Diamagnetism and Paramagnetism

Even without magnetic order, materials respond to an applied field: diamagnets weakly oppose it through induced currents, while paramagnets are drawn in as their existing moments partially align.

Definition

Diamagnetism is a weak, temperature-independent magnetization opposing an applied field, arising from field-induced changes in electronic orbital motion; paramagnetism is a magnetization parallel to the field produced by the partial alignment of pre-existing atomic or conduction-electron magnetic moments.

Scope

This topic covers the non-cooperative magnetic responses of matter: Langevin and Larmor diamagnetism from induced orbital currents, Curie paramagnetism of localized moments following the Curie law, and Pauli paramagnetism of conduction electrons set by the density of states at the Fermi level, together with Landau diamagnetism of the electron gas. It establishes the magnetic susceptibility and its temperature dependence as the baseline from which exchange-driven magnetic order departs.

Core questions

• How do induced orbital currents give every material a diamagnetic response?
• Why does the paramagnetic susceptibility of localized moments follow the Curie law in inverse proportion to temperature?
• Why is the Pauli paramagnetism of conduction electrons nearly temperature-independent?
• How do the various contributions combine to give the measured susceptibility of a real solid?

Key concepts

• Magnetic susceptibility
• Larmor and Langevin diamagnetism
• Curie-law paramagnetism of localized moments
• Pauli paramagnetism of conduction electrons
• Landau diamagnetism of the electron gas

Key theories

Curie law of paramagnetism

For localized non-interacting magnetic moments, the competition between field alignment and thermal disorder gives a susceptibility inversely proportional to temperature, the Curie law, which is the limiting behavior above any magnetic ordering transition.

Pauli paramagnetism

In a metal only conduction electrons near the Fermi surface can reorient in a field, so their paramagnetic susceptibility is set by the density of states at the Fermi level and is nearly independent of temperature, unlike the Curie response of localized moments.

Clinical relevance

Susceptibility measurements diagnose the magnetic character of materials, revealing local-moment versus itinerant behavior and the density of states in metals; diamagnetism and paramagnetism also underlie magnetic levitation, the contrast in magnetic resonance imaging, and the calibration of magnetic instruments.

History

Pierre Curie established the experimental law of paramagnetic susceptibility in the 1890s; Langevin gave the classical theory of dia- and paramagnetism in 1905, and Pauli's 1927 quantum treatment of conduction-electron paramagnetism, followed by Landau's diamagnetism, completed the picture for metals.

Key figures

• Pierre Curie
• Paul Langevin
• Wolfgang Pauli

Seminal works

• blundell2001
• ashcroft1976

Frequently asked questions

Do all materials show diamagnetism?

Yes; the induced orbital response that produces diamagnetism is universal, but it is very weak and is usually masked in materials that also have paramagnetic moments or magnetic order, which give larger, opposite contributions.

Why is Pauli paramagnetism so much weaker than Curie paramagnetism?

In a metal the Pauli principle blocks most conduction electrons from reorienting; only the small fraction near the Fermi surface can respond, so the susceptibility is much smaller and nearly temperature-independent compared with freely orientable localized moments.