Xb

Qn is the ratio of the remanence (Mn) to that induced by the Earth's magnetic field at the sampling site, whereas Qt is the ratio of the thermoremanent magnetization (A/t) acquired in the magnetic field B to the magnetization induced by the same field at room temperature.

2.1.2 Diamagnetism and Paramagnetism

Diamagnetism is a phenomenon common to all materials. Any moving charge, including orbital electrons, experiences a force (known as the Lorentz force) in a magnetic field B. This Lorentz force deflects the path of electrons in such a way that they precess clockwise about B (when viewed along a line in the direction of B). This is equivalent to a current anticlockwise about B, which produces a negative induced magnetic moment (compare with the current direction in Fig. 2.1) known as diamagnetism. Thus, the susceptibility is negative (Fig. 2.2a) and very small, typically on the order of 10"5.

If an atom has a resultant magnetic moment the application of a magnetic field tends to align these dipole moments along the direction of the field. Although the diamagnetic effect still occurs, it is swamped by the alignment of the atomic dipole moments. Substances that exhibit this effect are called paramagnetics, and the induced magnetization is in the same direction as the applied field giving a positive susceptibility (Fig. 2.2b) that lies typically between 10"3 and 10"5. In metallic substances a further situation arises because the individual atoms and their inner orbital electrons are closer together in the solid state than the virtual radii of the valence electrons. The outer valence electrons are thus no longer associated with individual atoms and they wander freely through the metal. In an atom devoid of its valence electrons, the net atomic dipole moment is zero. The application of a magnetic field causes the "free" electrons, equal numbers of which have opposite spins, to have their spins aligned parallel to the magnetic field. The substance thus acquires a dipole moment and paramagnetism results.

Fig. 2.2. Variation of magnetization with applied field for (a) diamagnetic and (b) paramagnetic material.

Fig. 2.2. Variation of magnetization with applied field for (a) diamagnetic and (b) paramagnetic material.

2.1.3 Ferro-, Antiferro-, and Ferrimagnetism

Diamagnetic and paramagnetic substances exhibit only weak magnetic effects because the dipole moments involved are relatively small. However, substances like iron, cobalt, and nickel exhibit strong magnetic effects resulting from a phenomenon known as ferromagnetism. These ferromagnetic substances are distinguished by the fact that the individual atoms, and their inner orbital electrons, are much closer together than the virtual radii of their valence electron orbits when compared with the other metallic paramagnetics. Also, there are more valence electrons available to move freely through the metal so that they become crowded together and react strongly with one another. The exchange forces between these electrons are such that their spins become aligned even in the absence of an applied magnetic field. Ferromagnetic substances therefore exhibit spontaneous magnetization because of exchange coupling between the electrons and may have a permanent dipole moment in the absence of an applied field. As the temperature is increased thermal agitation may destroy the alignment process. It becomes completely destroyed at a critical temperature for each substance called the Curie temperature or Curie point. The spontaneous magnetization reduces to zero at the Curie point and above this temperature the substance behaves like an ordinary paramagnetic. Figure 2.3 shows the variation of spontaneous magnetization, Ms, with temperature for magnetite and hematite, the two most common magnetic minerals in rocks.

Fig. 2.3. Variation of spontaneous magnetization, Ms, with temperature for magnetite and hematite. Ms is normalized to its value at 0°C. Redrawn from Pullaiah et al. (1975), with permission from Elsevier Science.

Temperature (°C)

Fig. 2.3. Variation of spontaneous magnetization, Ms, with temperature for magnetite and hematite. Ms is normalized to its value at 0°C. Redrawn from Pullaiah et al. (1975), with permission from Elsevier Science.

Some substances are characterized by a subdivision into two sublattices (usually designated A and B). The atomic moments of A and B are each aligned but antiparallel to one another. The ferromagnetic effects cancel one another out when the moments of the two sublattices are equal (Fig. 2.4) and there is no net magnetic moment. This phenomenon is known as antiferromagnetism. Such

Canted

Ferromagnetic Antiferromagnetic Ferrimagnetic antiferromagnetic

Canted

Ferromagnetic Antiferromagnetic Ferrimagnetic antiferromagnetic

Resultant spontaneous magnetization

Fig. 2.4. Cartoon of the different exchange-coupled spin structures, together with the resultant spontaneous magnetization.

substances do not have a Curie temperature because there is no net ferromagnetism. In this case the ordering of the atomic moments is destroyed at a critical temperature called the Neel temperature, above which the substances behave like ordinary paramagnetics. If the atomic moments of the A and B sublattices are unequal, then there is a net spontaneous magnetization and a weak ferromagnetism results that is known as ferrimagnetism. Alternatively, the equal atomic moments in the two sublattices may not be exactly antiparallel and a small spontaneous magnetization results (Fig. 2.4). Such a substance is called a canted antiferromagnetic. Both the ferrimagnetic and canted antiferromagnetic substances behave as ordinary ferromagnetics; they have a Curie temperature and all the properties of ferromagnetics. The important minerals in rock magnetism are of these two types, to which the basic theories of ferromagnetism may be applied.

2.1.4 Hysteresis

When a ferromagnetic substance, initially in a demagnetized state, is placed in an applied magnetic field B, the specimen follows the magnetization curve from the origin as in Fig. 2.5. As B is increased from zero the magnetization M initially rises linearly as shown by the portion a of the curve. If B is reduced to zero at this point the process is reversible and M also falls to zero. The initial susceptibility (x = \LqM/B since B = \x{jH) of the ferromagnetic substance can be obtained from the slope of the M-B curve here. As B is increased further, the slope of the curve increases (in region b)\ if B is now reduced to zero, M does not fall to zero but follows the path c, and an isothermal remanent magnetization (IRM) given by Mr results. Further increases in B beyond point d on the magnetizing curve would produce no further increases in M, and a saturation magnetization, Ms, is reached at the saturating field 6sat. On reducing the field to zero (along portion e) the saturation IRM, or simply saturation remanence, MIS, occurs. On applying a field in the opposite direction, the IRM is overcome and M is reduced to zero in a field Bc, called the coercivity or coercive force. Coercive force, however, is more usually given in terms of the equivalent field, Hc, although often quoted in units of B. Further increases of B in the negative direction causes saturation to occur in the opposite direction and repeated cycling of the field cause the magnetization to follow a hysteresis loop as shown in Fig. 2.5. The largest hysteresis loop occurs when the field is cycled with saturation being reached, and in this case Bc (and Hc) has its maximum value called the maximum coercive force. If the field is cycled without saturation being reached, then a smaller hysteresis loop results as shown.

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