4 X-ray Dichroisms in Spherical Tensor and Green’s Function Formalism
119
Fig. 4.12 Conductivity tensor of a d 9 ion in an octahedral crystal field (10D q = 1.1 eV). Re and
Im are the real and imaginary parts of the tensor
Rot =
⎡
⎢
⎢
⎢
⎢
⎢
⎣
1
√
2
0 0 0
1
√
2
0 0 1 0
0
0
i
√
2
0
i
√
2
0
0
1
√
2
0 −
1
√
2
1
i
√
2
0 0 0 −
i
√
2
⎤
⎥
⎥
⎥
⎥
⎥
⎦
.
(4.84)
The rotated conductivity tensor is shown in Fig. 4.13. Only diagonal elements
exist now. These are separated into two types: three (t 2g ) that are equal with transition
operators, C
2
xy , C
2
yz and C
2
xz , and two (e g ) that are equal with transition operators,
C
2
z 2 and C
2
x 2 −y 2 .