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Magnetic Diffraction
'
'*'1
)(jj
iijjcoh
elnuc
jjeebbN
S RκRκ
),('
),()ˆˆ('
'
2
2
22
κκκκ nucmag S
k
kNS
mc
e
k
kN
dEd
d
'
''21
'21 )()(
1)( jj ii
TjjTjjj
j
elmag eeJgFJgF
NS RκRκ
Difference to nuclear scattering: Formfactor ... no magnetic signal at high angles
Polarisationfactor ... only moment components normal to κ contribute
j
gF )(21
)ˆˆ( κκ
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Bestimmung von Formfaktoren: polarisierte Neutronen
Formfaktor
)(2
)()( 20 jg
gjF
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Atomgitter
Magnetisches Gitter
Ferromagnet
Antiferro-magnet
Überstruktur - reflexe
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In 1951 Shull showed the magnetic structure of the MnO crystal, which led to the discovery of antiferromagnetism (where the magnetic moments of
some atoms point up and some point down).
TN=122K
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TN= 42 K M [010]TR= 10 K q = (2/3 1 0) Magnetic Structure from
Neutron Scattering
GdCu2
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
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Magnetic Diffraction using Laue Method (LADI – ILL)
4% Ga doped FeGe2
This material undergoes a number of trans-itions and below 180K it locks into a non-harmonic spiral phase with a propagation vector of exactly 1/10. This gives rise to additional Bragg-peaks, which are shown in the second picture.
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NdCu2
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mehrere Kristallite(ca 120° verdreht)
lτ 3τ5τ
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AF2 Pattern
T=4.1KH=0T
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NdCu2 Magnetic Structures
at T=0
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Pattern T=0
h0.4 0.6 0.8 1.0
AF1
F1
F2
F3
τ=(0.6 0 0)5τ3τ
τ=(0.6666 0 0)
τ=(0.625 0 0) 2τ
2τ
2τ
k
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Komplexere Strukturen
F2
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|κ|[Å-1]
I(κ)
[co
unts
]
nichtkollineare Struktur(mcphase)
GdCu2In