Chemistry Reference
In-Depth Information
one obtains
12
MN
k
k
2
ω
k
π
(1)
γα
(1)
αγ
·
×
δ
ε
α
−
ω
k
n
k
+
δ
ε
α
−
ω
k
(
n
k
+
1)
ε
γ
+
ε
γ
−
MN
k
k
2
ω
k
π
(1)
γα
(1)
αγ
=
·
12
×
δ
ω
α
γ
+
ω
k
n
k
+
δ
ω
α
γ
−
ω
k
(
n
k
+
1)
(171)
Now recalling Eq. (53) one obtains
R
(1)
αβ,α
β
MN
k
πD
2
12
k
2
ω
k
=
αα
,γγ
δ
ω
α
γ
+
ω
k
n
k
+
δ
ω
α
γ
−
ω
k
(
n
k
+
1)
δ
β
β
Q
(1)
×
−
γ
δ
αα
γ
β
β,γγ
δ
ω
β
γ
+
ω
k
n
k
+
δ
ω
β
γ
−
ω
k
(
n
k
+
1
)
Q
(1)
−
β
)]
(172)
Q
(1)
+
αβ,α
β
[
δ
(
ω
αα
+
ω
k
)(
n
k
+
1)
+
δ
(
ω
αα
−
ω
k
)
n
k
+
(
α
→
where
β
β
/D
2
Q
(1)
(1)
αα
·
(1)
αβ,α
β
≡
(173)
is a dimensionless combination that characterizes the spin. Next, it is convenient
to go over from summation to integration,
v
0
N
k
d
3
k
(2
π
)
3
···
1
··· ⇒
(174)
where
v
0
is the unit-cell volume. Using
v
0
/M
v
t
k
one can in-
troduce the characteristic frequency
t
and the corresponding energy
E
t
of the
spin-phonon interaction
=
1
/ρ
and
ω
k
=
ρv
t
1
/
4
ρv
t
3
1
/
4
t
≡
E
t
≡
(175)
