Paramagnetism

Paramagnetism is a form of magnetism in which materials are weakly attracted to an external magnetic field. It arises from the presence of atoms or ions that contain unpaired electron spins, yielding net magnetic moments that tend to align with the field. In paramagnetic materials the magnetization is proportional to the applied field at small fields, and the magnetic susceptibility χ is positive but small.

For many materials with localized magnetic moments, the temperature dependence follows Curie’s law, with χ ∝ 1/T, leading to χ = C/T (Curie paramagnetism). When interactions between moments are present, the Curie-Weiss law χ = C/(T−θ) provides a better description; θ indicates the strength and sign of interactions. In metals, conduction electron spins contribute Pauli paramagnetism, which is typically weak and only weakly temperature dependent. The magnitude of χ is usually in the range 10^-5 to 10^-3 (dimensionless SI volume susceptibility).

Common sources include transition metal and rare-earth ions such as Fe3+, Mn2+, Gd3+, and organic radicals with unpaired electrons. Paramagnetism is opposed by diamagnetism (induced moments opposite field) and is distinct from ferromagnetism (spontaneous alignment).

Measurement and applications: a variety of magnetometers (including SQUID) measure χ. Paramagnetic materials are used in MRI contrast agents, such as gadolinium complexes, and in fundamental studies to characterize electronic structure.