Chemistry Reference
In-Depth Information
Γ(s
−1
)
10
7
k
= 1
10
5
10
3
k
= 1.5
10
1
10
-1
10
-3
T
= 2 Κ
10
-5
10
-7
10
-9
S
= 10
D
= 0.66 K
10
-11
10
-13
Ω
t
= 150
K
10
-15
T
= 1 Κ
10
-17
10
-19
g
μ
B
H
z
/D
=
k
10
-21
10
-23
10
-25
T
= 1 Κ
10
-27
10
-29
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
h
x
1/2
Figure 5.
Escape rate versus transverse field in the generic model of MM at different tempera-
tures, on- and off-resonance.
Figure 5 shows the dependence of the escape rate on the transverse field
h
x
at
different temperatures on- and off-resonance. For on-resonance at nonzero tem-
peratures, there are characteristic steps arising as a result of moving the blocking
level up or down the energy [11]. This phenomenon can be seen in Fig. 5 of [11],
obtained by the effective resistances method. One can see that for on-resonance,
k
1
,
the barrier goes to zero with increasing
h
x
,
so that above some critical
value of
h
x
, curves corresponding to different temperatures merge at the level of
the highest possible rate. At these transverse fields, the barrier off-resonance still
exists since the curves corresponding to different temperatures merge at higher
values of
h
x
.
The follwing figures show the numerical results for Mn
12
.
Because of the quartic
uniaxial anisotropy
B,
tunneling peaks in Fig. 6 are split, as explained in the
comment after Eq. (144). The right-most big peaks correspond to ground-state
tunneling, and smaller peaks to the left of them, seen at nonzero temperatures, are
due to tunneling via excited states. Graphed results of earlier calculations of this
kind for Mn
12
can be found in [20, 21]. In comparison to the results for the generic
model with the same barrier 66 K in Fig. 4, Mn
12
shows ground-state tunneling
up to higher temperatures.
Temperature dependences of the escape rate in Fig. 7 are different for different
bias fields. If for a given
H
z
there is a tunneling resonance at some energy between
=
