Physics of Magnetism

7

Itinerant-Electron Magnetism

7.1. INTRODUCTION

A situation completely different from that of localized moments arises when the magnetic

atoms form part of an alloy or an intermetallic compound. In these cases, the unpaired

electrons responsible for the magnetic moment are no longer localized and accommodated

in energy levels belonging exclusively to a given magnetic atom. Instead, the unpaired

electrons are delocalized, the original atomic energy levels having broadened into narrow

energy bands. The extent of this broadening depends on the interatomic separation between

W

the atoms. According to a calculation made by Heine (1967), the following relation applies

between the width of the energy bands and the interatomic separation

The most prominent examples of itinerant-electron systems are metallic systems based on
3d transition elements, with the 3d electrons responsible for the magnetic properties. For
a discussion of the magnetism of the 3d electron bands, we will make the simplifying
assumption that these 3d bands are rectangular. This means that the density of electron
states N(E) remains constant over the whole energy range spanned by the bandwidth W.
A maximum of ten 3d electrons per atom (i.e., five electrons of either spin direction)
can be accommodated in the 3d band. In the case of Cu metal, because each Cu atom
provides ten 3d electrons, the 3d band will be completely filled. However, in the case of
other 3d metals, less 3d electrons are available per atom so that the 3d band will be partially
empty. Such a situation is shown in Fig. 7.1.1a. In Fig. 7.1.1a, we have indicated that there
is no discrimination between electrons of spin-up and spin-down direction with respect to
band filling. Both types of electrons will therefore be present in equal amounts, meaning
that there is no magnetic moment associated with the 3d band in this case. However, this
situation is not always a stable one, as will be discussed below.
It is possible to define an effective exchange energy per pair of 3d electrons. This
can be regarded as the energy gained when switching from antiparallel to parallel spins. In
order to realize such gain in energy, electrons have to be transferred, say, from the spin-down
subband into the spin-up subband. As can be seen in Fig. 7.1.1b, this implies an increase in
kinetic energy, which counteracts this electron transfer. However, it will be shown below
that such transfer is likely to occur if is large and the density of states at the Fermi

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