Ferromagnetism

The hysteresis curves for a ferromagnetic material are more complex than those for diamagnets or paramagnets. Figure 3.3 shows the main features of such a curve for a simple ferromagnet.

Figure 3.3: Schematic of a magnetisation hysteresis loop in a ferromagnetic material showing the saturation magnetisation, $M_{s}$, coercive field, $H_{c}$, and remanent magnetisation, $M_{r}$. Virgin curves are shown dashed for nucleation (1) and pinning (2) type magnets.

In the virgin material (point 0) there is no magnetisation. The process of magnetisation, leading from point 0 to saturation at $M=M_{s}$, is outlined in Figure 3.4.[8] Although the material is ordered ferromagnetically it consists of a number of ordered domains arranged randomly giving no net magnetisation. This is shown in Figure 3.4(a) with two domains whose individual saturation moments, $M_{s}$, lie antiparallel to each other.

Figure 3.4: The process of magnetisation in a demagnetised ferromagnet.

As the magnetic field, $H$, is applied, (b), those domains which are more energetically favourable increase in size at the expense of those whose moment lies more antiparallel to $H$. There is now a net magnetisation, $M$. Eventually a field is reached where all of the material is a single domain with a moment aligned parallel, or close to parallel, with $H$. The magnetisation is now $M=M_{s}\cos\theta$ where $\theta$ is the angle between $M_{s}$ along the easy magnetic axis and $H$. Finally $M_{s}$ is rotated parallel to $H$ and the ferromagnet is saturated with a magnetisation $M=M_{s}$.

The process of domain wall motion affects the shape of the virgin curve. There are two qualitatively different modes of behaviour known as nucleation and pinning,[9] shown in Figure 3.3 as curves 1 and 2 respectively.

In a nucleation-type magnet saturation is reached quickly at a field much lower than the coercive field. This shows that the domain walls are easily moved and are not pinned significantly. Once the domain structure has been removed the formation of reversed domains becomes difficult, giving high coercivity. In a pinning-type magnet fields close to the coercive field are necessary to reach saturation magnetisation. Here the domain walls are substantally pinned and this mechanism also gives high coercivity.