Chemistry Reference
In-Depth Information
g
is the alternation parameter, where
g ¼
1 corresponds to a uniform chain limit,
while
0 corresponds to the dimer limit. According to the analysis by Ohama
et al. [
92
], which is based on the theory of Bulaevskii [
95
], the LT magnetic
susceptibility is approximated by
g ¼
Ng
2
m
B
2
a
ðJ
0
z=TÞ
x ¼
exp
k
B
T
where
a
and
z
are parameters that depend on the alternating parameter
g
and
approach unity as
g !
0 (the dimer model) and approach zero as
g !
1 (the
w
M
T
vs.
T
1
plot, the estimated
uniform chain model). By fitting the equation to a ln
value of
J
0
z
, is 95(7) K for 8 and
77(2) K for 9. When the lattice dimerizes, the two unequal and alternating
J
1
and
J
2
values are expressed as follows [
87
]
, which corresponds to an excitation energy gap
D
J
1
;
2
ðTÞ¼Jf
dðTÞg:
1
According to the mean field theory of Pytte, the relationship between
d
(
T
) and the
excitation energy gap
D
(
T
) at temperature
T
is expressed as [
96
]
dðTÞ¼DðTÞ=pJ
where the value of
p
is 1.637. Using this method,
d
(
T
)
¼
0.062 and
J
2
/
J
1
¼
0.88
for 8 and
0.90 for 9 have been obtained. The values of
2
D
(0)/
k
B
T
sp
of 8 and 9 are 4.04 and 4.28, respectively, which are larger than the
value of the typical spin-Peierls materials (TTF-CuBDT, MEM-(TCNQ)
2
[
97
],
and CuGeO
3
) that satisfy the BCS formula 2
d
(
T
)
¼
0.052 and
J
2
/
J
1
¼
D
(0)/
k
B
T
sp
¼
3.53 but are smaller
a
0
-NaV
2
O
5
(6.44) [
91
]. This discrepancy of 2
than that of
(0)/
k
B
T
sp
is attributed
to the larger fluctuation effects comparedtoordinaryspin-Peierlsmaterials.
According to the theory of Cross and Fisher [
98
],
T
sp
is given by
D
8
J
0
T
sp
¼
:
0
0
is the spin-lattice coupling constant and
0
¼
where
0.063 for 8 and 0.050 for 9,
which is smaller than the value of typical spin-Peierls materials (0.195, 0.209, and
0.146 for TTF-CuBDT, MEM-(TCNQ)
2
, and CuGeO
3
) but is relatively close to the
value of
a
0
-NaV
2
O
5
(0.079). The phase-transition temperatures of 8 and 9 are
suppressed since the coupling between the spin and lattice system is weak due to
the large 1D fluctuations. Parameters defining spin-Peierls systems are listed in
Table
9.7
.
On the other hand, the magnetic susceptibility of 10 gradually decreases with a
lowering of the temperature, as shown in Fig.
9.37c
and shows a broad minimum at
around 135 K. When the experimental data above 140 K are fitted by the
Bonner-Fisher equation, |
J
|/
k
B
is estimated to be 939(3) K. Below 135 K,
w
M
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