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Microscopic theory (quantum-mechanical) 281

properties only if some of the ions remain magnetic. This may happen in the
so-called ‘transition elements’, which have unfilled inner shells. The most not-
able of them is the 3d shell, but Table 4.1 shows that the 4d, 4f, 5d, and 5f shells
have similar properties.
Taking chromium again as an example, it has a valency of two or three;
hence, in a chemical bond it must lose its 4s electron [see Fig. 11.16(b)] and
one or two of its 3d electrons. The important thing is that there are a number
of 3d electrons left that have identical spins, being thus responsible for the
paramagnetic properties of the salt.

11.7.4 Antiferromagnetism

Let us now study the magnetic properties of solid chromium. From what we
have said so far, it would follow that chromium is a paramagnetic solid with a
susceptibility somewhat larger than that of other metals because free electrons
contribute to it, and the lattice ions are magnetic as well. These expectations
are not entirely false, and this is what happens above a certain temperature,
the Néel temperature (475 K for chromium). Below this temperature, how- Louis Néel received the Nobel
ever, a rather odd phenomenon occurs. The spins of the neighbouring atoms Prize in 1970.
suddenly acquire an ordered structure; they become antiparallel as shown in
Fig. 11.19. This is an effect of the ‘exchange interaction’, which is essentially
just another name for Pauli’s principle. According to Pauli’s principle, two elec-
trons cannot be in the same state unless their spins are opposite. Hence, two
electrons close to each other have a tendency to acquire opposite spins. Thus,
the electron-pairs participating in covalent bonds have opposite spins, and so
have the electrons in neighbouring chromium atoms. Besides chromium, there
are a number of compounds like MnO, MnS, FeO, etc. and another element,
(a)
manganese (Néel temperature 100 K) that have the same antiferromagnetic
properties.
Antiferromagnetics display an ordered structure of spins; so in a sense, they
are highly magnetic. Alas, all the magnetic moments cancel each other (in
practice nearly cancel each other) and there are therefore no external magnetic
effects.

11.7.5 Ferromagnetism
(b)
Leaving chromium and manganese, we come to iron, cobalt, and nickel, which
are ferromagnetic. In a ferromagnetic material the spins of neighbouring atoms
are parallel to each other [Fig. 11.19(b)]. Nobody quite knows why. There
seems to be general agreement that the exchange interaction is responsible for
the lining up of the spins (as suggested first by Heisenberg in 1928) but there
is no convincing solution yet. The simplest explanation (probably as good as
any other) is as follows.
Electrons tend to line up with their spins antiparallel. Hence, a conduction
(c)
electron passing near a 3d electron of a certain iron atom will acquire a tend-
ency to line up antiparallel. When this conduction electron arrives at the next Fig. 11.19
iron ion, it will try to make the 3d electron of that atom antiparallel to itself; The angular momentum vector for (a)
that is, parallel to the 3d electron of the previous iron atom. Hence, all the spins antiferromagnetic, (b) ferromagnetic,
tend to line up. and (c) ferrimagnetic materials.