Itinerant Spin Dynamics in Structures of ... - Jacobs University

Appendix D
Hamiltonian in [110] growth
direction
with
The Cooperon Hamiltonian in the 0-mode approximation is given as follows
⎛ ⎞
A B C
H c,0 = ⎜
⎝ B ∗ D E ⎟
⎠ +M q3,
(D.1)
C ∗ E ∗ F
A = 1
4q 2 W (q (
2 4k
2
x +3 (˜q 1 2 +q2
2 ))
W
( )
q2 W
−16k x˜q 1 sin + (˜q 1 2 −q 2
2
2)
sin(q2 W)), (D.2)
( ( ) )
i 4k x sin
q2 W
2
− ˜q 1 sin(q 2 W)
B = √ , (D.3)
2W
C = − q 2
(˜q
2
1 +q2
2 ) (
W + q
2
2 − ˜q 1
2 )
sin(q2 W)
, (D.4)
4q 2 W
D = q (
2 2k
2
x + ˜q 1 2 ) ( +q2 2 W + q
2
2 − ˜q 1
2 )
sin(q2 W)
, (D.5)
2q 2 W
( ( ) )
i 4k x sin
q2 W
2
+ ˜q 1 sin(q 2 W)
E = √ , (D.6)
2W
F = 1
4q 2 W (q (
2 4k
2
x +3 (˜q 1 2 +q2
2 ))
W
( )
q2 W
+16k x˜q 1 sin + (˜q 1 2 −q 2
2
2)
sin(q2 W)) (D.7)
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