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therefore gives values for the paramagnetic Curie temperatures which
depend on the highest temperature of the measurements. The fit to
the experimental results for Tm illustrated in Fig. 2.1, for example, in
which the mean-field corrections are taken into account, gives
θ
and
θ
⊥
3 K, which differ significantly from the
values deduced from a linear extrapolation of the same results, given in
Table 1.6. A similar analysis for Er yields 69 K and 46 K. The ordering
temperatures are determined either from bulk measurements or neutron
diffraction.
T
N
and
T
C
denote transition temperatures to magnetically-
ordered states without and with a net moment respectively, and values
are given for sites of both kinds of symmetry, in the light rare earths.
as respectively 52 K and
−
Tab l e 1 . 6 .
Magnetic properties of rare earth metals.
Metal Para.moment
Sat.moment
θ
θ
T
N
T
C
⊥
µ
Obs.
gJ
Obs.
hex.
cub.
Ce
2.54
2.51
2.14
0.6
13.7
12.5
2.7
a
Pr
3.58
2.56
3.20
0.05
2.2
a
Nd
3.62
3.4
3.27
19.9
8.2
Pm
2.68
2.40
0.13
a
Sm
0.85
1.74
0.71
106
14.0
5.1
a
Eu
7.94
8.48
7.0
90.4
Gd
7.94
7.98
7.0
7.63
317
317
293
Tb
9.72
9.77
9.0
9.34
195
239
230
220
Dy
10.65
10.83
10.0
10.33
121
169
179
89
Ho
10.61
11.2
10.0
10.34
73
88
132
20
Er
9.58
9.9
9.0
9.1
62
33
85
20
−
Tm
7.56
7.61
7.0
7.14
41
17
58
32
a
Values measured at 38 tesla.
A straightforward generalization of the above argument (see Sec-
tion 2.1) gives the response of the ions in the paramagnetic phase to a
spatially varying magnetic field with wave-vector
q
. The corresponding
susceptibility tensor (not to be confused with that for the conduction-
electron gas) is
1
−
1
χ
MF
(
q
)=
g
2
µ
2
B
J
(
J
+1)
N
V
−
J
(
q
)
J
(
J
+1)
3
k
B
T
C
=
.
3
k
B
T
T
−
T
N
(1
.
5
.
13)
Spontaneous ordering is therefore predicted to occur at the wave-vector
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