Every electron is a tiny magnet
In the electrical rung you asked what a material's electrons are allowed to do with their energy. Magnetism is the same cast of characters answering a different question: what do their little spins do? Every electron carries a magnetic dipole moment — it behaves like an unimaginably small bar magnet, with a north and a south. That moment comes from two sources: the electron orbiting the nucleus is a tiny loop of moving charge, which is a tiny electromagnet, and, more importantly, the electron has an intrinsic property called spin that makes it magnetic all on its own. The natural unit for this atomic-scale magnetism is the Bohr magneton, about 9.27 x 10^-24 ampere-metres-squared — roughly one electron's worth of magnet. Hold that picture: a solid is a vast crowd of these needles, and every magnetic property in this rung is a story about whether the needles cancel, wander, or lock together.
So why isn't every material magnetic? Because in most atoms the electrons pair up — two to a state, spins pointing opposite ways — and each pair's two moments cancel exactly. A filled electron shell is magnetically dead. A net atomic moment survives only when an atom has unpaired electrons left over, and that is a fussy condition met by just a few corners of the electron configuration table: chiefly the transition metals with a partly filled inner 3d shell (iron, cobalt, nickel) and the rare earths with a partly filled 4f shell. An iron atom, for instance, has about four unpaired 3d electrons, which in the metal average out to a net moment near 2.2 Bohr magnetons per atom. The valence electrons you have leaned on all ladder set bonding and conduction; here it is these deeper unpaired electrons that decide whether an atom is a magnet at all.
H, B, and M: the bookkeeping of a response
To do anything quantitative we need three symbols, and they are worth keeping straight because textbooks blur them. You apply an external magnetic field, written H and measured in amperes per metre — think of it as the field a coil produces, set by the current and the turns, nothing to do with the material yet. The material answers by developing its own magnetization M, also in amperes per metre — the density of aligned dipole moments it musters in response. The total magnetic flux density inside, the thing that actually threads the material and does work, is B = mu-0 x (H + M), measured in tesla, where mu-0 = 1.26 x 10^-6 henries per metre is a fixed constant of free space. So H is what you push with, M is how the stuff pushes back (or joins in), and B is the sum that results.
How eagerly a material responds is captured by one dimensionless ratio, the magnetic susceptibility chi = M / H — positive if the material reinforces the field, negative if it opposes it. Close cousins are the relative permeability mu-r = 1 + chi, and the permeability mu = mu-r x mu-0, which say the same thing from B's point of view: how many times more flux you get inside the material than you would in empty space at the same H. This single number sorts the whole subject. A diamagnet has chi about -10^-5 (a whisker of opposition). A paramagnet has chi about +10^-3 (a whisker of help). A ferromagnet blows both away with mu-r running from 10^3 up to 10^5. Concretely: wrap a coil around a soft-iron core with mu-r near 5000 and the flux B inside is five thousand times what the bare coil would make in air — which is exactly why every transformer, motor, and electromagnet has an iron core rather than an empty one.
Three ways to answer the field
With H, M, and chi in hand, the crowd of atomic needles sorts into three families by how they behave when a field arrives. The first is diamagnetism, which we already met: it needs no pre-existing atomic magnets at all, because the field itself induces feeble opposing moments in every atom. It is universal, always negative, and so weak it is only ever noticeable when nothing stronger competes — as in a graphite flake or a frog that can be floated in a strong enough field. The second is paramagnetism, the response of a material whose atoms do carry permanent moments from unpaired electrons, but whose moments sit loose and independent. Apply a field and they nudge partway into line; remove it and they instantly scatter back to random. It is a positive but small response, and it fights a constant enemy — heat.
That enemy is worth naming. In a paramagnet the atomic moments would love to line up with the field, but thermal agitation — the random jostling every atom suffers above absolute zero — keeps knocking them out of formation, like trying to keep a field of flags pointing one way in a gusty wind. The stronger the field and the colder the material, the better the alignment, but at room temperature only a tiny fraction ever line up, which is why chi is so small. Aluminium, titanium, and even the oxygen in the air are paramagnetic. Then comes the third family, the one that changes everything: ferromagnetism. Here the atomic moments do not merely nudge into partial alignment under a field — they snap into full, parallel alignment all by themselves, with no field applied, and they hold it. Only a handful of elements do this at room temperature: iron, cobalt, nickel, and gadolinium. Their response dwarfs the others by a factor of a million. Something extra must be forcing those needles together, and it is not ordinary magnetism.
THE MAGNETIC RESPONSES (chi = magnetic susceptibility = M / H)
type sign of chi size where it comes from example
------------ ----------- ----------- -------------------------- ------------
diamagnetic - ~1e-5 (tiny) field-induced opposing loops copper, water
paramagnetic + ~1e-3 (tiny) loose unpaired moments, half- aluminium, O2
aligned, fought by heat
ferromagnetic + ~1e3 to 1e5 exchange LOCKS moments iron, cobalt,
(enormous) parallel with NO field nickel
ferrimagnetic + large unequal antiparallel moments magnetite,
that don't fully cancel ferrites
Only ferro- and ferrimagnets are 'magnetic' in the everyday sense (fridge, compass, motor).The exchange interaction: why iron is special
The tempting guess is that the atomic magnets in iron simply pull each other into line by ordinary magnetic force, the way two compass needles brought close will swing to agree. That guess is wrong, and beautifully so. If you calculate the magnetic force between neighbouring atomic moments, it is far too weak — a hundred times too weak — to hold them aligned against room-temperature thermal jostling. Ordinary magnetism would give up its ordering well below the temperature of liquid nitrogen. The real cause is quantum-mechanical and goes by the name of the exchange interaction. It springs from the Pauli exclusion principle combined with the ordinary electrostatic repulsion between electrons: in a few elements, at just the right interatomic spacing, it turns out to cost less energy for neighbouring electron spins to point the same way than opposite ways. Nature slides downhill to that lower energy, and the spins line up.
This is the honest heart of ferromagnetism, and it is worth savouring the irony: the force that makes iron magnetic is essentially electrostatic, wearing a magnetic mask. Only iron, cobalt, and nickel (and a couple of rare earths) have their 3d electron shells and atomic spacing tuned so this exchange favours parallel alignment; nudge the spacing wrong and it flips to favour antiparallel, which is why manganese, a near neighbour on the periodic table, is not ferromagnetic. Where it does win, the consequence is dramatic: within a small region every atomic moment locks parallel to its neighbours, and the material reaches its saturation magnetization — the maximum M it can possibly have, with every needle aligned — spontaneously, at zero applied field. For iron that saturation is about 1.7 x 10^6 amperes per metre. This is a magnet built from the inside, by quantum mechanics, not by any field you supplied.
Which raises the puzzle that the next two guides exist to solve. If every iron crystal is spontaneously saturated, why doesn't a fresh iron nail stick to your fridge on its own? The answer is that a bulk piece of iron does not magnetize as one block. It splits into many small magnetic domains, each one internally saturated but pointing a different way, so that from the outside their fields cancel and the nail looks unmagnetized. Applying an external field does not create magnetism from nothing — it merely persuades the favourably-oriented domains to grow at the expense of the others, and swings the rest into line. Because the domains do not fully spring back when the field is removed, the material remembers — and that memory, traced out as you cycle the field, is the hysteresis loop. That loop, and the domains behind it, are exactly where guide 2 begins.
Ferrimagnetism, the ferrites, and the Curie temperature
There is a fourth response, and it is the reason your microwave oven and your radio antenna work. In some compounds the exchange interaction makes neighbouring moments line up antiparallel — pointing opposite ways — which by itself would cancel to nothing. But if the two opposing sets of atoms are unequal in strength, they do not fully cancel, and a net moment survives. This is ferrimagnetism: strong magnetism assembled out of an imbalance between opposing spins. The classic material is magnetite, Fe3O4 — the original lodestone that first showed humans a compass — where iron ions on two different sites oppose but do not match. The broad family of ferrimagnetic ceramics built on this idea are the ferrite ceramics (not to be confused with ferrite the iron-carbon phase from the steel rung — same word, unrelated thing).
Why go to the trouble when iron is a stronger magnet? Because a ferrite is a ceramic, and ceramics are electrical insulators, whereas iron is a metal that conducts. When a magnetic material sits in a rapidly changing field — the core of a switching power supply, an antenna, a microwave device — a conducting core would let wasteful swirling eddy currents flow, heating it up and bleeding away energy. A ferrite carries the magnetic flux while blocking those currents cold, which is why high-frequency magnetics are almost always ferrite, not iron. The honest tradeoff: a ferrite's saturation magnetization is markedly lower than iron's, so you would not build a big 60-hertz power transformer from it. Metals for brute low-frequency flux, ferrites for clean high-frequency work — a materials-selection split you will meet again.
One more fact ties the whole picture together and sets a hard ceiling on every magnet: temperature. All this spontaneous ordering is a delicate victory of the exchange interaction over thermal agitation, and heat is on agitation's side. Raise the temperature and the atomic needles jitter harder, until at a sharp threshold called the Curie temperature the jitter finally overwhelms the exchange, the long-range alignment collapses, and the material stops being ferromagnetic — it becomes an ordinary, feeble paramagnet. The change is reversible: cool it back below the Curie point and the ferromagnetism returns. The threshold is a real material property with real numbers — iron at 770 degrees C, cobalt at 1121, nickel at 358, magnetite around 585 — and it explains why a magnet dropped in a hot enough fire goes dead, and why you cannot record data on a disk if its film runs too warm.
What magnetism is for, and the road ahead
All of engineering magnetism then splits into two camps by the shape of that hysteresis loop, and the split maps neatly onto two jobs. A soft magnetic material has a thin, narrow loop: it magnetizes and demagnetizes easily, following a reversing field with almost no lag and almost no energy lost per cycle. That is exactly what you want in a transformer or motor core, where the field flips 50 or 60 times a second and every scrap of loss becomes wasted heat — so soft iron, silicon steel, and the ferrites do that work. A hard magnetic material has a fat, wide loop: once magnetized it stubbornly refuses to let go, which makes it a permanent magnet — the pull on your fridge door, the field in a loudspeaker, the rotor of a brushless motor. Same physics of domains and exchange, opposite design goal: forget easily, or never forget.
Between those two extremes lies a third job worth a special mention, because you are almost certainly using it right now: magnetic storage. A hard-disk platter is a film of countless microscopic hard-magnetic grains, and each bit of your data is a tiny patch magnetized one way for a 1 and the other way for a 0. The grains must be hard enough that a stray field — or their own neighbours — cannot flip them and erase your files, yet not so hard that the write head cannot flip them on purpose. That razor's-edge compromise, engineered grain by grain, is one of materials science's quiet triumphs, and it is why 'hard' and 'soft' are not vague adjectives here but precisely tuned properties.
So here is the map of this rung. You now have the foundation: magnetism starts at the electron, the response is measured by chi and mu, and the everyday magnets are the ferro- and ferrimagnets whose spins are locked by the exchange interaction until heat breaks them at the Curie point. Guide 2 builds the domains and the hysteresis loop into a real, quantitative picture; guide 3 turns that into the practical soft-versus-hard divide and the temperature limits. Then guides 4 and 5 pivot to the other great functional family of this rung — optics — where the very same theme returns in a new key: a material's behaviour written by what its electrons are allowed to do, now expressed as refraction, colour, luminescence, the laser, and the optical fibre that carries the internet. Function beyond strength, in two flavours: magnetic and optical.