Physics with Neutrons WS 2011/2012 - E21 - Technische Universität ...

e21.ph.tum.de

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


2 z


1

x

1


2 z


2

M

Q

x

dS y

M

Q

dS

z

dS x ,dS y

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