Magnetic Neutron Scattering and Spin-Polarized Neutrons

Magnetic Neutron Scattering
and
Spin-Polarized Neutrons
C. Ulrich
Department Prof. B. Keimer
Max-Planck-Institute for solid state research, Stuttgart, Germany

Nuclear Neutron Scattering:
- Elastic Neutron Scattering
Diffraction – Crystal Structure
- Inelastic Neutron Scattering
Excitations - Phonons
Magnetic Neutron Scattering:
- Elastic Neutron Scattering
Diffraction – Spin Structure
- Inelastic Neutron Scattering
Excitations - Magnons
ferro / antiferromagnetic
magnetic moment
direction of the spins

(1/2, 1/2, 1/2) - Bragg Reflection
T < 77 K
G -ty p e
Integrated Intensity (cnts/10 sec)
10000
1000
0 50 100 150 200 250
Temperature (K)
µ 0 = 1.72 µ B / V 3+ -ion

TYPE:
Ferromagnet
Antiferromagnet
G-type A-type C-type

(1/2, 1/2, 0) - Bragg Reflection
7 7 K < T < 116 K
C -typ e
Integrated Intensity (cnts/10 sec)
10000
1000
0 50 100 150 200 250
Temperature (K)
µ 0 = 1.05 µ B / V 3+ -ion

QHXWURQ
VSLQ
PDJQHWLF
ILHOG

Q=k f -k i

e -

M(r)
f(Q)
f(Q)
Fourier
Transform
distribution of the e - -spins
around the atom
magnetic form factor
Q

mag. Formfactor of the free Fe 4+ - ion
Intensity (arb. units - [ 1/2 g f mag
])
3000
2500
2000
1500
1000
500
SrFeO 3
mag F. Fe 4+
mag F. Fe 3+
S2
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
sin(Θ)/λ (Å -1 )

Crystal Structure of LaTiO 3

How to distinguish between
magnetic and nuclear Neutron Scattering
- temperature dependence
magnetic Bragg peaks vansih above the
magnetic ordering temperature
- magnetic form factor decreases with Q
- polarized neutrons

2000
1800
1600
magnetic
Sr 3
Fe 2
O 7
1800
1600
Int1
Int3
Intensity (cnts/12 sec)
1400
1200
1000
800
600
400
200
AM am 39
AL
38 al
1 234 56 78 91011 1213 14 151617 18 1920 2122324 26
AB 25 2728293031323 34 353637 C DEF GH I JKLMNOPQ RSTUV WX Y AK
a b cd e f gh i j k l mn op q ak
r s t u vw x y ZAABACADAEAFAGAHAIAJ
z a abacadaeafag ah aiaj
magnetic
nuclear
AO
40 4142 aoap AP
AQ
AN an 43 aq
AR ar
44
AS 45 as ATAUAVAWAXAYAZBABBCBD
4647 atauavawax 484950 515253545565758 ay az bab bcbdbebfbg BEBFBG 59 BHBI 6061626364656 bhbibjbkblbmbnbobpbqbrbsbtbubvbw BJBKBLBMBNBOBPBQBRBSBTBUBVBWBXBY 67 68 6970717273 74
75 767 bxby BZCACBCC 78798081 bzcacb cc
0
0.6 0.8 1.0 1.2 1.4
Intensity (cnts / 12 sec)
1400
1200
1000
800
600
400
200
0
0 20 40 60 80 100 120 140 160 180 200
(Q H
, 0, 0 )
Temperature (K)

Lecture Notes
X-Ray and Neutron Scattering
B. Keimer and C. Ulrich

Inelastic Neutron Scattering
magnon dispersion
Heisenberg Hamiltonian:
H = Σ i j J S i • S j
J = exchange interaction
IUHTXHQF\HQHUJ\
PRPHQWXP
band width ∝ J

Magnon Dispersion Relation in LaMnO 3
inelastic neutron scattering
Q (A -1 )
[1,1,0] [0,0,1]
K. Hirota et al., Physica B 237, 36 (1997)

75,636SHFWURPHWHUDW)50
,,

20
Magnon Dispersion YTiO 3
18
16
14
Energy (meV)
12
10
8
6
4
2
0
(0 0 2)
(0 0 1)
(0 -1 1)
(0 K L) (r.l.u.)
(0 -1 2)
(0 0 2)
Intensity (cnts/70 sec)
400
300
200
100
T = 5 K
T = 50 K
0
0 5 10 15 20 25
Energy (meV)

Y 1-x
Ca x
VO 3
(1 %)
35
Data2 Data3 Data1
Data4
30
YVO 3
1 %
5 %
Energy (meV)
25
20
15
10
5
Y 1-x
Ca x
VO 3
QL
(0.5, 0.5, 1)
QHKL
(0.25, 0.25, 1.5)
0
0.50 0.55 0.60 0.65 0.70 0.75 1.0 1.1 1.2 1.3 1.4 1.5 1.4 1.3 1.2 1.1 0.50 1.0 0.45 0.40 0.35 0.30 0.25
(0.5, 0.5, 0)
(0.5, 0.5, 1)
Qhk
(0.75, 0.75, 0)
(0.25, 0.25, 1)
QHKL
(0.5, 0.5, 1.5)