Chemistry Reference
In-Depth Information
the top of the classical barrier and the ground state, thermally activated tunneling
via this resonant pair is a relaxation channel competing with the two channels
considered above. As a result, there are two different slopes in the Arrhenius part
of the plot, such as for
k
1
.
006
.
This value of
k
corresponds to the high blue
peak in Fig. 6 that disappears at
T
=
=
0
.
H.
Discussion
Existing work on molecular magnets using the density matrix equation can be
split up into two groups: (1) by using the natural or
m
-basis and (2) by using
the diagonal basis. In all known cases, the DME is reduced to the system of rate
equations for the diagonal DM elements, the level populations. Using the natural
basis is justified if the terms in the spin Hamiltonian that are noncommuting with
S
z
are a small perturbation. However, even a small noncommiting perturbation can
severely distort the levels near the top of the barrier that are mostly inportant in
thermal activation. On the other hand, tunneling via robuster low-lying levels at
low temperatures can be well described perturbatively in the
m
-basis.
In [22], the thermal activation rate of a generic MM was calculated in the
m
-basis
in the absence of tunneling
via the
integral relaxation time
. Tunneling
has been taken into account in [11] by adiabatically eliminating fast nondiago-
nal DM elements, which amounts to using the high-order perturbation theory in
calculating tunnel splittings [23]. The resulting system of rate equations with res-
onance tunneling was solved by the method of
effective resistances
[11] using
the idea of the solution of the Fokker-Planck equation at low temperatures in the
classical case. Later, the system of rate equations in the
m
-basis was employed
in [21, 24, 25].
In particular, [21] repeats the steps of [11] using the realistic model of Mn
12
with
B/
0 in Eq. (140). A new element of [21] is the erroneous considera-
tion of spin-phonon interactions leading to the spin-phonon coupling of the type
=
D
S
2
yy
,
αα
being components of the deformation tensor, be-
cause of tilting the easy axis by transverse phonons at
second
order in the small
tilting angle
δϕ.
This leads to nonexistent direct processes with changing
m
by
2. In fact, as we have seen above, second-order terms in
δϕ,
Eq. (151), give rise
to Raman processes rather than to direct processes. The error made in [21], ne-
glection of a part of
δϕ
2
terms that cancel the result, has been explained in [26].
Nevertheless, the appeal of
m
xx
−
S
2
−
+
+
2 direct processes has been remaining strong,
so that the relevance of Eq. (A12) in [21] for explanation of experiments on molec-
ular magnets is still disputable. The recent examples are experimental works on
Fe
8
,
[27, 28]. Whereas in [27], Eq. (A12) in [21] is used with success. Here [28]
states that direct processes with
m
=
2 do not fit the data. On the other hand, for
Fe
8
these processes were shown to arise from rotations around the easy axis, the
=
