CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 312

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CRYSTAL-FIELD EXCITATIONS IN
THE LIGHT RARE EARTHS

A magnetic ion in a rare earth metal experiences a crystalline electric
field from the surroundings, which gives rise to an overall splitting of
the order 10-20 meV of the ionic ground-state J-multiplets. Crystal-
field excitations are collective normal modes of the system, associated
with transitions between the different levels of the ground-state multi-
plets. Even though there is an obvious qualitative difference between
the crystal-field excitations in paramagnetic Pr and the spin waves in
the isotropic ferromagnet Gd, it is not in general easy to give a precise
prescription for differentiating between the two types of excitation. The
spin-wave modes are derived from the precession which the moments ex-
ecute when placed in a magnetic field. The two transverse components
of a single moment change in time in a correlated fashion in such a pre-
cession, and this phase-locking is only possible when the time-reversal
symmetry is broken. Hence the spin waves may be considered as the
magnetic excitations related to the broken time-reversal symmetry of
a magnetically ordered phase. However, spin waves may exist in the
paramagnetic phase in the vicinity of the phase transition, if the time-
reversal symmetry is broken locally. In the ordered phase, there may
be additional magnetic excitations, associated either with the longitu-
dinal fluctuations of the moments, or with further transitions between
the MF levels, made possible by a strong mixing of the J z > -states in

the crystal field, as discussed in Section 5.3.2. Depending on the cir-
cumstances, these additional excitations may be named crystal-field or
molecular-field excitations. The effects of the crystal field, relative to
that of the exchange field, are important in the four heavy rare earths
Tb - Er, but not suciently to produce other well-defined magnetic ex-
citations, in addition to the spin waves. In their paramagnetic phases,
the temperature is suciently high, compared with the crystal-field split-
tings, that potential crystal-field excitations have such low intensity, and
are so damped, as to be unobservable. Among the rare earth metals,
crystal-field excitations are consequently only found in the light half of
the series, and in Tm (McEwen et al. 1991) where, as discussed in the
previous section, the crystal-field effects are relatively stronger because
of the de Gennes scaling of the exchange.
We shall therefore concentrate our discussion on Pr, the paradigm

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