Magnetism

• 1. Introduction

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  Magnetism is one of two aspects of electromagnetism, and almost nobody who handles a magnet realizes that. The thing pinning a note to a refrigerator runs on the same physics as light itself. The source defines magnetism as the class of physical attributes that occur through a magnetic field, a field that lets objects attract or repel each other. Both electric currents and the magnetic moments of elementary particles give rise to that field. So why do only a handful of metals stick to a magnet while everything else seems to ignore it. Why does cutting a magnet in half never give you a lonely north pole. And why did it take quantum mechanics, not classical physics, to explain why iron behaves the way it does. The answers move from naturally magnetized stones in the ancient world to a phenomenon observed at 140 millikelvins in a laboratory lattice. Along the way, a Danish professor's compass needle twitches by accident, and a physicist predicts a particle that no search since 1931 has ever found.

• 2. The Stone That Pointed South

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  Lodestones, naturally magnetized pieces of the mineral magnetite, attracted iron, and ancient people noticed. The word magnet comes from the Greek term magnetis lithos, the Magnesian stone, lodestone. In ancient Greece, Aristotle credited the first scientific discussion of magnetism to Thales of Miletus, who lived from about 625 BCE to about 545 BCE. The ancient Indian medical text Sushruta Samhita describes using magnetite to draw arrows out of a person's body.

  In ancient China, the earliest literary reference appears in a 4th-century BCE book named after its author, Guiguzi. The 2nd-century BCE annals Lushi Chunqiu noted that the lodestone makes iron approach, that some force is attracting it. A 1st-century work called Lunheng, or Balanced Inquiries, gave the earliest mention of a needle being pulled, stating simply that a lodestone attracts a needle.

  Shen Kuo, the 11th-century Chinese scientist, was the first to write of the magnetic needle compass in the Dream Pool Essays. He noted that it improved navigation by employing the astronomical concept of true north. By the 12th century, the Chinese were using the lodestone compass at sea, sculpting a directional spoon from lodestone so its handle always pointed south.

  Alexander Neckam, by 1187, was the first in Europe to describe the compass and its use for navigation. In 1269, Peter Peregrinus de Maricourt wrote the Epistola de magnete, the first surviving treatise on the properties of magnets. In 1282, the Yemeni physicist, astronomer, and geographer Al-Ashraf Umar II discussed magnets and dry compasses. Leonardo Garzoni's only surviving work, written in years near 1580 and never published, became the first modern treatment of magnetic phenomena, later reworked by Niccolo Cabeo in his Philosophia Magnetica of 1629.

• 3. The Earth Is The Magnet

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  William Gilbert published De Magnete in 1600, and in it he built a small model of the planet. He called this model earth the terrella. From experiments with it, he concluded that the Earth itself was magnetic, and that this was why compasses point north. Earlier thinkers had blamed the pole star Polaris or a great magnetic island sitting on the north pole.

  Hans Christian Orsted, a professor at the University of Copenhagen, turned a lucky observation into a turning point in 1819. He noticed a compass needle twitch near a wire and realized an electric current could create a magnetic field. The episode is remembered as Orsted's Experiment. In 1820, Jean-Baptiste Biot and Felix Savart produced the Biot-Savart law, an equation for the magnetic field from a current-carrying wire.

  Andre-Marie Ampere, working around the same time, ran systematic experiments on the forces between currents. He found that the magnetic force between two DC current loops of any shape equals the sum of the individual forces between their current elements. In 1831, Michael Faraday discovered that a time-varying magnetic flux induces a voltage through a wire loop.

  Carl Friedrich Gauss hypothesized in 1835 that all magnetism arises from elementary point charges moving relative to each other. Wilhelm Eduard Weber advanced this into Weber electrodynamics. From around 1861, James Clerk Maxwell synthesized these insights into Maxwell's equations, uniting electricity, magnetism, and optics. In 1905, Albert Einstein drew on Maxwell's equations in motivating special relativity, requiring the laws to hold in all inertial reference frames.

• 4. Where Magnetism Comes From

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  Three sources give rise to magnetism at its root: electric current, the spin magnetic moments of elementary particles, and changing electric fields. In materials, the magnetic properties come mainly from the magnetic moments of atoms' orbiting electrons. The magnetic moments of atomic nuclei run thousands of times smaller, so they are negligible for magnetizing materials, though they matter enormously in nuclear magnetic resonance and magnetic resonance imaging.

  The enormous number of electrons in a material usually arranges itself so their magnetic moments cancel out. The Pauli exclusion principle pushes electrons into pairs with opposite intrinsic moments, and filled subshells carry zero net orbital motion. Even where unpaired electrons exist, their moments often point in random directions, leaving the material non-magnetic.

  Sometimes, either spontaneously or under an applied field, the electron magnetic moments line up on average. A suitable material can then produce a strong net field. Temperature works against this. At high temperatures, random thermal motion makes it harder for electrons to hold their alignment, which sets the stage for why heat can erase a magnet entirely.

• 5. The Family Of Behaviors

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  Diamagnetism appears in every material, the universal tendency to oppose an applied field and be repelled by it. Copper and carbon are diamagnetic. In a purely diamagnetic substance there are no unpaired electrons, so the effect arises from the electrons' orbital motions, shaped by the Lorentz force in accordance with Lenz's law. The Bohr-Van Leeuwen theorem shows diamagnetism is impossible under classical physics and demands a quantum-mechanical description.

  Paramagnetic materials, such as aluminium and oxygen, carry unpaired electrons free to align with an applied field, weakly reinforcing it. Ferromagnets also have unpaired electrons, but their moments line up parallel to each other even with no field applied, settling into a lowered-energy state. Only a few substances are ferromagnetic: iron, nickel, cobalt, their alloys, and some rare-earth alloys.

  Every ferromagnet has its own Curie temperature, the Curie point, above which it loses ferromagnetic properties as thermal disorder overwhelms magnetic order. Inside a ferromagnet, atoms behave like tiny permanent magnets and gather into regions of uniform alignment called magnetic domains, or Weiss domains. A magnetic force microscope can reveal the boundaries between them.

  When an external field is applied, domain boundaries shift so aligned domains grow and dominate. Remove the field and the domains may not return to an unmagnetized state, leaving a permanent magnet. When a single domain overruns all others, the material is magnetically saturated. Heat a magnetized ferromagnet to the Curie point and the domains lose their organization; cool it again and the alignment structure spontaneously returns, roughly like a liquid freezing into a crystalline solid.

• 6. Opposites And Exceptions

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  Antiferromagnets reverse the ferromagnetic picture: neighboring valence electrons' intrinsic moments point in opposite directions. When every neighbor sits anti-parallel, the net magnetic moment is zero and no field is produced. These materials are less common and mostly appear at low temperatures, and at varying temperatures they can show diamagnetic and ferromagnetic properties. Where no geometry lets every neighbor sit anti-aligned, the result is a canted antiferromagnet or spin ice, an example of geometrical frustration.

  Ferrimagnets retain magnetization with no field applied, like ferromagnets, yet their neighboring spins point in opposite directions, like antiferromagnets. The two facts coexist because one sublattice carries more magnetic moment than the opposing one. Most ferrites are ferrimagnetic. Magnetite, the first discovered magnetic substance and a ferrite, was originally believed to be a ferromagnet until Louis Neel disproved that by discovering ferrimagnetism.

  Superparamagnetism appears when a ferromagnet or ferrimagnet is small enough to act like a single magnetic spin subject to Brownian motion, responding to a field like a paramagnet but much more strongly. A Japanese physicist conceived of Nagaoka magnetism in a square two-dimensional lattice with one electron per node, where removing one electron under specific conditions minimizes the lattice energy only when all spins are parallel.

  A variation was achieved experimentally in a triangular moire lattice of molybdenum diselenide and tungsten disulfide monolayers. A weak magnetic field and a voltage produced ferromagnetic behavior when 100 to 150 percent more electrons than lattice nodes were present. The extra electrons delocalized and paired with lattice electrons to form doublons, which created localized ferromagnetic regions at 140 millikelvins.

• 7. Forces, Dipoles, And A Missing Particle

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  An electromagnet produces its field from an electric current, and the field vanishes the moment the current stops. It is usually built from closely spaced turns of wire wound around a magnetic core of iron or another ferromagnetic or ferrimagnetic material, which concentrates the flux. Its advantage over a permanent magnet is control, since the field changes quickly with the current, but it demands a continuous supply of power. Electromagnets appear in motors, generators, relays, solenoids, loudspeakers, hard disks, and MRI machines, and in industry they lift scrap iron and steel. Electromagnetism was discovered in 1820.

  The magnetic force is mediated by the field. A charged particle moving through a magnetic field feels a Lorentz force, given by a cross product, that acts perpendicular to both its motion and the field. The right-hand rule fixes the direction, reversed for a negative charge. Maxwell's equations, which reduce to the Biot-Savart law for steady currents, govern these forces, so magnetism appears wherever charged particles move.

  All known magnets are dipoles, with a north and a south pole, named because the Earth's field pulls a magnet's poles toward the north magnetic pole and the south magnetic pole. A north pole is attracted to another magnet's south pole. Cut a bar magnet in half and each piece becomes a smaller bar magnet, because its ferromagnetism comes from electrons spread evenly throughout. The two poles cannot be separated.

  A monopole would be a fundamentally different object, an isolated north or south pole carrying magnetic charge analogous to electric charge. Despite systematic searches since 1931, none has ever been observed. Paul Dirac argued in 1931 that if monopoles exist they would explain why charges come in multiples of the electron's charge. Certain grand unified theories predict monopoles as solitons, and early estimates suggested the Big Bang would have made them so plentiful and massive that they would have halted the universe's expansion, a problem that helped motivate the idea of inflation.

• 8. Relativity, Life, And Quantum Roots

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  Special relativity makes electricity and magnetism inseparable. Magnetism without electricity, and electricity without magnetism, are each inconsistent with relativity because of length contraction, time dilation, and the velocity-dependent magnetic force. A phenomenon that looks purely electric to one observer may be a mix of both to another, with the relative contributions depending on the frame of reference. Relativity mixes the two into a single phenomenon, much as general relativity mixes space and time into spacetime, and perturbations in the magnetic field propagate at the speed of light.

  Some organisms detect magnetic fields, an ability called magnetoception. Certain materials in living things are ferromagnetic, though whether this serves a function or is a byproduct of iron remains unclear. Chitons, a type of marine mollusk, make magnetite to harden their teeth, and even humans produce magnetite in bodily tissue. Magnetobiology studies the effects of fields on organisms, while biomagnetism describes fields organisms make themselves. Because water is diamagnetic and organisms are mostly water, extremely strong fields can repel living things.

  Diamagnetism, paramagnetism, and ferromagnetism can be fully explained only with quantum theory. Walter Heitler and Fritz London built a successful model in 1927, deriving how hydrogen molecules form from hydrogen atoms. Their work introduced the exchange interaction, an effect rooted in the indistinguishability of identical particles. That interaction runs stronger than electrodynamic dipole-dipole energies, roughly by factors of 100 and even 1000.

  Pauli's principle ties orbital and spin functions together: a symmetric orbital pairs with an antisymmetric spin function, and the reverse. Antiparallel spins yield antiferromagnetism in a solid and diamagnetism in two-atomic molecules, while parallel spins yield ferromagnetism in a solid and paramagnetism in gases. The parallel tendency dominates in iron, cobalt, and nickel and in some rare earths. The oxygen molecule, through its pi-orbitals, stands as an exception important for the life sciences, a paramagnetic gas where chemistry and the origin of magnetism meet.