SPIN WAVES IN THE FERROMAGNETIC HEAVY RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 256

7 µ B to about 5.9 µ B , whereas the Tb moment is very close to saturation.
Furthermore, the first excited-state on the Tm ions is at a relatively low
energy, and the associated magnetic fluctuations are predominantly in
the c -direction, reflecting an incipient realignment of the moments, which
actually occurs at higher concentrations (Hansen and Lebech 1976). The
Tb fluctuations, on the other hand, are largely confined to the plane,
with the result that the neutron-scattering intensity stemming from the
c -axis fluctuations is comparable for the two types of site, even though
only 10% of the ions are Tm.
The CPA theory has not yet been applied to heavy rare earth-alloys.
The extra linewidth-effects due to the randomness are not expected to
be very pronounced in the 10% alloys. At low temperatures, they are of
the order of the contribution of the scattering against the electron-hole
pair excitations of the conduction electrons, and they become decreas-
ingly important compared with intrinsic effects at higher temperatures.
The CPA theory has been applied to the light rare earth-alloy Pr 95 Nd 5
(Jensen 1979a) in the paramagnetic phase, where the linewidth effects
predicted by the CPA at 9 K are found to be of the same order as the
intrinsic effects due to thermal disorder.
5.7 Conduction-electron interactions
As we have already discussed in Section 1.4, the conduction electrons
in the rare earth metals act as the medium through which the coupling
is established between the 4 f electrons localized on the ions. In this
section, we shall investigate this RKKY coupling in more detail, and
consider its influence on both the spin waves in the ferromagnetic phase,
andalsoonthe conduction electrons themselves. The indirect-exchange
interaction is first derived, and its effects in limiting the lifetimes of
thespinwavesandin polarizing the conduction electrons are deduced.
The enhancement of the effective mass of the conduction electrons by
the dynamical magnetic fluctuations is then calculated. Finally, the
modification of the electrical resistivity by the exchange interaction is
discussed, including the scattering of the conduction electrons by the
spin-wave excitations, and the influence of the magnetic ordering on the
conduction-electron band structure. For completeness, we include the
effect of magnetic superzones in periodic structures in this section.
5.7.1 The indirect-exchange interaction
The starting point for our consideration of the indirect exchange, or
RKKY coupling, of the localized moments is the Heisenberg-Dirac ex-
change between the 4 f electrons and the conduction electrons. The 4 f -
core electrons of the ion at site i are assumed to be described to a good
approximation by non-overlapping atomic wavefunctions φ 4 f ( r − R i ).