Physics with Neutrons WS 2011/2012 - E21 - Technische Universität ...
Physics with Neutrons
WS 2011/2012
Peter Böni
Physik-Department E21
Technische Universität München
D-85748 Garching
E-mail:Peter.boeni@frm2.tum.de
Web: www.ph.tum.de
https://campus.tum.de/tumonline/lv.detail?clvnr=950011566
22/05/2012
VL21, Physics with Neutrons II, June 4, 2012
Registration for Exams via TUMonline
2
Registration for the exams and seminars:
• via TUMonline (mandatory)
• period of registration: May 21 – June 30
• Exam dates: to be coordinated individually
Physics with Neutrons II
3
5. Neutron Scattering from Disordered Systems
5.1. Introduction
5.2. Pair correlation functions and structure factor
Determination of interactions potentials
5.3. Incoherent single particle dynamics and diffusion
5.4. Coherent dynamics and collective modes
The scattering law in the hydrodynamic limit
6. Magnetic Neutron Scattering: Structures, Magnons
6.1. Magnetic Cross Section
Master Formula
Spin and Orbital Coupling
6.2. Elastic Magnetic Scattering
Paramagnetism and magn. form factors
Ferro- and Antiferromagnetism
Helimagnetism
6.3. Inelastic Magnetic Scattering
Magnons
6.4. Flux Line Lattices in Superconductors
Antiferromagnetic Order
4
B ext = 0
magnetization is staggered: sub-lattice magnetization is N = order parameter
(recall ferromagnet: m = order parameter)
Antiferromagnetic Structure of MnAu
5
2a
a
a: lattice constant of nuclear unit cell
2a: lattice constant of magnetic unit cell
Magnetic Bragg Scattering from MnO
Intensity (Neutrons / minute)
6
Shull and Smart, Phys. Rev. 76, 1256 (1949).
MnO:
T N = 122 K
1 1 1
3 1 1 3 3 1 5 1 1
2
2
2
2
2
2
2
2
2
2
3
2
2
3
2
2
3
2
80 K
MnO
T N = 122 K
l = 1.057 Å
293 K
Scattering Angle
Intensity
7
Néel Temperature of MnO
T-dependence of (½ ½ ½)-Bragg reflection:
MnO:
T N = 122 K
for comparison:
T N from
neutron scattering:
zero field method!
Temperature (K)
T N
8
Crystal Structure – Fermi Surface of Cr
crystal structure: bcc
H
G
reciprocal space:
Fermi surface:
e
G
electrons
H
holes
Q - = (1-d 0 0)
Q + = (1+d 0 0)
magnetic structure:
Incommensurate Antiferromagnetic Order in Cr
9
crystal structure: bcc
nuclear peaks:
h + k + l = even (2 0 0), (1 1 0), etc.
magnetic peaks near: h + k + l = odd (1d 0 0), (1d 1d 1d ), etc.
measurements: PUMA @ FRM II
Crystal Structure of MnSi, Reciprocal Lattice
10
crystal structure: P2 1 3
strong nuclear peaks: (110), (111)
satellites at:
(hd kd ld)
l
(001)
(111)
(000)
(110)
hk ,
Diffraction Patterns of MnSi
11
l
small angle neutron
scattering:
SANS @ GKSS
(000)
(110)
h,k
triple axis:
TASP @ PSI
D. Lamago,
unpublished.
P. Böni et al., J. Phys.: Condens. Matter 23, 254209 (2011).
T-Dependence of Pitch in Ho
12
at low temperature:
commensurate structures:
2/12:
2/11:
Doon Gibbs et al., Phys. Rev. Lett. 55, 234 (1985).
spin slips
Skyrmion Lattice in MnSi
13
apply field B = 0.2 Tesla:
diffraction pattern:
real space pattern:
120 0
120 0
120 0
S. Mühlbauer et al., Science 323, 915 (2009).
Ferromagnetic Magnon
14
z-axis:
ground state: U 0 = -JNS 2
quantisation axis
for M -J -J -2J
J J +2J
1 st excited state: U 1 = U 0 + 4JS 2
Ferromagnetic Spin Waves
15
Distribution of excitation over all spins spin waves
Propagation of Ferromagnetic Spin Waves
16
direction of propagation
17
Cross Section for Spin Wave
M perpendicular Q:
M parallel Q:
z
dS
1
Qˆ
2 z
1
x
1
Qˆ
2 z
2
M
Q
x
dS y
M
Q
dS
z
dS x ,dS y
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