Chapter I
The Curie Point
A magnet heated red-hot stops being a magnet. In 1895 Pierre Curie measured this carefully for his doctoral thesis. Iron loses its strong magnetism abruptly at about 770 °C. Above that temperature it behaves like the many substances that are only weakly attracted to a magnet, and for those Curie found a simple rule: the magnetism induced by a field falls in proportion to the inverse of temperature. Heat jostles the atomic magnets out of line.
In 1907 Pierre Weiss explained the Curie point. Suppose each atomic magnet feels an internal field proportional to the magnetisation of its surroundings. Below a certain temperature this feedback sustains itself, and the magnets line up spontaneously. Above it, heat wins. The same kind of self-consistent argument would later become Landau's theory of phase transitions. Weiss also saw why an ordinary nail is not a magnet. It is divided into small domains, each fully magnetised but pointing in different directions. But his molecular field had to be enormous, more than a thousand tesla, far stronger than the magnetic field of any atom could be.
Chapter II
A Quantum Effect
Worse was to come. In his doctoral thesis of 1911, Niels Bohr proved that classical statistical mechanics allows no magnetism at all. In a field, electrons curve, but in thermal equilibrium their effects cancel exactly. Hendrika van Leeuwen proved the same in 1919. Magnetism, one of the oldest known forces, cannot be explained without quantum mechanics.
The electron's spin, discovered in 1925, made each electron a tiny magnet. In 1928 Werner Heisenberg found the force that aligns them. It is not magnetic at all. The exclusion principle forces two electrons with parallel spins to stay apart, and that changes their electric repulsion. So the energy of two neighbouring atoms depends on whether their spins are parallel. This exchange interaction is electric in strength, which is why it can hold spins in line at hundreds of degrees.
The exchange interaction can also favour opposite spins. Louis Néel predicted in 1936 that such materials would order with alternating magnets, showing no outward magnetism at all. In 1949 Clifford Shull confirmed it by diffracting neutrons from manganese oxide, since neutrons, unlike X-rays, feel the spins. In his Nobel lecture of 1970, Néel remarked that antiferromagnets were interesting but seemed to have no applications.
Chapter III
Frustration and Films
In some alloys the interactions are random, so no arrangement can satisfy every pair. The spins freeze into a disordered pattern, a spin glass. Sam Edwards and Philip Anderson wrote a model of this in 1975, and Giorgio Parisi solved a version of it in 1979, finding a rugged landscape of countless nearly equal frozen states. The mathematics proved useful far outside magnetism, in optimisation, in models of memory and in the theory of computation. Mathematicians took until 2006 to prove Parisi's solution rigorously.
Magnetism also became engineering at the scale of atoms. In 1988 Albert Fert and Peter Grünberg independently found that stacks of alternating iron and chromium layers, a few atoms thick, change their electrical resistance dramatically in a magnetic field. The iron layers are coupled antiparallel through the chromium, and electrons of one spin pass easily through layers magnetised one way. Within ten years the effect was reading data in hard drives, and it often used an antiferromagnet to pin one layer in place.
Chapter IV
A Closer Look: Why Magnetism Is Not Magnetic
Weiss's molecular field must be strong enough that an atomic magnet gains an energy comparable to the thermal energy at the Curie point. An electron's magnetic moment is the Bohr magneton, J/T. Setting gives a rough size for the field:
| Metal | Curie point | (meV) | Rough molecular field |
|---|---|---|---|
| Iron | 1043 K (770 °C) | 89.9 | 1,553 T |
| Cobalt | 1388 K (1115 °C) | 119.6 | 2,066 T |
| Nickel | 627 K (354 °C) | 54.0 | 933 T |
| Gadolinium | 292 K (19 °C) | 25.2 | 435 T |
These are order-of-magnitude estimates, since the exact factor depends on the atom's spin and number of neighbours. The strongest steady magnets in any laboratory reach about 45 T.
Now compare the real magnetic field one atomic magnet produces at its neighbour, about 0.25 nm away. The field of a magnetic dipole is
That is about 26,000 times too weak to explain iron. The energy is only 3.4 µeV, equivalent to a temperature of 0.04 K. If magnetic forces alone aligned the atoms, iron would be magnetic only within a few hundredths of a degree of absolute zero. The force that actually does it is Heisenberg's exchange, which is electric.
The consequence for technology is concrete. A magnetic bit is a patch of grains magnetised one way. At a storage density of one terabit per square inch, reached by hard drives in the 2010s, each bit occupies about 645 square nanometres, a square 25 nm on a side. At one gigabit per square inch, reached in the mid-1990s, the side was about 800 nm. Reading bits that small needed a sensor with a large response to weak fields, which is what giant magnetoresistance supplied.
Chapter V
Order of Every Kind
Magnetism turned out to be a laboratory for all of statistical physics. The Ising model of phase transitions is a model of a magnet, and magnets remain the cleanest test of theories of critical behaviour. Magnetic fluctuations are the leading suspect behind high-temperature superconductivity. And the search for quantum spin liquids, magnets that never order, joins the study of topological matter, where order is defined not by aligned spins but by the shape of quantum states.