Magnetic hysteresis

Ferromagnetic domains

A ferromagnet like iron is not uniformly magnetized. Instead, it is divided into magnetic domains — microscopic regions where the atomic magnetic moments are aligned in the same direction. Different domains point in different directions, so the net magnetization of an unmagnetized piece of iron is nearly zero. The boundaries between domains are called domain walls, thin transition regions where the magnetization rotates smoothly from one orientation to another.

The hysteresis loop

When you apply an external magnetic field H to a ferromagnet, domains aligned with the field grow at the expense of those opposed to it. Domain walls move, and some domains rotate their magnetization toward the field direction. If you increase H enough, all domains align: saturation. Now reduce H back to zero. The magnetization does not retrace its original path. Some domain wall motion is irreversible — walls get pinned on crystal defects and grain boundaries. The magnetization that remains at H = 0 is the remanence B_r. To force the magnetization back to zero, you must apply a reverse field: the coercivity H_c. Sweep the field through a full cycle and the B-H curve traces a closed loop — the hysteresis loop.

Remanence and coercivity

These two numbers characterize a magnetic material. Remanence is the residual flux density when the external field is removed — it measures how well the material retains its magnetization. Coercivity is the reverse field needed to demagnetize the material — it measures resistance to demagnetization. Soft magnetic materials like annealed iron have low coercivity (easy to magnetize and demagnetize, useful for transformer cores). Hard magnetic materials like alnico or rare earth magnets have high coercivity (they make good permanent magnets). The area enclosed by the hysteresis loop equals the energy dissipated per cycle — lost as heat in the material.

Soft iron vs hard steel vs rare earth

Soft iron has narrow hysteresis loops: low coercivity, low remanence, low energy loss. This makes it ideal for applications where the field must change rapidly, such as transformer cores and electromagnet yokes. Hard steel has wider loops: higher coercivity means the material resists demagnetization, useful for permanent magnets in motors and speakers. Rare earth magnets (neodymium, samarium-cobalt) have the widest loops of all: enormous coercivity and remanence, producing the strongest permanent magnets available. The trade-off is brittleness and cost.

Energy loss and Barkhausen noise

As domain walls move through a real material, they do not glide smoothly. They jump from one pinning site to the next in discrete steps, producing tiny bursts of magnetization change called Barkhausen noise. If you wrap a coil around the material and listen through an amplifier, you can literally hear the domain walls snapping free. Each jump dissipates energy. The total energy lost per hysteresis cycle is proportional to the area of the B-H loop — this is why transformer designers obsess over minimizing loop area, and why soft magnetic materials are so important in electrical engineering.