Ferromagnetism

Ferromagnetism is the collective quantum-mechanical behaviour that turns a pile of iron atoms into a bar magnet. In paramagnets, each atomic moment responds to the external field independently; in ferromagnets, neighbouring atomic moments talk to each other through the exchange interaction — a quantum-mechanical consequence of the Pauli exclusion principle that energetically rewards parallel spin alignment between nearby electrons. Below a critical temperature T_c (the Curie temperature, 1043 K for iron, 627 K for nickel, 1388 K for cobalt) the exchange coupling overpowers thermal randomisation, and huge collective regions of atoms align spontaneously. Above T_c, thermal motion wins and the material becomes an ordinary paramagnet.

The spontaneous alignment is local, not global. A bulk piece of iron would produce enormous external fields if every atom aligned with every other atom; instead, the material breaks up into domains, typically micron-scale regions each with uniform magnetization but pointing in different directions, so that the macroscopic average on the scale of a naked-eye sample is near zero. Apply an external field and the domains aligned with the field grow at the expense of the others — domain walls sweep across the material. The process is path-dependent: remove the field and some of the alignment persists, producing the remanence M_r that makes a magnetised nail still stick to a refrigerator. Further driving the field in the opposite direction eventually unpins the walls, and the whole curve traces out a hysteresis loop.

Ferromagnets are the strongest magnets in everyday experience. Their effective susceptibility is of order 10³–10⁶, their permeabilities are correspondingly enormous, and they can produce remanent magnetizations approaching the saturation limit, about 2 T for iron, 2.4 T for pure cobalt. They are also where twentieth-century condensed-matter physics was born: Weiss's 1907 molecular-field theory, Heisenberg's 1928 exchange-interaction paper, the 1930s domain studies by Landau and Lifshitz, and the modern micromagnetic simulations that design hard-disk heads and magnetic MRAM all come from the same continuous thread of ferromagnetism research.