MAGNETIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 113

ings 1968). There is in addition a competing anisotropy, which has its
origin in the spin-orbit coupling (1.2.13) of the conduction electron gas,
which restricts the free rotation of the spins relative to the lattice. The
indirect-exchange interaction then ensures that the localized spins are
correspondingly constrained. The magnitude of this effect could in prin-
ciple be calculated from the electronic structure, at least at absolute
zero, but no serious attempts have yet been made to do so.
The small anisotropy of Gd leads to an unusual sequence of struc-
tures when it is diluted with Y. The latter has a very strong tendency to
impose a periodic magnetic structure on dissolved rare earth moments
(Rainford et al. 1988a; Caudron et al. 1990) and, in a concentration
above about 30% in Gd, induces a helical structure below T N .The
magnetic behaviour of these alloys is completely dominated by the ex-
change, and the transition to the ferromagnetic structure, both with
increasing Gd concentration and, as occurs if the Y concentration is not
too high, with decreasing temperature, takes place by a continuous re-
duction of the turn angle of the helix (Palmer et al. 1986), as the peak
in

( q ) moves smoothly to the origin. At higher Y concentrations, a
longitudinal wave is also formed along the c -axis, over a temperature
range and with a wave-vector which are different from those of the he-
lix. As discussed in Section 2.1.5, this behaviour shows explicitly that
the exchange must be anisotropic. Furthermore, at Y concentrations
just above the critical value for the formation of a helix, a ferromagnetic
structure, with the easy direction along the c -axis, forms at T C ,istrans-
formed into a basal-plane helix through a first-order transition at a lower
temperature T N , and at an even lower temperature transforms back into
the aforementioned ferromagnetic structure, with the moments canted
away from the c -direction.
Tb and Dy both have large axial anisotropies which confine the mo-
ments to their basal planes, and the peaks in

J

( q ), illustrated in Fig.
1.17, induce helical structures at the respective Neel temperatures. In
Tb, this peak is very small, and the spin-wave measurements illustrated
in Fig. 6.1 indicate that it becomes even smaller as the helical phase
is established and the superzone energy-gaps grow. Simultaneously, the
(negative) anisotropy energy in the ferromagnetic phase increases, par-
ticularly the cylindrically-symmetric magnetoelastic term proportional
to C 2 in (2.2.27), which makes no contribution in the helical phase be-
cause of lattice clamping. Consequently, this anisotropy energy over-
whelms the exchange-energy difference (1.5.35) only ten degrees below
T N , and a first-order transition occurs to a ferromagnetic structure. The
peak in the exchange function in Dy is more robust, and the helical phase
correspondingly more stable but, as we have discussed in Section 1.5, a
ferromagnetic transition ultimately takes place at 85 K.

J