Hysteresis

Hysteresis is the effect where the magnetisation of a ferromagnetic material is not exactly proportional to the external magnetic field and depends on the magnetic pre-treatment of the material. This means that the magnetisation of an object containing iron, for example, does not double when the external magnetic field is doubled. Ferromagnetic materials, in particular, remain slightly magnetised when the external magnetic field is completely switched off. This remaining magnetisation is referred to as remanence.

The magnetisation of a ferromagnet initially increases with the external magnetic field. If the external magnetic field is reduced, the magnetisation also decreases again. However, this process is slower than the previous increase in magnetisation, so that magnetisation (remanence) remains even when the magnetic field is completely switched off. This non-proportional relationship is a certain "lagging" of the magnetic flux density behind the magnetising field strength. The term hysteresis comes from the Greek ηψστερoσ (hysteros = behind).

Hysteresis curve for ferromagnetic materials

A mathematical curve that indicates the respective magnetisation as magnetic flux density B with a certain external magnetic field H is called a hysteresis curve (see illustration).

Hysteresis loop = hysteresis curve

In scientific literature, the terms 'hysteresis curve' and 'hysteresis loop' refer to the same phenomenon observed in all ferromagnetic materials and other physical systems. It is generally understood to be the delay in the magnetisation of a material in relation to the applied magnetic field.

However, this delay is not meant in terms of time, but in terms of the achieved strength. If the magnetic field is varied, the magnetisation lags slightly behind the mathematically achievable value, which is shown in a diagram as a loop (illustration). This hysteresis loop is an important concept in materials science, as it provides insights into the magnetic properties and energy losses of the material.

The hysteresis curve is different for different materials and only occurs with ferromagnetic materials. A magnetically soft material is characterised by the hysteresis curve shown in the figure on the left, a magnetically hard material by the hysteresis curve on the right.

The area enclosed by the hysteresis curve has the dimension of an energy (The energy product for example, is the product of magnetic field H and magnetic flux density B, just as the area of a rectangle is the product of width and length). The area enclosed by the hysteresis curve is precisely the energy per unit volume of the magnet that must be expended during a magnetisation cycle from the positive saturation flux density B_S to the negative saturation flux density –B_S and the subsequent return path from –B_S to B_S. This energy is released as heat during the magnetisation process. This energy is greater for magnetically hard materials than for magnetically soft materials. The hard materials are respectively more resistant to small disturbances of the magnetisation caused by external magnetic fields, heat or impacts and are well suited as magnetic materials for permanent magnets. Soft magnetic substances are used for transformers, as changing magnetisation consumes little energy.

The initial magnetisation curve

In the illustration on the left, the red curve is an example showing the course of the magnetic flux density in a material that is not yet magnetised. It is also known as the initial magnetisation curve or 'virgin' curve.

Here, the magnetic flux density and thus also the magnetisation M of the material is approximately linear to the external magnetic field H. The formula is: M=(μ-1)•H, whereby μ denotes the magnetic permeability.

What happens to the magnetic field inside the material?

The magnetic field inside the material is the sum of the external magnetic field H and the magnetisation of the material M.

If the object is already magnetised, a magnetic field H, which is directed in the opposite direction to the magnetisation of the object, initially causes a weakening of the existing magnetisation. Only from the so-called coercive field strength H_c does magnetisation occur parallel to the external magnetic field, i.e. a magnetisation reversal. The new magnetisation increases non-linearly up to the saturation field strength B_S. If the external magnetic field is then reduced again, the magnetic flux density in the material decreases more slowly than it previously increased. And ultimately, the remanence B_R remains.

The physical basis of hysteresis

The physical basis of hysteresis lies in the existence of electron spins as elementary magnetic moments of ferromagnetic substances. The strong magnetisation of these substances in external magnetic fields occurs because the magnetic moments align themselves in an external magnetic field and are thereby stabilised by the exchange interaction. The aligned magnetic moments turn the ferromagnetic material itself into a magnet.

At the saturation field strength and the associated saturated magnetic flux B_S, all magnetic moments are aligned in parallel. This state is referred to as magnetic saturation.

After alignment, the magnetic moments of the electron spins are in mutual exchange interaction. The energy of this interaction must be expended in order to cancel the magnetisation of a material again, i.e. to destroy the alignment of the stabilised electron spins. This means that the magnetisation decreases more slowly than it was created because the magnetic moments of the sample stabilise each other. It takes energy to reverse this stabilisation. If the exchange interaction is large, the hysteresis curve covers a large area and we speak of magnetically hard materials.