MAGNETIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 114

An instructive example of competing anisotropy forces has been
observed in a Tb 0 . 5 Dy 0 . 5 crystal (Spano et al. 1988). This alloy, as would
be anticipated, forms a helical structure at 206 K, and transforms into a
ferromagnet at 152 K. At this temperature, the predominant anisotropy
is due to the Tb magnetoelastic forces in (2.2.28), since the coecient
A is almost zero for Dy (Martin and Rhyne 1977), and the hexagonal
crystal-field anisotropy for both types of ion has renormalized to a very
small value. Consequently, the easy axis of magnetization is the b -axis,
as in pure Tb. As the temperature is further reduced, however, the
crystal-field contribution grows, roughly as σ 21 , and since it is much
greater for Dy than Tb, the easy axis switches at about 100 K to the
a -direction, as in pure Dy.

Tab l e 2 . 1 . Crystal-field parameters (meV).

B 2 B 4 B 6 B 6

10 − 7 10 − 6 Ho 0.024 0.0 − 9.6 · 9.2 ·

10 − 4 10 − 6 10 − 6

Er − 0.027 − 0.3 · 1.3 · − 9.0 ·

10 − 6 10 − 5

Tm − 0.096 0.0 − 9.2 · 8.9 ·

Compared with these relatively straightforward systems, the be-
haviour of the remainder of the magnetic heavy rare earth series, Ho,
Er, and Tm, is more intriguing. As illustrated in Fig. 1.17, the peaks
in ( q ) are large, so that periodic structures are stabilized down to low

temperatures. The crystal-field anisotropy also allows the moments to
move out of the plane. In Table 2.1 are given the anisotropy parameters
deduced from studies of the magnetic structures and excitations. Al-
though these must to some extent be considered as effective values, sub-
suming for example the effects of two-ion and magnetoelastic anisotropy,
they are among the best estimates which we have for the crystal fields
in the rare earths, and they correlate well with the Stevens factors of
Table 1.4.
Ho demonstrates the interplay of the various interactions in an ex-
emplary manner. The positive value of B 2 and the peak in the exchange
function again stabilize the helix at T N .Thepeakvalue

J

( Q )isnowso
large, however, that the cylindrically-symmetric magnetoelastic energy,
which is substantially smaller than that of Dy, is unable to induce a
ferromagnetic transition. On the other hand, the hexagonal crystal-field
anisotropy is nearly three times as big as in Dy, and distorts the helix
drastically when the temperature is reduced, as revealed by the appear-

J