallel stares of lower energy. The number of electrons which can change orientation and still reduce the total energy are those which were within in the absence of the field. The Pauli paramagnetic susceptibility , where M is the magnetization of magnetic moment per unit volume, is

(7.1)

Since

(7.2)

χ P ≈ 10^-10 and is dependent entirely on the small fraction of electrons residing close to E_F .