ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 2

indirect exchange and other mechanisms. The magnetoelastic effects ,
due to the coupling between the lattice strains and the magnetic mo-
ments, are also discussed. The manner in which these interactions and
the characteristics of the 4 f electrons combine to determine the magnetic
properties of the metals is described in the last section. The observed
magnetic structures of the heavy rare earths are presented and their
occurrence under different circumstances discussed. Some features of
the structures and their temperature dependence are described in terms
of an elementary mean-field theory . The magnetism of the light rare
earths is then briefly treated and the importance of the crystal fields
emphasized. The effect of a magnetic field on the magnetic structures
is mentioned, and the factors which determine the magnetic anisotropy
discussed. Finally, the way in which magnetostriction can change the
crystal symmetry and influence the magnetic structure is illustrated.

1.1 A brief history
The quantum theory of magnetism was first placed on a sound foot-
ing in 1932 by J.H. Van Vleck in his classic monograph The Theory
of Electric and Magnetic Susceptibilities . In it, he extended the cal-
culations of the magnetic susceptibilities of isolated rare earth ions,
which had been performed by Hund (1925), to encompass the anoma-
lous cases of Eu and Sm, which have low-lying multiplets, giving rise to
Van Vleck paramagnetism . He was thus able to obtain good agreement
with experiment over the whole series from La to 'Casseiopaium' (now
Lu). The study of the metallic elements began in earnest when Urbain,
Weiss, and Trombe (1935) discovered the ferromagnetism of Gd. Klemm
and Bommer (1937) determined the paramagnetic Curie temperatures of
the heavy rare earths and Neel (1938) showed that, in the presence of
strong spin-orbit coupling on the ion and an interionic exchange inter-
action between the spins, these should be proportional, as observed, to
( g

1) 2 J ( J + 1). This later became known as the de Gennes factor .
Very little work was done on the rare earths during the war, but im-
mediately afterwards F.H. Spedding, at Iowa State University, resumed
his programme of producing the pure elements, and by the early 1950s
relatively large quantities had become available. One of the first fruits
of this programme was the extension of physical measurements to the
light rare earths, when Parkinson, Simon, and Spedding (1951) detected
a number of anomalies of magnetic origin in the heat capacity .Ju t
previously, Lawson and Tang (1949) had showed that the γ - α phase
transition in Ce, which can be induced either by pressure or cooling, re-
sulted in no change of the fcc symmetry, but a substantial reduction of
the lattice parameter. Zachariasen and Pauling independently ascribed
this shrinking to the transfer of the localized 4 f electron to the conduc-

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