Neutron Scattering from Magnetic Materials part 2 doc
Neutron Scattering from Magnetic Materials part 2 doc
... 3d
n
SLJGround-state
term
Ti
3+
,V
4+
3d
1
1
2
2
3
2
2
D
3
2
V
3+
3d
2
13 2
3
F
2
Cr
3+
,V
2+
3d
3
3
2
3
3
2
4
F
3
2
Mn
3+
,Cr
2+
3d
4
22 0
5
D
0
Fe
3+
,Mn
2+
3d
5
5
2
0
5
2
6
S
5
2
Fe
2+
3d
6
22 4
5
D
4
Co
2+
3d
7
3
2
3
9
2
4
F
9
2
Ni
2+
3d
8
13 4
3
F
4
Cu
2+
3d
9
1
2
2
5
2
2
D
5
2
Magnetic ... 0,
1
2
)
∗
(
1
2
, 0, 0)(
1
2
,
1
2...
Neutron Scattering from Magnetic Materials part 9 docx
... this the scattering cross-section can be written as
d
2
σ
dΩ dE
±
=
γe
2
mc
2
2
1
2
gF(Q)
2
k
k
exp
−2W(Q)
1 +Q
2
z
1
2
S
×
2
3
v
0
q,τ
n
q
+
1
2
±
1
2
δ(
¯
hω
q
∓
¯
hω)δ(Q ... lowering
operators as
d
2
σ
dΩ dE
=
γe
2
mc
2
2
1
2
gF(Q)
2
k
k
exp
−2W(Q)
×
1 −Q
2
z
1
2
¯
h
∞
−∞
dt exp(−iωt)
S
z...
Neutron Scattering from Magnetic Materials part 1 pps
... 17
6.5.Spinwaves 18
6.6.Scatteringfromspinwaves 20
6.7.Paramagneticscattering 21
6.8.Crystal-fieldexcitations 22
7.Concludingremarks 23
References 23
NEUTRON SCATTERING FROM MAGNETIC MATERIALS
Edited ... r
0
)
2
(2 )
3
2N
m
v
0
g
2
S
4
1 +
Q
2
z
f
2
(Q)e
−2W(Q)
×
τ q
n
q
+1δ(Q −q −τ )δ
E −
¯
hω(q)
, (79)
d
2
σ
dΩ dE
m,−1
=
k
1
k
0
(γ r
0
)
2
(2...
Neutron Scattering from Magnetic Materials part 4 pdf
... G
1
, g
2
∈ G
2
) we have g
1
g
2
= g
2
g
1
.LetR
1
:G
1
→ G(E
1
) be
a representation of G
1
and R
2
:G
2
→ G(E
2
) a representation of G
2
. The tensor product
R
1
⊗R
2
of R
1
and R
2
is the ... E
1
⊗E
2
) associating to each g =g
1
g
2
in G, where g
1
∈ G
1
and g
2
∈ G
2
, the operator R(g) such that ∀
V
1
∈ E
1
, ∀
V
2
∈ E
2
,
R(g)[
V
1
⊗
V
2
]=[R...
Neutron Scattering from Magnetic Materials part 7 ppsx
... 6 2 4 2. 333
f
5
(Sm
3+
)55 /25 /2 6.000
f
6
(Eu
3+
) 3 3 0 No moment
f
7
(Gd
3+
)07 /27 /2 0.000
f
8
(Tb
3+
) 3 3 6 0.333
f
9
(Dy
3+
)55 /21 5 /2 0.500
f
10
(Ho
3+
) 6 2 8 0.600
f
11
(Er
3+
)63 /21 5 /2 ... spin-flip
1 82 J. Schweizer
Table 1
Coefficients C
2
for the different fillings of an f shell
f shell LS J c
2
=2/ g
J
−1
f
1
(Ce
3+
)31 /25 /2 1.333
f
2
(Pr
3+
) 5 1 4 1.50...
Neutron Scattering from Magnetic Materials part 8 pptx
... was correct.
23 2 P.J . B ro w n
incident polarisation is parallel to z is
P
2
zz
+P
2
yz
1 /2
=
((R
zz
−R
yy
)
2
+R
2
yz
)
1 /2
R
zz
+R
yy
=
1 −
J
2
yz
(R
zz
+R
yy
)
2
1 /2
(22 )
when J
yz
is ... M
⊥x
M
⊥y
M
⊥z
|M
⊥
|
2
(a) 0
√
2A cosφ
√
2A 2A
2
(1 +cos
2
φ)
(b) 0 2A cosφ 04A
2
cos
2
φ
(c) 0 0 2A 4A
2
.
Fig. 9. Possible magnetic structures for a tetragon...
Neutron Scattering from Magnetic Materials part 10 pot
... equations
2
¯
hω
q,0
=(a
1
+a
2
+b
1
−b
2
) +2 (q), (49)
2
¯
hω
q,1
=−(a
1
+a
2
+b
1
−b
2
) +2 (q), (50)
where
2 (q) =
(a
1
−a
2
+b
1
+b
2
)
2
−S
1
S
2
4J (q)
2
1 /2
, (51)
a
1
=g
1
µ
B
H, ( 52)
a
2
=g
2
µ
B
H, ... written as
¯
hω
q,a
−J (0)(S
2
−S
1
)(−1)
a
+
J (0)(S
1
−S
2
)
2
−
16
3
S
1
S
2
q
2
J (0)J
(2)
J (0)(S
1
−S
2
)
1 +(−1...
Neutron Scattering from Magnetic Materials part 12 ppt
... 21 5 80 5.51 2. 05
EuO 69 12 6 2. 01 1. 02
EuS 10. 62. 62. 31. 82 1.61
been investigated by inelastic neutron scattering. The neutron scattering investigation of
the spin dynamics of the doped ferromagnetic ... above T
C
a damped
harmonic oscillator form given by
F
α
(Q,ω)=
¯
h
2
γ
2
ω
2
0
(
¯
h
2
ω
2
−
¯
h
2
ω
2
0
)
2
+γ
2
¯
h
2
ω
2
(16)
was used. Here γ is...
Neutron Scattering from Magnetic Materials part 14 pot
... material
−
¯
h
2
2m
∇
2
+V(r)
Ψ =EΨ, (2)
where
∇
2
=
∂
2
∂x
2
+
∂
2
∂y
2
+
∂
2
∂z
2
, (3)
and where the first term of the Hamiltonian operator in the brackets on the left-hand side
(LHS) of (2) represents ... Phys. Rev. 181 920 (1969).
[20 ] G.M. Drabkin et al., JETP Lett. 2 353 (1965).
[21 ] S. Brehmer et al., Phys. Rev. B 60 329 (1999).
[22 ] M. Muller et al., Ph...
Neutron Scattering from Magnetic Materials part 15 pptx
... required,
ˇ
U
SAM→LAB
=
cos
ε
2
isin
ε
2
00
isin
ε
2
cos
ε
2
00
0 0 cos
ε
2
+isin
ε
2
00+isin
ε
2
cos
ε
2
. ( 120 )
The inverse of ( 120 ) is
ˇ
U
−1
SAM→LAB
=
cos
ε
2
−isin
ε
2
00
−isin
ε
2
cos
ε
2
00
0 ... by
t
+
t
−
iQ
2
t
+
iQ
2
t
−
=
1
l=N
A
11
A
12
A
13
A
14
A
21
A
22
A
23
A
24
A
31
A
32
A
33
A
34
A
4...
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