Paramagnetism

Paramagnetic materials contain unpaired electrons in their atoms, giving each atom a finite magnetic dipole moment. Unlike diamagnetic materials, paramagnets possess a net magnetic moment due to these unpaired electrons. In the absence of an external field, these moments are randomly oriented, resulting in zero net magnetization. When exposed to a magnetic field, paramagnets are attracted to it and develop a magnetization proportional to the applied field strength.

Two competing effects determine moment alignment in paramagnets. An external field exerts torque to align moments along its direction, while random thermal motion creates opposing torque that tries to disorient them. At room temperature, thermal energy is roughly 100 times greater than the magnetic dipole energy, so thermal collisions prevent complete alignment. Consequently, only a small fraction of magnetic dipoles align with the applied field at any instant.

Curie's Law states that magnetization in paramagnetic materials is directly proportional to the applied magnetic field and inversely proportional to absolute temperature. As temperature increases, thermal motion intensifies, making it harder for external fields to align magnetic moments. This temperature dependence means paramagnetic susceptibility decreases at higher temperatures, reflecting the reduced fraction of aligned dipoles available to contribute to magnetization.

Magnetization represents the total magnetic moment per unit volume in a paramagnetic material. The induced magnetic field generated by paramagnets is proportional to their magnetization. The resultant field is the vector sum of the external applied field and this induced field. Since paramagnetic susceptibility is positive and temperature-dependent, the relative permeability of paramagnets is slightly greater than unity, distinguishing them from diamagnetic materials.

An atom's net magnetic dipole moment results from the vector sum of its orbital and spin magnetic moments. In paramagnetic materials, unpaired electrons contribute significantly to this net moment. When randomly oriented without an external field, these individual atomic moments cancel out, producing zero net magnetization. Under an external field, the torque acting on these moments tends to align them, generating the additional magnetic field characteristic of paramagnetic materials.

The magnetic dipole energy is the energy difference between dipoles aligned with and against a magnetic field, equal to twice the product of dipole moment magnitude and applied field strength. For a hydrogen atom in a 1 Tesla field, this energy is approximately 10-23 joules. At room temperature, thermal energy per atom is roughly 10-21 joules, making thermal energy about 100 times larger. This vast energy difference explains why only a small fraction of dipoles align despite the external field.

Paramagnets attract magnetic fields due to unpaired electrons and possess positive susceptibility, while diamagnets repel fields and have negative susceptibility. The relative permeability of paramagnets is slightly greater than unity, whereas diamagnets have relative permeability slightly less than unity. Additionally, paramagnetic susceptibility is temperature-dependent, decreasing as temperature increases, whereas diamagnetic susceptibility remains essentially temperature-independent.