ferromagnetism

Ferromagnetism is the property of iron and a handful of other materials that lets them become permanent magnets: below a certain temperature their internal magnetism switches on spontaneously and stays on, with no applied field needed to sustain it. The fridge magnet, the compass needle, and the data on a hard disk all rest on the same quiet miracle, countless atomic spins choosing, of their own accord, to point the same way.

Below the Curie temperature T_c, the electron spins in a ferromagnet align spontaneously, producing a net magnetization even when no external field is applied; this is a textbook case of spontaneous symmetry breaking, the material picking a direction and thereby breaking rotational symmetry. The origin is deeply quantum: the alignment is driven by the exchange interaction, a joint consequence of the Pauli exclusion principle and Coulomb repulsion, which makes parallel-spin configurations lower in energy. The Heisenberg model captures this as H = -J sum over neighbours of S_i . S_j, where a positive coupling J favours parallel alignment. Above T_c thermal agitation overwhelms the ordering and the material becomes an ordinary paramagnet, its susceptibility following the Curie-Weiss law. Real ferromagnets break into magnetic domains, and moving the domain walls under an applied field produces the hysteresis loop that gives permanent magnets their memory.

Ferromagnetism powers electric motors, generators, transformers, and magnetic data storage, and it serves as the classic laboratory for the physics of phase transitions, the Ising and Heisenberg models, Landau theory, and critical phenomena. The single most important honesty is about the cause: the spins align because of the electrostatic exchange interaction, not because of the magnetic dipole-dipole forces between them, which are thousands of times too weak to hold magnetic order together at room temperature.