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CDW (M = Pd and Pt)
X
-
4+
2+
M
d
z
2
M
d
z
2
Mott Insulator (M=Ni)
X
-
3+
M
d
z
2
Fig. 8.1 Schematic picture of electron and halogen-lattice configurations
The metal ion is more closely surrounded by the ligands or more specifically by their
N coordination atoms than the halogen ions. This structure relatively lowers the level
of
d
z
2
compared with that of
d
x
2
y
2
, leading to the situation of a half-filled band of
d
z
2
as the average. Returning to the case of Ni, we also see an antiferromagnetic spin
order at least within a short range. This monovalency and spin correlation are the
central issues in the Ni complexes and we will discuss them extensively in later
sections. We here only emphasize that the main driving force of this singly occupied
electron configuration is the Coulombic repulsion working between the two
electrons (spin
) occupying the same site.
Regarding the lattice configuration, the halogens dimerize in the Pt and Pd
complexes. This dimerization inevitably makes two nonequivalent sites for Pt and
Pd sites; the site to which the two neighboring halogens come closer and the site
from which the same halogens apart. When we recall a general tendency that the
halogens take (
ΒΌ"
and
#
1) valency, it will be easily understood that the electrostatic site
energy goes higher (lower) for the former (latter). Meanwhile, the halogens in the
Ni complexes make a striking contrast. It was experimentally observed that they
reside at the midpoints. Thus, the monovalency in the Ni complexes is very
consistent with its lattice configuration. The first purpose of theories is thus to
describe these very different states in a unified manner, in other words, using a
model that is almost common but a few key parameter values.
8.1.2 Model
First of all, we explain the simplest model, i.e., an extended Peierls-Hubbard
model [
1
-
4
]:
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