DiamagnetismEdit

Diamagnetism is a fundamental form of magnetism in which materials generate an induced magnetic moment in the direction opposite to an externally applied magnetic field. This weak, universal response arises from the quantum-mechanical behavior of electrons in atoms and molecules and is distinct from the more familiar, stronger forms of magnetism such as paramagnetism and ferromagnetism. In most everyday materials, the diamagnetic signal is small and easily overshadowed by other magnetic effects, but it becomes noticeable in certain substances (for example, bismuth and graphite) and, in the case of superconductors, can approach perfect diamagnetism due to the Meissner effect. For a physicist, diamagnetism is a clean demonstration of how quantum mechanics governs electronic motion in a material, even in the absence of permanent magnetic moments.

Overview

Diamagnetism reflects the tendency of the orbital motion of electrons to oppose an applied magnetic field. The induced current patterns generate a magnetic field that cancels part of the external field inside the material.
The effect is characterized by a negative magnetic susceptibility, typically very small in magnitude (on the order of -10^-5 to -10^-6 in SI units) and only weakly temperature dependent. In contrast, paramagnets have positive susceptibility that often decreases with temperature according to Curie or Curie–Weiss behavior.
All atoms and molecules exhibit some diamagnetic response, but in many materials it is masked by stronger magnetic contributions. In special cases, such as graphite or bismuth, the diamagnetic signal becomes a dominant feature of the material’s magnetism.
A key real-world manifestation of strong diamagnetism occurs in superconductors, where magnetic flux is expelled from the interior, a phenomenon known as the Meissner effect and related to perfect diamagnetism.

Historical background

Diamagnetism was first observed in materials such as bismuth in the early 19th century by experimentalists who noticed that certain substances weakly repelled magnetic fields. The term and the underlying concepts were developed as scientists sought to explain how materials respond to magnetic fields beyond the scope of permanent magnets. Over time, the development of quantum theory clarified that diamagnetism emerges from the quantized motion of electrons and their orbital currents, rather than from fixed magnetic moments. The discovery and interpretation of diamagnetism sit alongside broader efforts to understand magnetism as a spectrum that includes paramagnetism, ferromagnetism, and more exotic forms.

Theory

Classical picture

In a purely classical view, an external magnetic field would induce circulating charges that create internal magnetic fields opposing the applied field. However, a purely classical treatment of magnetism faces limitations: certain conclusions, such as the absence of magnetism in a purely classical, non-quantized gas, are highlighted by the Bohr-van Leeuwen theorem. This theorem shows that classical statistical mechanics cannot account for magnetic ordering or a net diamagnetic/paramagnetic response in equilibrium, underscoring the essential role of quantum mechanics in magnetism.

Quantum mechanical foundations

The modern understanding of diamagnetism rests on quantum mechanics. The orbital motion of electrons in atoms and molecules generates small currents that oppose the applied field, leading to a negative susceptibility. Two important quantum descriptions are: - Landau diamagnetism, which describes the response of free or nearly free electrons in a metal and is essential for understanding the weak diamagnetic response in many metals. - Orbital contributions in molecules and solids, where the arrangement of electrons in orbitals and their energy structure determine the sign and magnitude of the diamagnetic response.

Key concepts and related phenomena

Magnetic susceptibility and shielding: The degree to which a material reduces the effect of an external field is captured by its susceptibility. Diamagnetic materials have negative susceptibility, and this plays a role in phenomena such as NMR shielding, where both diamagnetic and paramagnetic contributions influence the observed shielding constants. See magnetic susceptibility and NMR for related topics.
Lenz’s law and induced currents: The induced currents that oppose the applied field embody Lenz’s law, a general principle of electromagnetism, and are central to the diamagnetic response at the microscopic level. See Lenz's law.
Van Vleck and beyond: Beyond the simple orbital picture, more sophisticated quantum treatments explain temperature dependence and anisotropy in certain materials through mechanisms such as van Vleck paramagnetism and related effects, where virtual transitions between quantum states contribute to magnetic behavior.

Bohr-van Leeuwen theorem

This theorem demonstrates a fundamental limit of classical physics in explaining magnetism, asserting that classical statistical mechanics yields zero net magnetization in thermal equilibrium. The observed diamagnetic and paramagnetic responses thus require quantum mechanics for a correct description, reinforcing the view that magnetism is inherently a quantum phenomenon in ordinary matter.

Materials and measurements

Typical magnitudes and trends

Most materials exhibit a small, negative susceptibility, with the diamagnetic signal becoming more noticeable when other magnetic effects are weak or absent.
Materials with lightweight, tightly bound electrons and closed shells tend to show stronger diamagnetic responses.
The temperature dependence of diamagnetism is generally weak, in contrast to some paramagnetic materials whose susceptibility follows Curie-like laws. However, in some materials, especially where orbital and spin contributions compete, temperature can play a more nuanced role.

Notable examples

bismuth and graphite are classic examples of materials with discernible diamagnetic behavior and are frequently cited in introductory discussions of magnetism. See bismuth and graphite.
Copper and many other metals exhibit a small, negative susceptibility, illustrating that even conductors can display diamagnetism, though their overall magnetic behavior is often dominated by other effects.
Water and biological tissues typically show weak diamagnetism, which can contribute to NMR shielding and other magnetic resonance phenomena. See water and biological tissue.

Experimental techniques

Magnetic susceptibility measurements can be performed using Gouy balance methods, Faraday or AC susceptometry, and modern SQUID-based sensors for high sensitivity. See Gouy balance and SQUID for related instrumentation.
Magnetic resonance techniques rely on shielding constants that have diamagnetic contributions, highlighting the practical link between diamagnetism and spectroscopy. See NMR.

Applications and implications

Diamagnetic levitation: Because diamagnetic materials repel magnetic fields slightly, they can be made to levitate in strong magnetic gradients, a striking demonstration of diamagnetic response. Materials such as graphite and water can exhibit levitation under appropriate conditions.
Magnetic shielding and precision measurements: The negative susceptibility of diamagnetic materials can contribute to shielding environments used in precise magnetic measurements and some experimental setups.
Relationship to superconductivity: In superconductors, the Meissner effect expels magnetic flux from the interior, effectively producing perfect diamagnetism at low temperatures. This phenomenon is central to superconductivity and has wide-ranging technological implications. See Meissner effect and superconductivity.

Controversies and debates

The boundaries between classical intuition and quantum mechanics in magnetism are often clarified through discussions of the Bohr-van Leeuwen theorem, which shows the insufficiency of classical theories to account for magnetism in equilibrium. The ongoing development of quantum mechanical descriptions—such as Landau diamagnetism for conduction electrons and van Vleck paramagnetism for more complex systems—illustrates how modern theory resolves apparent paradoxes and explains material-specific behavior without resorting to ad hoc explanations.
Some discussions in the history of physics emphasize how early models balanced between orbital motion and spin contributions, leading to a nuanced view of when diamagnetic and paramagnetic terms dominate in complex materials. These debates helped sharpen the understanding that magnetism is a broad, context-dependent phenomenon rather than a single simple rule.