The coercive field, $ H_{c}$, is the field at which the remanent magnetisation is reduced to zero. This can vary from a few Am for soft magnets to 10$ ^{7}$Am for hard magnets. It is the point of magnetisation reversal in the sample, where the barrier between the two states of magnetisation is reduced to zero by the applied field allowing the system to make a Barkhausen jump3.3 to a lower energy. It is a general indicator of the energy gradients in the sample which oppose large changes of magnetisation.

The reversal of magnetisation can come about as a rotation of the magnetisation in a large volume or through the movement of domain walls under the pressure of the applied field. In general materials with few or no domains have a high coercivity whilst those with many domains have a low coercivity. However, domain wall pinning by physical defects such as vacancies, dislocations and grain boundaries can increase the coercivity.

Figure 3.5: Shape of hysteresis loop as a function of $ \theta _{H}$, the angle between anisotropy axis and applied field $ H$, for: (a) $ \theta _{H} = 0^{\circ }$, (b) $ 45^{\circ }$ and (c) $ 90^{\circ }$.

The loop illustrated in Figure 3.3 is indicative of a simple bistable system. There are two energy minima: one with magnetisation in the positive direction, and another in the negative direction. The depth of these minima is influenced by the material and its geometry and is a further parameter in the strength of the coercive field. Another is the angle, $ \theta _{H}$, between the anisotropy axis and the applied field. Figure 3.5 shows how the shape of the hysteresis loop and the magnitude of $ H_{c}$ varies with $ \theta _{H}$. This effect shows the importance of how samples with strong anisotropy are mounted in a magnetometer when comparing loops.

Dr John Bland, 15/03/2003