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Fig. 12.4 Secondorder
processes with respect to
t
MM
and
t
MXM
in the CDW and CP
phases
CDW
t
MM
U
M
X
X
t
MXM
CP
t
MM
2
β
y
X
X
t
MXM
Though the effects of the longrange interactions are discussed later, it is here noted
that
V
MM
increases the energy of the CDW phase and stabilizes the CP phase. The
secondorder processes with respect to
t
MM
shown in Fig.
12.4
lower the energy by
2
t
MM
2
/
U
M
in the CDW phase and by
t
MM
2
=ð
2
bjyjÞ
in the CP phase. That is why the
CDW phase is relatively stable for large
and the CP phase for large
U
M
.Ina
similar manner, the effect of
t
MXM
can be discussed from the secondorder pertur
bation theory. It does not affect the relative stability between the CDW and CP
phases. That is why the phase boundary is insensitive to
t
MXM
. It is noted that, if the
longrange interactions are included, the secondorder terms with respect to
t
MXM
for the CDW and CP phases become different. Even in such a case, the phase
boundary is more sensitive to
t
MM
.
Experimentally, the ground states of K
4
[Pt
2
(pop)
4
X]
n
H
2
O with X
b
¼
Cl, Br and
n ¼
2, 3 are shown to be in the CDW phase [
1

4
]. In general, when the halogen X
ion is either Cl or Br, so far all the ground states are known to be in the CDW phase.
For X
Cl and Br, the X p
z
level is so deep that the effective nearestneighbor
transfer integral
t
MXM
mediated by charge transfers through the X p
z
orbital is
small. Meanwhile, the sitediagonal electronlattice coupling
¼
is large owing to
the short distance between the neighboring M and X ions,
d
MX
. Thus, the CDW
phase for X
b
¼
Cl and Br is understood from the dominance of the electronlattice
coupling
over electronelectron interactions other than the onsite repulsion
U
M
,
which is strong enough to suppress a phase with bipolarons discussed later.
In R
4
[Pt
2
(pop)
4
X]
n
H
2
O with X
b
I, depending on the cation R and on the
number of water molecules
n
, three electronic phases are suggested to appear: the
AV phase, the CDW phase, and the CP phase in the order of increasing of
d
MXM
[
7
].
Though we have not obtained a phase diagram with the CDW phase between the
other two, we believe that, for small
d
MXM
, the effect of
t
MXM
is larger than those
of various interactions so that the larger
t
MXM
stabilizes the AV phase. Meanwhile,
for intermediate to large
d
MXM
, the competition between the electronlattice
and electronelectron interactions discussed here and/or the competition between
the short and longrange electronelectron interactions discussed later determine
the relative stability between the CDW and CP phases. As
d
MXM
increases, the site
diagonal electronlattice coupling
¼
b
becomes weak, while the onsite repulsion
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