# Level 1. Qualitative understanding.

Magnetic domains are areas with homogeneously distributed magnetization vector inside. The domains existence was proved by many experiments. But what is the reason for domain appearance in a sample? Domains appear to minimize the total system energy. Fig. 1 shows qualitative mechanism of the domain formation. As you know a magnetic arrow always tries to orient itself parallel to magnetic force lines (like a compass arrow in the magnetic field of the Earth). Let two magnetic arrows be parallel each other. This is an unstable configuration because the magnetic lines from the left arrow are trying to reorient the right arrow to the opposite direction. Obviously, two antiparallel magnetic arrows have less energy than those for parallel orientation. In a homogenously magnetized film the positive and negative magnetic poles (charges) distributed on the different film surfaces (top and bottom). However, similar to the two parallel oriented magnetic arrows, the given magnetic pole configuration is unstable. In such a case the system is searching ways to reach a more stable magnetic pole distribution. The example of the two arrows show us that a state with spatially remixed magnetic poles has a lower energy than the homogeneous one. This implies that in order to reach equilibrium the film should somehow redistribute its magnetic poles, for example, as it is shown in Fig.1d where several magnetic domains are shown. Thus, magnetic domains appear to decrease the sample energy associated with the magnetic charges on the film surfaces. This energy is known as the magnetostatic energy. In Fig.1 you can see the boundaries between two neighboring domains. Such a boundary has finite energy and width (typically hundreds of nanometers) and represents a domain wall – area in which the magnetization vector continuously rotates between its directions in the neighboring domains. The adding a domain wall into the film increases its total energy. The spatial period of domains is fixed by the competition between decreasing of the magnetostatic energy and increasing of so-called the domain wall energy. In zero filed case the sizes “up” and “down”-magnetized domain are the same. So, the film magnetization (the mean film magnetic moment) is zero. This is a demagnetized state of the film. Applying an external magnetic field parallel to the film normal one can change ratio between up and down-domains as well as their period. The applied filed increases the domains with the parallel magnetization orientation while the domains with the opposite magnetization are squeezed (see the Animation).. As the field increases the film magnetization grows and finally reaches the saturate state (homogenously magnetized state or monodomain state). The magnetic field strength at which the saturation reaches is named as the saturation field. In the next experimental task you can observe the domain evolution with changes of the applied magnetic field and determine by eye the saturation field.

Fig 1.1 Qualitative picture explaining mechanism domain formation (see text). There are different conventions : “+” means “N” – north magnetic pole; “-” means “S” – south magnetic pole.