The loop's shape is the fork in the road
Guide two built the hysteresis loop out of domains: as you sweep the applied field H up and down, the magnetization B does not retrace its path — it lags, tracing a closed loop instead of a line. Two numbers name that loop. The coercivity Hc is the reverse field you must apply to knock B back to zero — a measure of how stubbornly the material clings to its magnetization. The remanence Br is the magnetization the material keeps at H = 0, once you switch the field off. Everything a magnet is good for is written in those two numbers, and in the fatness of the loop between them.
Here is the fork. A tall, skinny loop — tiny Hc, upright sides — is a soft magnet: it flips its magnetization with almost no push, and the area enclosed by the loop (which is the energy dumped as heat each time you cycle it) is small. A fat, square loop — huge Hc, wide as a barn door — is a hard magnet: it clings to its magnetization and refuses to be reversed, and the enclosed area is large. Same underlying physics from guide two — domains and the walls between them — but the two loop shapes serve opposite jobs. And the gap is not subtle: a soft nickel-iron alloy has Hc around 1 A/m, while a hard neodymium magnet has Hc around 1,000,000 A/m. A factor of a million separates the two families.
Soft magnets: the skinny loop that runs the grid
A soft magnetic material is for anything whose magnetization must flip back and forth, over and over, at speed: the iron core of a transformer, the stator of every motor and generator, the core of an inductor. Every cycle of the alternating current drags the material once around its loop, and the loop's area is heat left behind in the iron — the hysteresis loss. At 50 or 60 hertz that is fifty or sixty trips around the loop every second, so a fat loop would cook the transformer. The whole design goal is therefore a loop as skinny as possible (low Hc) and as tall as possible for a given push (high permeability — a lot of B for a little H).
How do you get a skinny loop? You make the domain walls glide effortlessly — and this is the beautiful inversion of everything from the mechanical rungs. The very same defects that pin a dislocation and strengthen a metal — dissolved impurity atoms, a grain boundary where two crystal patches meet crooked, tangles left by cold work — also pin the domain walls and make the material magnetically hard. So to make iron magnetically soft you do the exact opposite of strengthening it: you purify it and you anneal it, growing big clean grains so the walls have nothing to snag on. Magnetically soft iron is metallurgically the same recipe as mechanically soft iron — mobile walls and mobile dislocations both come from a clean, well-annealed crystal.
But hysteresis loss is only half the enemy. A transformer core is metal, and a changing B field induces swirling eddy currents in that metal — circulating loops of current that dump I-squared-R heat all on their own, quite apart from the loop area. Engineers fight eddy currents two ways. First, add about 3 percent silicon to the iron, which raises its resistivity several-fold and chokes those currents — that is 'electrical steel' or silicon steel. Second, build the core not from a solid block but from a stack of thin, varnish-insulated laminations, so the eddy loops are broken into small, feeble ones. A last refinement exploits anisotropy: 'grain-oriented' steel is rolled so the grains' easy magnetization axis lines up with the flux, letting the walls sweep even more freely. (The faint 50 Hz hum of a transformer is the laminations physically twitching as the domains reorient — magnetostriction, the sound of soft magnetism at work.)
Hard magnets: the fat loop in your pocket
A hard magnetic material, or permanent magnet, wants the opposite of everything above. It must hold its field with no power source, forever, and resist being wiped out by stray fields, by its own reverse (demagnetizing) field, and by heat. So you want a huge Hc (fiercely hard to reverse) and a high Br (a strong field kept at H = 0). The single figure of merit that captures both is the maximum energy product, written (BH)max — roughly the biggest B-times-H rectangle you can fit under the second-quadrant curve, and a direct measure of the magnetic energy the material can store per unit volume. A bigger (BH)max means a smaller, lighter magnet does the same job.
The trick to a hard magnet is to make the domain wall not move — to forbid the very glide that soft magnets crave. Two routes do it. One is high magnetocrystalline anisotropy: pick a crystal whose magnetization overwhelmingly prefers one axis, so reversing it means dragging the moment through a costly hard direction — this is the secret of the rare-earth compounds like Nd2Fe14B and SmCo, whose anisotropy is enormous. The other is to make the grains so small they cannot even hold a domain wall — single-domain particles — so the only way to reverse one is to rotate its whole moment coherently against that stiff anisotropy, which takes a ferocious field. Both routes pin the magnetization in place; both make the loop fat and square.
The history of permanent magnets is a climb up the energy-product ladder: from carbon-steel magnets (weak), to Alnico in the 1930s (strong Br and a very high Curie point, but modest Hc), to cheap ceramic ferrites in the 1950s, to SmCo in the 1970s, to the reigning champion Nd2Fe14B in 1984. The table below lines the families up. Notice the honest sting in its last row: neodymium is by far the strongest magnet ever made, yet it has the lowest Curie temperature of the lot — only about 310 degrees C — so it fades fastest when it gets hot, and a warm motor or generator often has to fall back on pricier SmCo (or NdFeB doped with dysprosium) instead. Strongest is not the same as most robust.
SOFT vs HARD -- the loop's width (Hc) is the whole difference
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Hc (A/m) B_sat (T) (BH)max Curie Tc
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soft Ni-Fe permalloy ~ 1 ~ 0.8 (not the goal) ~ 450 C
soft Fe-3%Si steel ~ 40 ~ 2.0 (not the goal) ~ 745 C
soft Mn-Zn ferrite ~ 20 ~ 0.4 (not the goal) ~ 200 C
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hard Alnico ~ 50,000 ~ 1.2 ~ 45 kJ/m^3 ~ 860 C
hard Ba/Sr ferrite ~ 250,000 ~ 0.4 ~ 30 kJ/m^3 ~ 450 C
hard Nd2Fe14B ~ 1,000,000 ~ 1.3 ~ 350 kJ/m^3 ~ 310 C
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soft -> hard is a MILLION-fold jump in coercivity Hc.
note Nd2Fe14B: the STRONGEST magnet, yet the LOWEST Curie Tc
-> it loses its grip fastest when hot.Ferrimagnetism and the ferrites: magnets that don't conduct
So far every magnet has been a metal. But there is a whole ceramic branch, and it works by a subtler mechanism than plain ferromagnetism. In a ferromagnet the exchange interaction lines every atomic moment parallel. In these oxides the crystal has two interpenetrating sublattices whose moments are forced antiparallel — pointing opposite ways — but the two sublattices carry unequal moments, so they do not cancel. A net magnetization survives. That is ferrimagnetism: weaker overall than iron, because much of the moment is spent cancelling itself, but genuinely and permanently magnetic. Magnetite, Fe3O4 — the ancient lodestone that pointed the first compasses — is the archetype.
Why go to this trouble when iron is stronger? Because these ferrites are ceramic oxides, and unlike metallic iron they are electrical insulators — a large band gap means almost no free electrons. No free electrons means no eddy currents. That single fact lets a ferrite core work at high frequency, up in the megahertz, where a solid metal core would drown in eddy-current heat. So soft Mn-Zn and Ni-Zn ferrites are the core material of nearly every switching power supply, RF inductor, and antenna rod — including that little cylindrical lump moulded around your laptop charger cable. And hard ferrites (barium or strontium) are the cheap, black, rust-proof magnets in loudspeakers and on your refrigerator: feeble compared to neodymium, but almost free and effectively eternal.
The Curie temperature: where magnetism simply switches off
Every ferromagnet and ferrimagnet exists only because the exchange interaction is strong enough to align neighbouring moments against the constant thermal jostling that tries to randomize them. Heat the material and you strengthen the jostling. At a sharp threshold — the Curie temperature Tc — thermal agitation wins outright, the long-range alignment collapses, and the material abruptly becomes an ordinary, feeble paramagnet. Iron loses its ferromagnetism at 770 degrees C, cobalt at about 1120, nickel at only 358, magnetite at about 585. Above Tc there are no domains, no remanence, no permanent magnet — just weakly responsive paramagnetic atoms.
Two honest points. First, this is not melting: at the Curie temperature the crystal lattice is perfectly intact — nothing has moved, only the magnetic ordering has vanished — and it is fully reversible, so cooling back below Tc restores the ferromagnetism completely. Tc is a real material property, set by the strength of the exchange coupling, as fixed for a material as its melting point. Second, a magnet weakens long before it reaches Tc: a permanent magnet loses a fraction of a percent of its strength for every degree of warming, which is exactly why the low-Tc neodymium magnet is the wrong choice for a hot motor and high-Tc Alnico or SmCo is worth its higher price.
The Curie point even does housework. The classic electric rice cooker switches itself off with pure Curie physics: a permanent magnet is held against a little slug of a ferromagnetic alloy whose Tc is tuned to just above the boiling point of water. While there is still water in the pot, evaporation pins the temperature near 100 degrees C and the slug stays magnetic, holding the switch closed. The instant the water boils dry the temperature shoots upward, the slug passes its Curie point, its magnetism vanishes, the magnet lets go, and a spring flips the cooker to 'keep warm'. A whole appliance built on the fact that magnetism turns off at a temperature you can choose.
Magnetic storage: writing bits into remanence
Pull all these threads together and you get the hard disk drive. A platter is a film of countless tiny hard-magnetic grains. To write a bit, the head applies a strong local field that sets one small patch's magnetization one way (call it 1) or the other (0); remove the field and remanence holds that state — the bit survives for years with no power, because that is what a hard magnet does. To read, the head flies over and senses the fringing field of each patch. The patch must be magnetically hard — high Hc — so a stray field or its neighbour cannot flip it and corrupt the data, yet it must still be writable by the finite field a real head can produce. That is a genuine tension: too soft and it self-erases, too hard and you cannot write it.
Push storage density up by shrinking the grains and you slam into a wall. A grain's resistance to flipping is its anisotropy energy, roughly K times V — the anisotropy constant times the grain's volume. Shrink V far enough and eventually ordinary thermal energy, kT, is enough to flip the grain all by itself: the bit spontaneously scrambles and the data rots. This is the superparamagnetic limit, and it sets a floor on how small a stable grain can be. The escape is to switch to a material with a much larger K (like iron-platinum), so a tiny grain still stays put — but that huge anisotropy is exactly what makes the field needed to write it impossibly large. Storage engineers are trapped between thermal stability and writability.
And here the whole guide closes its own loop, because the escape route is the Curie temperature. Heat-assisted magnetic recording (HAMR) uses a tiny laser to warm the target spot for a few nanoseconds to near its Curie point, where its coercivity briefly collapses — soft enough for a modest head field to write it. Then the spot cools in nanoseconds, its coercivity slams back up, and the bit is locked hard against thermal erasure. Coercivity and remanence, hard versus soft, the Curie temperature — the same small handful of ideas from this guide, now cooperating to pack tens of terabytes onto a platter. Read the shape of the loop, and you have read the whole engineering story.