Diamagnetism
Diamagnetism is a fundamental magnetic property observed in all materials, characterized by the creation of an induced magnetic field that opposes an externally applied magnetic field, leading to a weak repulsion of the material from the field. This effect arises from the orbital motion of electrons within atoms, which generates small current loops that produce a magnetization opposite to the applied field, analogous to Lenz's law at the atomic scale.[1] Unlike paramagnetism or ferromagnetism, diamagnetism is independent of temperature and is typically very weak, with magnetic susceptibility values on the order of -10^{-5} to -10^{-6}.[2] The phenomenon was first systematically investigated by Michael Faraday in 1845, who discovered that certain substances, such as bismuth and antimony, are repelled by magnetic poles, demonstrating that magnetism affects all matter.[3] Earlier observations date back to 1778, when Sebald Justinus Brugmans noted the repulsion of bismuth by magnetic fields.[3] Common examples of diamagnetic materials include water, copper, silver, gold, bismuth, and noble gases like helium and neon; bismuth exhibits one of the strongest diamagnetic responses among elements.[4][2] Theoretically, diamagnetism is explained by Paul Langevin's classical model from the early 1900s, which attributes the effect to the Larmor precession of electron orbits in a magnetic field, inducing a change in angular momentum that opposes the field.[5] Quantum mechanical treatments yield similar results, confirming the effect's universality. In superconductors, diamagnetism reaches perfection through the Meissner effect, where magnetic fields are completely expelled from the interior below the critical temperature.[6] This property enables applications such as magnetic levitation demonstrations with materials like pyrolytic graphite or bismuth.[7]Fundamentals
Definition and Basic Properties
Diamagnetism is the property of materials to generate an induced magnetic field that opposes an applied external magnetic field, leading to a weak repulsive force from the field. This opposition arises from the orbital motion of electrons within atoms and molecules, which produces currents that create the counteracting field. As a result, diamagnetic materials are repelled from regions of stronger magnetic fields toward weaker ones. The key characteristic of diamagnetism is the negative induced magnetization, described by the relation M = \chi H, where M is the magnetization, H is the applied magnetic field strength, and \chi is the magnetic susceptibility. For diamagnets, \chi < 0, so \chi = M / H yields a negative value, indicating the magnetization direction opposes the field. The susceptibility is typically weak, with magnitudes on the order of -10^{-5} to -10^{-6} (in SI units), and it remains independent of temperature, unlike paramagnetic or ferromagnetic behaviors. Diamagnetism is a universal phenomenon present in all materials, stemming from the inherent orbital electron motion in every atom or molecule, though it is often masked by stronger magnetic effects in certain substances.Comparison to Other Magnetisms
Magnetic materials are broadly classified based on their response to an external magnetic field into diamagnetism, paramagnetism, ferromagnetism, and antiferromagnetism. Diamagnetic materials are weakly repelled by the field and lack permanent magnetic moments, arising solely from induced effects. Paramagnetic materials show weak attraction as atomic moments align with the field under thermal agitation. Ferromagnetic materials display strong attraction due to spontaneous alignment of moments into domains, enabling permanent magnetization. Antiferromagnetic materials feature aligned neighboring moments in opposite directions, resulting in zero net magnetic moment despite the ordered structure.[8] A fundamental distinction lies in the origin and behavior of these phenomena. Diamagnetism is universally induced in all materials, opposing the applied field without requiring unpaired electrons, and produces a negative magnetic susceptibility that is independent of temperature. In contrast, paramagnetism relies on unpaired electrons or other permanent moments that align with the field but are randomized by thermal energy, leading to a positive susceptibility that follows Curie's law, inversely proportional to temperature. Ferromagnetism involves cooperative interactions that maintain alignment below the Curie temperature, yielding a much larger positive susceptibility, while antiferromagnetism cancels out moments through antiparallel coupling, often resulting in weak paramagnetism above the Néel temperature.[1][9] The following table summarizes key comparative aspects:| Type | Susceptibility Sign/Magnitude | Temperature Dependence | Examples |
|---|---|---|---|
| Diamagnetic | Negative (~10^{-5}) | Independent | Water, copper |
| Paramagnetic | Positive (~10^{-5} to 10^{-3}) | Inversely proportional to T (Curie's law) | Aluminum, oxygen |
| Ferromagnetic | Positive (>10^{3}) | Persistent below Curie temperature | Iron, nickel |
| Antiferromagnetic | Positive (small, ~10^{-3}) | Ordered below Néel temperature | MnO, Cr |
History
Early Observations
The earliest reported observation of what would later be recognized as diamagnetism occurred in 1778, when Dutch physicist Sebald Justinus Brugmans noted that bismuth was repelled by the poles of a magnet, placing itself across the magnetic equator rather than aligning with the field.[3] This effect was subtle and not immediately interpreted as a distinct magnetic property, with similar deflections observed in other non-iron substances like antimony by researchers such as T.J. Seebeck in the 1820s, though these were often attributed to impurities or other forces.[3] A pivotal advancement came in 1845 through experiments by Michael Faraday, who used a powerful electromagnet constructed by William Sturgeon to systematically investigate magnetic interactions with various materials. On November 4, 1845, Faraday suspended a piece of dense lead borate glass—known as heavy glass—between the poles of the electromagnet and observed it being repelled from the stronger field regions, moving toward the weaker parts, in contrast to the attraction seen in iron.[12] Extending these tests, Faraday found the same repulsive behavior in bismuth and several other substances, including antimony, phosphorus, and sulfur, confirming a universal property of matter opposite to paramagnetism. He coined the term "diamagnetic" in 1846 to describe this repulsive effect.[3][12] He further demonstrated this by rotating bars of bismuth in a uniform magnetic field, where the material aligned perpendicular to the field lines, highlighting the oppositional nature of the force.[12] Throughout the mid-19th century, Faraday and contemporaries like Julius Plücker and John Tyndall expanded these findings by testing hundreds of substances with improved electromagnets, clearly distinguishing diamagnetic materials—those repelled by magnets, such as bismuth, copper, and water—from paramagnetic ones attracted to the field, like platinum and aluminum.[3] This classification relied on precise measurements of deflection under controlled conditions, establishing diamagnetism as a fundamental, albeit weak, response inherent to all matter not exhibiting stronger magnetic behaviors.[13] Early detection of diamagnetism posed significant challenges due to its feeble intensity, often orders of magnitude weaker than paramagnetic or ferromagnetic effects, necessitating electromagnets capable of producing fields far stronger than those from natural lodestones or early permanent magnets.[3] Additionally, observations were frequently confounded by competing influences, such as electrostatic attractions between charged surfaces or gravitational settling, which could mimic or obscure the subtle magnetic repulsion in unrefined setups.[3] These difficulties delayed widespread recognition until Faraday's rigorous isolation of the phenomenon in 1845.[12]Theoretical Foundations
Pre-quantum theoretical attempts to explain diamagnetism began with Michael Faraday's classical views in the mid-19th century, where he conceptualized it as an intrinsic property of matter arising from the interaction of magnetic fields with atomic structures, though without a detailed mechanism.[14] James Clerk Maxwell advanced this in the 1860s and 1870s through his molecular vortex model, proposing that diamagnetism results from induced currents in hypothetical molecular "vortices" or loops of ether, which generate opposing magnetic moments to an applied field.[15] These classical models, while intuitive, failed to quantitatively predict the observed weak susceptibility, as later highlighted by the Bohr-van Leeuwen theorem, which demonstrated that classical statistical mechanics cannot account for any permanent magnetism, including diamagnetism. The transition to quantum theory was bridged by Paul Langevin's 1905 classical derivation, which treated electrons as bound particles in circular orbits around atomic nuclei and showed that an external magnetic field induces a Larmor precession of these orbits, producing a net magnetic moment opposing the field and yielding a diamagnetic susceptibility proportional to the square of the atomic number.[16] This precursor model provided the first quantitative expression for diamagnetic behavior in atoms with closed shells, serving as a conceptual foundation despite its classical assumptions. In the 20th century, quantum mechanics confirmed and refined these ideas, resolving diamagnetism through the Larmor precession of electron wavefunctions or angular momenta in a magnetic field, where the precession frequency is given by the Larmor frequency, leading to an induced orbital moment that opposes the applied field.[14] Niels Bohr's 1913 atomic model incorporated quantized electron orbits, which naturally included diamagnetic effects via this precession, though it initially predicted paramagnetism for hydrogen that conflicted with observations, prompting further quantum developments.[17] Full quantum confirmation emerged in the 1920s with the Schrödinger equation, treating diamagnetism as an orbital response in perturbation theory.[14] Key milestones include refinements in the 1940s, such as those exploring diamagnetism in quantum many-body systems, and later identifications of diamagnetism as partly a relativistic effect arising from second-order perturbations in the Dirac equation, where the diamagnetic term "redresses" paramagnetic contributions in heavy atoms.[18] These advancements solidified diamagnetism as a universal quantum phenomenon inherent to all matter.Materials
Everyday Diamagnetic Substances
Diamagnetic substances are ubiquitous in everyday materials, exhibiting a weak repulsion from magnetic fields due to their negative magnetic susceptibility. Common examples include water, with a volume magnetic susceptibility of χ ≈ -9 × 10^{-6} (SI units), which arises from the orbital motion of its electrons opposing applied fields.[19] Bismuth stands out as one of the strongest diamagnetic metals among non-superconductors, possessing χ ≈ -1.66 × 10^{-4}, making it particularly useful in demonstrations of diamagnetic effects.[20] Graphite, a form of carbon, displays anisotropic diamagnetism, with susceptibility values around -1.6 × 10^{-5} perpendicular to its planes, attributed to its layered structure.[21] Copper, another prevalent metal, has χ ≈ -9.7 × 10^{-6}, while noble gases like helium and neon exhibit even weaker diamagnetism, with χ values on the order of -10^{-9} (SI units at STP), due to their stable atomic configurations and low density.[22] Insulators and semiconductors frequently demonstrate pure diamagnetism without significant paramagnetic contributions, as their bound electrons do not produce net magnetic moments in the absence of a field.[4] This behavior is enhanced in materials with filled electron shells, where all electrons are paired, preventing permanent magnetism and allowing only induced opposing currents.[23] For instance, noble gases and water molecules exemplify this, as their closed-shell structures lead to negligible unpaired spins. Magnetic susceptibility values for these substances are typically measured using techniques like the Gouy balance or Faraday method and compiled in standard references such as handbooks of physical constants.[24] The strength of diamagnetism, expressed as volume susceptibility χ, depends on factors like atomic density; higher density generally amplifies the effect by concentrating more inducible moments per unit volume, though molar susceptibility remains relatively constant for a given material.[25] In biological contexts, diamagnetism plays a subtle role in living tissues, primarily driven by their high water content, which imparts an overall negative susceptibility similar to pure water.[26] For example, soft tissues like muscle and the heart exhibit weak diamagnetism (χ ≈ -9 × 10^{-6}), enabling applications in magnetic resonance imaging where field distortions from tissue water are minimal but measurable.[27]| Material | Volume Susceptibility χ (SI) | Notes |
|---|---|---|
| Water | -9 × 10^{-6} | Liquid, isotropic |
| Bismuth | -1.66 × 10^{-4} | Strongest common metal |
| Graphite | ≈ -1.6 × 10^{-5} (⊥ planes) | Anisotropic |
| Copper | -9.7 × 10^{-6} | Metal, weakly diamagnetic |
| Helium (gas) | ≈ -1.0 × 10^{-9} | Noble gas, at STP |