Section 1.5.4.1. 180° domains

Neither symmetry nor energy considerations can determine the alignment of the magnetization vector in a non-chiral easy-axis magnetic (of ferro- or antiferromagnetic type). The vector may be aligned parallel or antiparallel to the positive direction of the z axis. Therefore, specimens of any magnetic are usually split into separate regions called domains. In each domain of an easy-axis magnetic, the vector has one of its two possible directions. Such domains are called 180° domains. Adjacent domains are separated by a domain wall, in which the magnetic moments are no longer strictly parallel (or antiparallel). As a result of this, both the exchange and the anisotropy energy rise inside the volume of the domain wall.

In ferromagnets (and ferrimagnets), the loss in the exchange and anisotropy energy in a multidomain sample is compensated by the gain in the magnetostatic energy. The existence of the domain structure is responsible for the behaviour of a ferromagnet in an applied magnetic field. There are two kinds of magnetization processes that one has to distinguish: the displacement of the domain walls and the rotation of the spontaneous magnetization vector from the easy direction to the direction of the applied magnetic field. The magnetization process will first be considered without taking the demagnetizing field into account. If the magnetic field is applied parallel to the axis of an easy-axis ferromagnet, the displacement of the domain wall will completely determine the magnetization process. If the sample contains no impurities and crystal defects, such a displacement must take place in an infinitely small magnetic field [see curve (1) in Fig. 1.5.4.1 and Fig. 1.5.4.3a]. If the magnetic field is applied perpendicular to the easy axis, the size of the domains does not change but their magnetization vectors rotate. Let us denote the spontaneous magnetization by . Then the sample magnetization M rises linearly with respect to the applied magnetic field: where is defined by relations (1.5.3.8)–(1.5.3.10). Some nonlinearity in H can arise from the fourth-order term with [see curve (2) in Fig. 1.5.4.1 and Fig. 1.5.4.3c]. When , the magnetizations of all the domains are rotated by 90° and the magnetization of the sample becomes oriented along the magnetic field; its value is saturated and is equal to the spontaneous magnetization . If  K, there is an additional rise in magnetization with the magnetic field. This rise, which is called true magnetization, is relatively very small at all temperatures except for the temperature region close to the transition temperature. If the magnetic field is applied at an arbitrary angle to the easy axis, the magnetization process occurs in two steps [see curves (2) in Fig. 1.5.4.2 and Fig. 1.5.4.3b]. First, as a result of the wall displacement, the magnetization jumps to the value in a small magnetic field. Next, the rotation process follows and at the sample becomes saturated [see curves (2) in Fig. 1.5.4.2]. It is essential to take the shape of the sample into account in considering the problem of the magnetization processes in ferromagnets, as the demagnetizing field can be up to . In real materials, the displacement process is partly (at low fields) reversible and partly (at higher fields) irreversible. Therefore, complicated hysteresis processes arise in magnetizing ferromagnets.

Figure 1.5.4.1 | top | pdf | Magnetization curves of hexagonal cobalt for two main crystallographic directions: (1) and (2) .

Figure 1.5.4.2 | top | pdf | Magnetization curves of two cubic crystals (iron and nickel) for three crystallographic directions.

Figure 1.5.4.3 | top | pdf | Schematic display of the magnetization: (a) along the easy axis; (b) at an arbitrary angle to the easy axis; (c) perpendicular to the easy axis.

The problem of 180° domains in antiferromagnets is not as clear. These domains differ in the sign of the antiferromagnetic vector . This vector was defined as the difference of the vectors of sublattice magnetizations in a two-sublattice antiferromagnet, i.e. . Thus two such antiferromagnetic domains differ only by the numbering of the sites in the sublattices. Antiferromagnetic 180° domains are also called S-domains. The wall between two S-domains is schematically represented in Fig. 1.5.4.4.

Figure 1.5.4.4 | top | pdf | A 180° domain wall in an antiferromagnet.

The origin of the antiferromagnetic S-domains cannot be explained from the point of view of energy balance as in a ferromagnet. These domains give rise to additional exchange and anisotropy energies which are not compensated by a decrease of any other kind of energy. Thus the S-domain structure is thermodynamically not stable. However, experiments show that S-domains exist in most easy-axis antiferromagnets.

The formation of S-domains can be explained by assuming that when the material is cooled down to the Néel temperature, antiferromagnetic ordering arises in different independent regions. The direction of the vector in these regions is accidental. When growing regions with different directions of meet, the regular alternation of the directions of magnetic moments of the ions is broken on the border between these regions. Domain walls are created on such borders. Such domain structures can be metastable.

The existence of S-domains in easy-axis antiferromagnets was first proved in experiments in which effects that depend on the sign of were investigated. These are piezomagnetism, linear magnetostriction and the linear magnetoelectric effect. The sign of these effects depends on the sign of . We shall discuss this problem in detail in Sections 1.5.7 and 1.5.8. Later, 180° domain walls were observed in neutron scattering experiments (Schlenker & Baruchel, 1978), and the domains themselves in magneto-optical experiments (see Kharchenko et al., 1979; Kharchenko & Gnatchenko, 1981).