Redundancia

When a solid is placed in a magnetic field H, it develops a magnetization (magnetic moment per unit volume) M, given by M=/H, where %, is the magnetic susceptibility. The magnetic induction, B, is defined as:-

B = H + 4nM = fjM (23)

where p is the permeability. Substances with a weak negative magnetic susceptibility are called diamagnetic (diamagnetic substances tend to move towards the weakest region of a magnetic field) while those with a positive susceptibility are called paramagnetic (paramagnetic substances tend to move towards the strongest part of a magnetic field).

The magnetic properties of solids are determined by orbital and spin motions of electrons in atoms and their interaction with each other. The relationship between the magnetic moment, p, and angular momentum, J, of an electron of charge, e, and mass, m, can be expressed as>

l À - - { e llm ) J (24)

The angular momentum, J, is quantized and the lowest value of, p, is the Bohr magneton, pp. The orbital motion of an electron in an atom gives rise to a magnetic moment, which is related to the orbital angular momentum, L, by

= (25)

The spin magnetic moment is then given by

//=—=#(&+or

(

)

^ ^ me

where S is the spin angular momentum.

The observed magnetic moment can therefore be used to determine the number of unpaired electrons in each atom. The magnetic susceptibility %m of a paramagnetic

ion has a temperature dependence as described by the Curie-Weiss law where (27)

2.5.3.1 Magnetism in Bulk Materials

The magnetism in solids is more complicated than that of the isolated atoms because of the possibility of interaction (coupling) between atomic moments. The origin of the coupling comes from the Pauli exclusion principle namely that electrons of parallel spin are correlated as to avoid the same region of space. Thus, a pair of electrons of like spin will be higher in energy than a pair with opposite spin by an amount known as the interatomic exchange energy, and known as exchange coupling. Direct exchange, occurs between moments on atoms which are close enough to have significant overlap. This exchange is strong but decreases with increasing distance. Indirect exchange, couples moments over a larger distance. Exchange can also occur through intermediary nonmagnetic ions which is known as superexchange, which occurs predominantly in insulators or through itinerant electrons (Ruderman, Kittel, Kasuya and Yosida [20]- often reffered to as RKKY) in metals.

The exchange energy. Hex, of two atoms, i and j, separated by a distance ry, with spins

Si and Sj respectively is given by

H . = -'L‘^(r,?SrSj

(

»)

ij

where J is the exchange parameter. For electrons belonging to the same atom, J is positive. For direct interatomic exchange, J can be positive (parallel alignment of spins) or negative (antiparallel alignment of spins and lower energy). For indirect exchange, J can be positive or negative in the case of superexchange or oscillatory for RKKY [21].

Superexchange describes interactions between localised moments of ions in insulators that are too far apart to interact by direct exchange and operates through an intermediary nonmagnetic ion. The strength of the exchange is determined by the extent of orbital overlap [22]. Localised electron states are stabilised by a mixture of exited states involving electron transfer between the cation and anion.

2.S.3.2 Types of Magnetism in Bulk Materials

There are five basic types of magnetism found in solids, which can be co-operative (mutual interaction between moments) and non co-operative (individual moments behave independently of each other) these include:

a) Diamagnetism (non co-operative):

A diamagnetic material has closed electron shells, and displays weak temperature independent magnetic susceptibility.

b) Ideal Paramagnetism (non co-operative)

Ideal paramagnetic materials atoms have identical atomic moments and located in isotropic surroundings that are sufficiently separated from one another. The temperature dependence of the susceptibility follows the Curie-Weiss law at temperatures above which any ordered magnetic states exist.

Ferromagnetic materials have a long-range colinear order in which magnetic moments align in a parallel fashion to give a net permanent magnetic moment within a domain. Illustrated in figure 2.10. Applying an external field then enlarges the domains of an orientation parallel to the field at the expense of others. The spontaneous magnetisation decreases with increasing temperature (as the thermal energy increases and becomes comparable to and eventually exceeding the exchange energy) and then disappears at the Curie temperature where a ferromagnet becomes paramagnetic obeying the Curie-Weiss law.

d) Antiferromagnetism (co-operative)

Antiferromagnetic materials have a long range ordering but the exchange parameter J is negative and the moments of neighbouring atoms are exactly opposed so there is no overall spontaneous magnetization (figure 2.10b). Below the ordering temperature (called the Neel Temperature) an antiferromagnet consists of two identical interpenetrating sublattices in which the spins of one lattice are opposed the to the spin of the other. Most antiferromagnetic material are non-metallic solids e.g. MnO, NiO etc [22] but some metals e.g. Cr, PtFes also exhibit antiferromagnetic properties.

e) Ferrimagnetism (co-operative)

Ferrimagnetic materials occur when two or more different magnetic species are present. They occupy different kinds of lattice sites producing two sublattices (as in spinels [20]) Figure 2.10c. The moments within each sublattice are ferromagnetic and but the coupling between the sublattices is antiferrimagnetic. As the overall moments of the two sublattices are different, there is an overall magnetization, the temperature

dependence of which is similar to that of ferromagnetic materials but decreases more rapidly with increasing temperature.

i i i i i

i n n

^ Î ^ Î ^

Figure 2.10 Magnetic moment alignment o f individual atoms (top ferromagnetism, middle antiferromagnetism and bottom ferrimagnetism)

There are other types of magnetism, which are predominantly subdivisions of the five main types described above. For example, metamagnetism, in which there is a field induced magnetic transition from a state of low magnetization to one of relatively high magnetization [21]. The temperature dependence is similar to that of ferromagnetic materials although at lower temperatures the moment initially increases and the reaches a maximum (over a low temperature range).