Magnetic Hysteresis: Domains and the B-H Loop

A piece of iron is carved into tiny regions called domains, each already magnetized, but pointing every which way so they cancel out. Turn on an external field and they start to line up; turn it off and they do not all snap back, because flipping a domain takes a shove and many stay where the field left them. So the magnetization lags the field, and the iron remembers where it has been. That memory is hysteresis. Cycle the field and the magnetization traces a loop instead of a line: it keeps some magnetization at zero field (remanence, the whole reason permanent magnets exist), it takes a reverse field to wipe it out (coercivity), and the area inside the loop is energy lost to heat every cycle, which is why transformer cores are made of soft, skinny-loop iron. The scene shows the domains flipping as the field drives them; the diagnostic traces the magnetization against the field, the hysteresis loop itself.

Figure 1. Ferromagnetic hysteresis (Jiles-Atherton model). Top: magnetic domains flipping as the driving field H sweeps up and down, with the net magnetization. Bottom: M versus H tracing the hysteresis loop, marking the remanence (M at H = 0), the coercivity (H at M = 0), and the loop area (energy dissipated per cycle). Method: Jiles-Atherton ODE with the anhysteretic Langevin curve.

materialhard steel

drive5.0

WHAT TO TRY

Watch the domains near the coercive field: they hold against the reversing field, then avalanche over all at once.
Switch to soft iron: the loop collapses to a thin sliver, almost no memory and very little energy lost, ideal for transformer cores.
Switch to hard steel: a fat loop with strong remanence, the stuff of permanent magnets and fridge magnets.
Lower the drive below saturation and the loop shrinks into a minor loop nested inside the full one.