the hysteresis loop
/ hiss-ter-EE-sis /
Hysteresis means the present depends on the past. Magnetize a piece of iron, then remove the field, and it does not simply forget, it stays partly magnetized. Plot the magnetic field inside the material (call it B) against the applied field driving it (call it H) as you cycle the field up, down, and back, and instead of a single line you trace a fat closed loop. That loop, the hysteresis loop, is the fingerprint of a ferromagnet and it encodes almost everything a magnet designer cares about.
Read the loop by walking around it. Start unmagnetized and raise H: B climbs steeply, then flattens out at saturation, where all domains are aligned. Now lower H back to zero: B does not return to zero but stays at a value called the remanence, the leftover magnetism that makes a permanent magnet. To kill that remaining magnetism you must reverse H to a value called the coercivity; the larger the coercivity, the harder the magnet is to demagnetize. Cycle fully and you close the loop, whose enclosed area equals the energy lost as heat each cycle.
The shape of the loop is the whole game. A tall, skinny loop with tiny coercivity and small area is a soft magnetic material: easy to flip, little wasted heat, ideal for transformer and motor cores that reverse fifty or sixty times a second. A fat, wide loop with huge coercivity and large area is a hard, permanent magnet that clings to its magnetization. So the same B-H picture, read for its width, sorts every magnet into soft or hard, and read for its area, tells you the energy cost of using it in alternating current.
Silicon transformer steel has a slim loop with coercivity around 40 A/m, while a neodymium magnet has a huge coercivity near a million A/m; both are ferromagnets but their loops could not look more different.
Loop width is coercivity (soft vs hard); loop area is the heat lost each cycle.
The loop only exists below the Curie temperature; the enclosed area is real energy lost as heat every cycle, which is why transformer designers fight to make it as thin as possible.