Environmental Engineering Reference
In-Depth Information
There are a number of different experimental methods for obtain-
ing values for the microscopic and macroscopic anisotropy parameters.
The susceptibility in different directions, or equivalently the torque on
a crystal in a field, can be measured either in the paramagnetic or mag-
netically ordered phases and, as we shall discuss in detail later, much
information may be obtained from the excitation spectrum and its field
dependence. The values of
κ
l
(0) obtained from these various sources
for the different elements have been reviewed and tabulated by McEwen
(1978).
In order to deduce the crystal-field parameters
B
l
in the absence
of exchange and magnetoelastic effects, Touborg and his collaborators
studied the crystal-field states of dilute alloys of the magnetic rare earths
in the non-magnetic hosts Sc, Y, and Lu, utilizing magnetization mea-
surements and, to a limited extent, neutron spectroscopy. Their results
for heavy rare earth solutes have been reviewed by Touborg (1977) and,
for the light elements, by Touborg
et al.
(1978). Within the uncertainty
of the measurements and of the interpretation, and with the exception
of Ce in Y, which behaves anomalously, they found that a common set of
parameters
B
l
/α
l
accounts for the behaviour of all solutes in a particu-
lar host.
B
4
/β
and
B
6
/γ
are roughly 10 K/ion and 15 K/ion respectively
in all cases, while
B
6
is close to the value
8
B
6
which the point-charge
model would predict.
B
2
/α
increases from about 30 K/ion in Sc, to 45
K/ion in Lu, to 100 K/ion in Y, which correlates with the deviation of
the
c/a
ratio of the host metal (1.592 for Sc, 1.584 for Lu, and 1.573 for
Y) from the ideal value of 1.633 (Orlov and Jensen 1988). It is note-
worthy that the parameters
B
l
77
−
/α
l
show no obvious correlation with
r
l
, as would be anticipated from (1.4.4).
The values of
B
l
from these studies of dilute alloys may be com-
pared with those from other sources. In particular,
B
2
may be estimated
for the pure metals by interpolating between the
c/a
ratios of the non-
magnetic hosts. These values may then be compared with those deduced
from the difference between the paramagnetic Curie temperatures par-
allel and perpendicular to the
c
-axis, which is shown in Section 2.1 to
be given by
5
k
B
(
θ
⊥
−
θ
)
B
2
=
2
)(
J
+
2
)
.
(1
.
5
.
26)
1
6(
J
−
The agreement for the heavy rare earths is in all cases good (McEwen
1978), indicating that the crystal fields measured in dilute alloys are re-
lated to those acting in the pure metals. On the other hand, the values
deduced from torque and magnetization measurements at low tempera-
tures in the ferromagnetic state show large discrepancies with those in
the paramagnetic phase. For Tb and Dy, the former are roughly three
times the latter. Despite this discrepancy, which is probably primarily
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