(1) Ferromagnetic domains (regions of spontaneous magnetization) are parts of the volume of a ferromagnet that are magnetized to saturation (their linear dimensions are usually 10^-3-10^-2 cm), into which the ferromagnet divides at temperatures below the Curie point. In the absence of an external magnetic field the magnetization vectors of a domain are usually oriented in such a way that the resultant magnetization of the ferromagnetic sample as a whole is equal to zero. Domains can be observed directly (by means of a microscope) if the surface of the ferromagnet is covered with a layer of a suspension that contains ferromagnetic powder. The particles of the powder precipitate mainly at the boundaries of the domains and trace their contours. Other methods of studying domain structure, particularly the magneto-optical method, which has high resolution, are also widely used.

The division of a ferromagnet into domains is a result of the following factors. If an entire ferromagnet were magnetized to saturation in one direction, then magnetic poles would appear on its surface and a magnetic field would be created in the surrounding space. More energy is required for this than when the ferromagnet is divided into domains, a process during which there is no magnetic field outside the sample (the magnetic flux is enclosed within the sample). At constant volume and temperature, only those domain structures for which the free energy is minimal are realized in a ferromagnet.

The direction of the magnetization vectors of a domain usually coincides with the directions of the axes of easy magnetization. In this case the condition of the minimum energy of magnetic anisotropy is satisfied for the ferromagnet. If the size of the ferromagnet is reduced to some critical quantity, division into domains may become unfeasible in terms of energy, and so-called single-domain structure forms: each ferromagnetic particle is one domain. In practice this is realized in ferromagnetic powder materials and in a number of heterogeneous alloys.

(2) Ferroelectric domains are domains of homogeneous spontaneous polarization in ferroelectrics. The presence of polarization in the absence of an external electrical field (spontaneous polarization) is a distinctive feature of ferroelectrics. However, ferroelectric crystals usually are not homogeneously polarized. They are almost always divided into domains, since the multidomain state is characterized by lower energy than the single-domain state.

In neighboring domains the direction of the spontaneous polarization vector is different (Figure 1). The transverse dimensions of domains are usually of the order of 10^-5-10^-3 cm. The transitional region between domains (the domain boundary, or wall) is about 10^-7 cm wide (sometimes up to 10^-5 cm). The domain configuration depends on the dimensions and shape of the sample, on the presence of heterogeneities and crystal defects, and on the symmetry of the crystal, which determines the number of possible directions of spontaneous polarization. For example, Rochelle salt has two possible antiparallel directions, and barium titanate, BaTiO₃ (the tetragonal modification), has six directions (Figure 2).

Figure 1. Change in polarization upon passage across a domain boundary

The presence of domains essentially influences all properties of ferroelectrics, above all their electrical properties. Under the influence of an electrical field, the dimensions of opposite polarization decrease (because of the movement of domains with polarization directed along the field increase, and those of domains with opposite polarization decrease (because of the movement of the domain walls). New domains may also form and grow. The change and formation of new domains bring about the high dielectric constant, as well as the type and dimensions of the hysteresis loop, of ferroelectrics. The movement of domain boundaries is responsible for most of the dielectric losses.

Figure 2. Diagram of domains and their polarization in a tetragonal modification of BaTiO³; the symbols ⊙ and ⊕ show that the polarization is perpendicular to the plane on which they are marked and is directed as shown by the arrows on the planes

Domains can be observed and studied using various methods. The most important information on the structure of domains was obtained through optical methods, by means of a polarizing microscope. In polarized light some domains appear brighter and others darker. Domains at the surface of a crystal can be observed by the etching and powder methods. The first method uses the difference in the rates of etching, and the second uses the difference in the intensity of precipitation of particles of powder at points where domains with different polarization emerge on the surface of the crystal.

(3) Regions of a semiconductor with different specific resistance and different electrical field intensity are also called domains. A semiconductor with an N-shaped current-voltage characteristic stratifies into such domains in a sufficiently strong external electrical field.