The Hysteresis Loop: A Magnet's Memory

Why magnetization lags the field

A ferromagnetic material is built from microscopic domains, each already magnetized to full saturation internally but pointing in different, essentially random directions, so an unmagnetized bulk sample shows little net magnetization overall. Apply an external field H and domains whose orientation is favourable grow at the expense of their neighbours through domain-wall motion; push H higher still and remaining domains rotate to align with the field directly. Domain walls, however, do not glide freely — they catch on crystal defects, grain boundaries and impurities, and unsticking them dissipates energy. That dissipative, largely irreversible process means magnetization does not retrace the same path when the field is reduced again, and the result, plotted in the B-H plane, is an open loop rather than a single curve: the hysteresis loop.

Reading the loop: saturation, remanence, coercivity

Sweep H from a large negative value up to a large positive one and back down again, and the material traces a closed loop. Three landmarks describe it fully:

at H = ±Hmax:                B → ±Bs    // saturation — all domains aligned
at H = 0  (descending arm):  B = +Br    // remanence — leftover field-free magnetization
at B = 0  (descending arm):  H = -Hc    // coercivity — reverse field needed to erase it

Saturation is reached once every domain is aligned with the field, beyond which pushing H harder buys almost nothing more. Remanence is how strongly the material stays magnetized once the external field is switched off entirely — literally what makes a permanent magnet permanent. Coercivity is the size of the reverse field required to bring the magnetization back down to zero, a direct measure of how hard the material resists being demagnetized.

Hard versus soft magnets

Soft magnetic materials — silicon steel in a transformer core, ferrite in an inductor — have thin, narrow loops: low coercivity, easy to magnetize and demagnetize, minimal energy lost per cycle. They are chosen wherever a field alternates rapidly, in transformers, motor cores, inductors and recording heads, precisely because the material must follow the changing field without fighting it. Hard magnetic materials — neodymium, alnico, ferrite permanent magnets — have wide, fat loops: high coercivity and high remanence, strongly resisting demagnetization once set. They are chosen for permanent magnets in speakers and motors, and for magnetic recording media, precisely because the stored state needs to survive stray fields without drifting.

Hysteresis loss: the area inside the loop

Every full trip around the loop dissipates energy as heat, and the amount is exactly proportional to the loop's enclosed area in the B-H plane:

energy dissipated per unit volume per cycle = ∮ H dB     // loop area, B-H plane

total AC core loss ≈ hysteresis loss (∝ f) + eddy current loss (∝ f²)

Because this loss scales with how many times per second the material is cycled, and because it is one of two dominant loss mechanisms in an AC magnetic core (the other being eddy currents induced in the core itself), transformer and motor designers deliberately choose thin-loop, soft magnetic materials specifically to keep this area small — otherwise a device running at line frequency would waste a meaningful fraction of its power as heat, cycle after cycle, all day.

Hysteresis as a general memory phenomenon

The same lagging, path-dependent behaviour shows up well outside magnetism. Stretched rubber and metals under cyclic mechanical loading trace their own stress-strain hysteresis loops; ferroelectric capacitors show an analogous polarization-versus-field loop; even some ecological and economic models describe path-dependent behaviour using hysteresis mathematics borrowed directly from magnetism. The common signature in every case is the same: the system's state depends not just on the current input but on the whole history of inputs that got it there, usually because some internal population of microscopic elements — domain walls, dislocations, or an internal switching threshold — flips irreversibly rather than responding smoothly and reversibly to the applied stimulus.

Frequently asked questions

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