Anti-ferromagnetism and ferrimagnetism

5.8.5 Anti-ferromagnetism and ferrimagnetism

Apart from the more usual dia-, para- and ferromagnetic materials, there are certain substances which are termed anti-ferromagnetic; in these, the net moments of neighboring atoms are aligned in opposite directions, i.e. anti-parallel. Many oxides and chlorides of the transition metals are examples, including both chromium and α-manganese, and also manganese–copper alloys. Some of the relevant features of anti-ferromagnetism are similar in many respects to ferromagnetism, and are summarized as follows:

1. In general, the magnetization directions are aligned parallel or anti-parallel to crystallographic axes, e.g. in MnI and CoO the moment of the Mn 2 + and Co 2 + ions are aligned along a cube edge of the unit cell. The common directions are termed directions of anti-ferromagnetism.

2. The degree of long-range anti-ferromagnetic ordering progressively decreases with increasing temperature and becomes zero at a critical temperature, T n , known as the Néel temperature; this is the anti-ferromagnetic equivalent of the Curie temperature.

3. An anti-ferromagnetic domain is a region in which there is only one common direction of anti-ferromagnetism; this is probably affected by lattice defects and strain.

The most characteristic property of an anti-ferromagnetic material is that its susceptibility χ shows

a maximum as a function of temperature, as shown in Figure 5.35a. As the temperature is raised from

0 K the interaction which leads to anti-parallel spin alignment becomes less effective until at T n the spins are free. Similar characteristic features are shown in the resistivity curves due to scattering as a result of spin disorder. However, the application of neutron diffraction techniques provides a more direct method of studying anti-ferromagnetic structures, as well as giving the magnetic moments associated with the ions of the metal. There is a magnetic scattering of neutrons in the case of certain magnetic atoms, and owing to the different scattering amplitudes of the parallel and anti-parallel atoms, the

σ ⫽ 8.85 A T ⫽ 80 K

T ⫽ 293 K Susceptibility

Scattering angle (2u)

(a)

(b)

Figure 5.35 (a) Variation of magnetic susceptibility with temperature for an anti-ferromagnetic material. (b) Neutron diffraction pattern from the anti-ferromagnetic powder MnO above and below the critical temperature for ordering (after Shull and Smart, 1949).

282 Physical Metallurgy and Advanced Materials possibility arises of the existence of superlattice lines in the anti-ferromagnetic state. In manganese

oxide (MnO), for example, the parameter of the magnetic unit cell is 0.885 nm, whereas the chemical unit cell (NaCl structure) is half this value, 0.443 nm. This atomic arrangement is analogous to the structure of an ordered alloy and the existence of magnetic superlattice lines below the Néel point (122 K) has been observed, as shown in Figure 5.35b.

Some magnetic materials have properties which are intermediate between those of anti- ferromagnetic and ferromagnetic. This arises if the moments in one direction are unequal in magnitude to those in the other, as, for example, in magnetite (Fe 3 O 4 ), where the ferrous and ferric ions of the FeO · Fe 2 O 3 compound occupy their own particular sites. Néel has called this state ferrimagnetism and the corresponding materials are termed ferrites. Such materials are of importance in the field of electrical engineering because they are ferromagnetic without being appreciably conducting; eddy- current troubles in transformers are therefore not so great. Strontium ferrite is extensively used in applications such as electric motors, because of these properties and low material costs.