The hysteresis loop

The hallmark of a magnetic system is the hysteresis loop. This is traditionally represented graphically as the overall magnetisation of the sample against some applied magnetic field. The value of the applied field where the loop crosses zero magnetisation is known as the coercive field $H_c$ or $B_c$, and this therefore represents the amount of applied field required to reverse the magnetisation direction of the magnet. The remanent magnetisation $M_r$ is the magnetisation which remains when the applied field is reduced to zero. $H_c$The coercive field i.e. the applied field where the overall magnetisation of a sample is zero $B_c$The coercive field i.e. the applied field where the overall magnetisation of a sample is zero ( $B_c=\mu_0H_c$) $M_r$The remanent magnetisation i.e. the magnitude of the magnetisation of a sample when the applied magnetic field is zero

Comparing the hysteresis loops, such as those in figure 2.10, of a soft and a hard magnet, one can make the observation that the softer magnet will have a narrow hysteresis loop, i.e. the applied field necessary to reverse the magnetisation is relatively low, and the hard magnet will possess a comparatively wide hysteresis loop.

The point at which the overall magnetisation of a sample can no longer be increased (as all the magnetisation is pointing utterly in a single direction) -- the saturation point or $M_s$ -- is identified as a plateau at the extremes of applied field in a hysteresis loop. $M_s$The saturation point i.e. the magnitude of the maximum possible magnetisation of a sample

Also one should note that the area underneath the hysteresis loop is equivalent to the energy which, when the field is reversed, is converted into heat.

For the long-term storage of data, it is desirable to have a material with a wide hysteresis loop, and therefore a large coercive field, as this makes it more difficult for the said material to lose its magnetisation state. A narrow hysteresis loop is a characteristic beneficial for applications such as recording heads, as in these temporary magnetisation promotes easy switching between magnetisation states. The ideal hysteresis loops for applications in magnetic media can be seen in figure 2.11.

Figure 2.10: Two typical hysteresis loops -- the left loop shows some permanently magnetic material, the right loop a softer magnet. The solid blue line indicates reducing field, the dashed red line indicates increasing field

Figure 2.11: Magnetic recording ideals. A square loop with a high coercivity is good for the long-term storage of data; an infinitely narrow loop with diagonal characteristics is desirable for the field switching required of read heads in magnetic media applications