Magnetism at the Particle Level

What spin really is

Electrons, protons, neutrons, and quarks all possess spin — a quantized, intrinsic angular momentum. The name is misleading: an electron is (as far as we know) point-like and doesn't "rotate" in the classical sense — there's simply no extent that could be spinning. Instead, spin is a property attached to a particle just as firmly as its mass or charge — for the electron, always exactly ±½ (in units of ħ), no matter how it's measured.

It was discovered in 1922 in the Stern-Gerlach experiment: a beam of silver atoms was sent through an inhomogeneous magnetic field. Classically, one would have expected a continuous smear, since the atoms' orientation should have been random. Instead, exactly two separate spots were observed — the first direct proof that spin (and with it the magnetic behavior of matter) is quantized and can only take two orientations relative to a field.

How spin creates a magnetic field

Because an electron is electrically charged, its spin — its intrinsic angular momentum — automatically creates a magnetic dipole moment, without anything actually moving. The strength of this moment depends on the so-called g-factor, which for the electron isn't exactly 2 but 2.00232 — the tiny deviation is a prediction of quantum electrodynamics and one of the most precisely confirmed values in all of physics.

Besides spin, the electrons' motion around the nucleus also contributes a magnetic moment (orbital magnetism) — but for most atoms, the spin contribution dominates. Whether an atom shows a net magnetic moment overall depends on how the individual electron moments add up.

Why some substances respond to magnetism, others don't

Whether an atom has a net magnetic moment is decided by the Pauli exclusion principle: two electrons in the same orbital must have opposite spin, so their moments cancel out exactly. Atoms with completely filled shells — all spins paired — show no magnetic moment externally. Atoms with unpaired electrons, on the other hand, possess a real, though usually weak, magnetic moment.

The three basic types of magnetism all build on this simple distinction:

Why iron, of all things, is ferromagnetic

An iron atom has four unpaired 3d electrons — following Hund's rule, electrons first occupy as many orbitals singly as possible before pairing up. That alone would only explain paramagnetism, which other metals show too. What's truly special is the quantum-mechanical exchange interaction between neighboring iron atoms: at exactly the atomic spacing and 3d electron configuration found in iron, it energetically favors parallel rather than antiparallel alignment of neighboring spins. Below the Curie temperature (770 °C), neighboring atoms therefore align spontaneously — with no external field at all.

A piece of unmagnetized iron nevertheless usually shows no magnetism externally, because it breaks up into many small magnetic domains (Weiss domains): within each domain, all moments are perfectly aligned in parallel, but the orientation changes randomly from domain to domain, so the contributions cancel out on average. An external field lets favorably oriented domains grow at the expense of the others (the domain walls shift) — the material becomes magnetized, and part of this alignment can persist as remanence even after the field is switched off: a permanent magnet.

What particle-level magnetism is used for in practice

From the hospital to the hard-drive — the targeted use of spin and magnetic moment of individual particles is embedded in many technologies that, at first glance, seem to have nothing to do with particle physics.