The difference between Pauli Paramagnetism and Curie Paramagnetism

14.5    PARAMAGNETISM  

Paramagnetism is exhibited by a substance with unfilled electron shells. In the absence of a magnetic field such atoms and ions exhibit no magnetic moment. Following are some of the systems with unfilled electron shells:

(i) Atoms and molecules having an odd number of electrons, since the total spin of such systems is nonzero
Examples: Alkali atoms, nitric oxide, organic free radicals

(ii) Atoms and ions with a partly filled inner shell
Examples: Transition elements (Mn2+, Gd3+, U4+), rare earths, actinide group elements

(iii) Certain molecules and compounds with even number of electrons
Examples: Molecular oxygen, boron, organic biradicals.

In simple metals like sodium or aluminum, the valence electrons are no longer attached to any particular atom. As a result, although the metal ions do not contribute to the magnetic moment, the moving electrons produce a non zero magnetic moment. This free electron paramagnetism is a weak phenomenon and is often referred to as Pauli paramagnetism or paramagnetism of conduction electrons. In an applied magnetic field, these magnetic moments align in the direction of the field, and therefore the Pauli paramagnetism gives a positive contribution to c. For many metals such as copper, silver and gold, the diamagnetic contribution is larger in magnitude than the paramagnetic contribution. Therefore, these materials display diamagnetic properties. The Pauli paramagnetism is also constant with temperature. Pauli, using the Fermi–Dirac distribution for the free electrons, derived the expression for susceptibility

where TF is the Fermi temperature defined by Eq. (10.43), k is the Boltzmann constant, and N is the number of atoms per unit volume. It is obvious from Eq. (14.22) that the susceptibility c is independent of tempertature. The observed values are in broad agreement with the values given by Eq. (14.22).

There are other paramagnetic materials which show strong magnetic behaviour. In transition metals, rare earths and actinide group, the electronic structure is very different from that of the simple metals. In the iron group transition elements, the 4s state is filled before the 3d ones are filled. The inner electrons form an incomplete shell and give rise to a permanent magnetic moment. In other words, the transition elements are capable of producing a significant susceptibility. In the other transition metals groups, it is the 4d and 5d sub shells that are incomplete. In the rare earths and actinide group, it is the 4f and 5f sub shells that are not filled. These elements give rise to what is called as Curie paramagnetism.

Based on quantum mechanical considerations, it can be shown that this susceptibility is inversely proportional to the temperature. That is



where C is a constant called Curie constant and p is the effective number of Bohr magnetons. This relationship is known as Curie’s law. In the diamagnetism or Pauli paramagnetism, a weak magnetic response is experienced. In Curie paramagnetism, the susceptibility is much larger; however, an external magnetic field is still required to align the magnetic dipoles. The variation of susceptibility of diamagnetic and paramagnetic materials with temperature is shown in Fig. 14.2.

Reference: Engineering Physics    page 296