paramagnets

Paramagnets are materials that are weakly attracted to external magnetic fields and do not retain magnetization when the field is removed. Their magnetic moments arise from unpaired electron spins or from conduction electrons, and these moments tend to align with an applied field but are random in zero field due to thermal motion.

The magnetic response is described by the susceptibility χ, defined by M = χH, where M is the magnetization and H is the applied field. In many paramagnets, χ is small and positive. A common temperature dependence is given by Curie’s law, χ = C/T, or the Curie-Weiss law, χ = C/(T − θ), where C is the Curie constant and θ is a parameter reflecting interactions among moments. If θ ≈ 0, the material behaves nearly as independent spins; a positive θ indicates ferromagnetic-like interactions, while a negative θ suggests antiferromagnetic-like interactions. Paramagnetism typically exists above any magnetic ordering temperature.

Mechanisms of paramagnetism include spin paramagnetism from unpaired electron spins, Pauli paramagnetism from conduction electrons in metals (usually weak and weakly temperature dependent), and Van Vleck paramagnetism, which arises from mixing of ground and excited states and can be temperature independent. The latter is common in ions with partially filled d or f shells and strong spin-orbit coupling.

Paramagnetism contrasts with diamagnetism (χ < 0) and with ferromagnetism (spontaneous magnetization and hysteresis). Common examples include many transition-metal salts and rare-earth compounds, as well as metals where conduction electrons contribute to the paramagnetic response.