29.21 : Paramagnetism

Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the field direction, which generates an additional magnetic field proportional to the material's magnetization. Thus, in a paramagnetic material, only a small fraction (roughly one-third) of the magnetic dipoles are aligned with the applied field.

The relative importance of these two competing processes can be estimated by comparing the energies involved. The magnetic dipole energy is the energy difference between magnetic dipoles aligned with and against a magnetic field. It is twice the product of the magnitude of the dipole moment and the applied magnetic field. Considering a magnetic field of 1 Tesla acting on a hydrogen atom, the energy difference is of the order of 10^-23J. At room temperature, the thermal energy per atom is of the order of 10-²¹J. Clearly, the thermal energy is 10²times greater than the magnetic dipole energy. Thus, energy exchanges in thermal collisions interfere with the magnetic dipole alignment, and only a small fraction of dipoles are aligned at any instant. Curie's law gives the magnetization in paramagnetic materials.

The magnetic permeability of paramagnets is slightly greater than unity. Their susceptibility is positive and temperature-dependent.