How Magnets Work at the Atomic and Quantum Level

A Refrigerator Magnet Holds Against Gravity While Earth's Entire Gravitational Field Pulls the Other Way

That simple demonstration reveals something profound about the relative strength of electromagnetic force. A small magnet sticking to a refrigerator has its electromagnetic attraction overpowering the gravitational pull of a 6 × 10²⁴ kg planet. Magnetism is not a mystery — but the full explanation requires quantum mechanics, and the quantum story is stranger than most intuitive models suggest.

Magnetism was first described systematically in ancient Greece and China, where naturally occurring magnetite (Fe₃O₄) was observed to attract iron. For millennia, the mechanism was unknown. A complete understanding only became possible after the development of quantum mechanics in the 1920s. Without quantum mechanics, there is no explanation for why iron is magnetic while aluminum is not, or why heating a magnet past 770°C destroys its magnetism permanently.

Where Magnetism Comes From: Moving Charges

Classical electromagnetism establishes that moving electric charges produce magnetic fields. In atoms, electrons produce magnetic fields in two ways:

• Orbital magnetic moment: An electron orbiting a nucleus is a current loop — a moving charge — and produces a magnetic dipole moment. For most atoms in solid materials, orbital moments cancel or are quenched by crystal field interactions.
• Spin magnetic moment: Electrons possess an intrinsic quantum property called spin — quantized angular momentum that has no classical analogue. Each electron behaves as a tiny bar magnet with a spin magnetic moment of approximately one Bohr magneton (μ_B = 9.274 × 10⁻²⁴ J/T). This spin moment is the dominant source of magnetism in iron, nickel, and cobalt.

An electron can spin "up" (parallel to an applied field) or "down" (antiparallel). By the Pauli exclusion principle, no two electrons in an atom can share all quantum numbers — in a filled orbital, one spin-up and one spin-down electron pair, and their magnetic moments cancel exactly. Magnetic atoms must have unpaired electrons.

Why Iron Is Magnetic and Copper Is Not

Iron has electron configuration [Ar] 3d⁶ 4s². By Hund's rules, electrons fill the 3d orbitals to maximize unpaired spins — iron has four unpaired 3d electrons. Each contributes roughly one Bohr magneton. Copper has configuration [Ar] 3d¹⁰ 4s¹ — a completely filled 3d shell means all 3d electrons are paired. The single 4s electron produces a tiny magnetic moment, but copper as a solid is essentially diamagnetic.

The Exchange Interaction: Quantum Mechanics Creates Order

Individual magnetic atoms do not automatically create macroscopic magnets. Thermal energy tends to randomize atomic magnetic moments. For a bulk material to be permanently magnetic, neighboring atoms must align their spins cooperatively — and sustain that alignment against thermal disruption.

This alignment is caused by the exchange interaction — a purely quantum mechanical effect arising from the combination of the Pauli exclusion principle and electrostatic repulsion. When two electrons are in the same spatial region, the Pauli principle forces them to have opposite spins (anti-symmetric spin state). This reduces their ability to exchange positions — reducing kinetic energy. Whether parallel or antiparallel spin alignment results in lower total energy depends on the specific geometry and orbital overlap of the atoms.

In iron, cobalt, and nickel, the geometry of 3d orbitals relative to interatomic distances makes parallel spin alignment energetically favorable — a positive exchange integral J > 0. This is ferromagnetism. In manganese and some oxides, J < 0, favoring antiparallel alignment — antiferromagnetism.

Magnetic Domains: Why Large Objects Aren't Always Magnetized

If exchange interactions align all spins in iron, why isn't every piece of iron a magnet? The answer is magnetic domains.

A uniformly magnetized iron sample would have a large external magnetic field, storing significant energy in that stray field. The material reduces its total energy by breaking into magnetic domains — regions where spins are uniformly aligned, but adjacent domains point in different directions. Domain walls separate them. The stray field energy saved by demagnetization outweighs the energy cost of maintaining domain walls.

• Typical domain size in iron: 1–100 µm
• Domain wall thickness: 100–300 nm (set by competition between exchange energy and magnetocrystalline anisotropy)
• Demagnetized iron: many domains, random orientations, zero net moment
• Magnetized iron: domains aligned with field grow at expense of others through domain wall motion

Permanent Magnets: Trapping Domain Alignment

A permanent magnet retains magnetization because domain walls cannot move freely — they are pinned by grain boundaries, crystal defects, or second-phase particles. Hard magnetic materials have high coercivity: they resist demagnetization. The best permanent magnets combine high remanence (magnetization after the applied field is removed) with high coercivity.

Neodymium iron boron (Nd₂Fe₁₄B) magnets, developed in 1984 by General Motors and Sumitomo, are the strongest permanent magnets known. Their maximum energy product (BH)_max — the figure of merit for magnet strength — is approximately 400 kJ/m³, compared to 8 kJ/m³ for alnico and 35 kJ/m³ for ferrite. This extraordinary performance comes from the tetragonal crystal structure of Nd₂Fe₁₄B, which creates strong uniaxial magnetocrystalline anisotropy — the crystal "wants" to be magnetized only along one axis.

The Curie Temperature: When Magnets Die

Above the Curie temperature, thermal energy overcomes exchange interactions. Atomic spins become randomly oriented, destroying ferromagnetism. The material becomes paramagnetic — weakly attracted to external fields with no spontaneous alignment. This transition is a classic second-order phase transition.

The relatively low Curie temperature of neodymium magnets (312°C) limits their use in high-temperature environments like motors in hybrid vehicles, which must operate reliably above 150°C during regenerative braking. This limitation drives ongoing research into dysprosium-doped NdFeB formulations that maintain coercivity at higher temperatures.

Quantum Magnetism in Modern Technology

Spintronics — electronics that exploit electron spin as well as charge — is built on quantum magnetic effects. Giant magnetoresistance (GMR), discovered in 1988 and awarded the 2007 Nobel Prize in Physics, arises when current flows through alternating ferromagnetic and non-magnetic layers. The electrical resistance changes dramatically with the relative spin orientation of adjacent magnetic layers. This effect enabled magnetic hard drive read heads to detect nanoscale magnetic domains — shrinking hard disk data density by a factor of 1,000 between 1990 and 2010.