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12.7 Combined Effects of the Competitions Above
Here, we further include the long-range interactions
V
MM
,
V
MXM
, and
V
2
:
V
MM
¼
3
and
V
2
¼
2 in addition to the parameters in Fig.
12.6b
,
U
M
¼
6. We show phase
diagrams in Fig.
12.7a
for
V
MXM
¼
3. The AV
phase is destabilized by the long-range interactions, which favor modulation of
charge densities in the purely electronic origin and compete with the on-site
repulsion
U
M
. The ACP phase is realized in a wide parameter space. The nature
of the ACP phase changes continuously from small-
2 and in Fig.
12.7b
for
V
MXM
¼
,
electrons are more localized so that the singlet pair of electrons is well described in
the Heitler-London picture. For large
a
to large-
a
ranges. For small
a
, the neighboring M d
z
2
orbitals through the
Xp
z
orbital are strongly overlapped to form a doubly occupied bonding orbital so
that the electrons are as in a covalent molecule. Comparing Fig.
12.7a
with
Fig.
12.7b
, one sees that the nearest-neighbor repulsion through an X site,
V
MXM
,
suppresses the ACP phase and stabilizes the other phases relative to the ACP phase,
as already discussed through the aid of Fig.
12.5
.
The ACP phase is clearly observed in Pt
2
(
n
-C
4
H
9
CS
2
)
4
I below 200 K [
11
]. It is,
indeed, nonmagnetic as expected. The electronic structure of Pt
2
(CH
3
CS
2
)
4
I is also
suggested to be the ACP phase below 80 K, though the magnetic susceptibility does
not drop at low temperatures [
10
]. Since the lattice displacements are very small in
the latter case, this electronic state would be close to a paramagnetic phase such as
the AV or CP phase. The CP phase is actually proposed above 80 K [
10
]. Because the
spin excitation spectrum is gapless in the CP phase, it can generally gain more free
energy than the ACP phase from the entropy term at high temperatures so that it is
possible from the theoretical viewpoint. The X p
z
orbitals ignored in this section are
expected to be quantitatively important for the “metallic” (i.e., the resistivity
increases with temperature) conductivity above 300 K (note that a small but finite
gap is observed in the optical conductivity spectrum) and the small
a
lattice
displacements in the ACP phase.
We show phase diagrams containing all of the AV, ACP, CP, and CDW phases
in Fig.
12.8
. Note that
K
MXM
is not set to be zero or infinity here. These phase
diagrams may become useful when experimental data are accumulated. The long-
range interactions are weaker than those in Fig.
12.7
. In Fig.
12.8a
, we use
t
MM
¼
1,
t
MXM
¼
increases, the
ground state changes from the AV phase, the CP phase, to the CDW phase, as in the
case of infinitely large
K
MXM
. It finally becomes the BCDW phase for very large
0.8,
K
MX
¼
6, and
U
M
¼
6 as before. For small
a
,as
b
b
(not shown). For large enough
a
, the ACP phase appears as usual. The critical
strength of
for the ACP phase is the smallest at the boundary between the AV and
CP phases. In Fig.
12.8b
, we change only
K
MX
from the parameters of Fig.
12.8a
:
K
MX
¼
a
4. The MX bonds are more easily distorted by the smaller
K
MX
, while the
distances between the neighboring binuclear units are almost unaffected because
K
MXM
is not changed. Consequently, the CP and CDW phases are stabilized to shift
the phase boundaries to the small-
side, while the ACP phase is destabilized
relative to these phases and invaded by them. In other words, some of the ACP
b
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