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Magnetic Neutron Scattering. Martin Rotter, University of Oxford. Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering. Contents. Neutrons and Magnetism. Macro-Magnetism: Solution of Maxwell´s Equations – Engineering of (electro)magnetic

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slide1

Magnetic Neutron Scattering

Martin Rotter, University of Oxford

NESY Winter School 2009

contents
Introduction: Neutrons and Magnetism

Elastic Magnetic Scattering

Inelastic Magnetic Scattering

Contents

NESY Winter School 2009

neutrons and magnetism
Neutrons and Magnetism

Macro-Magnetism:

Solution of Maxwell´s

Equations – Engineering

of (electro)magnetic

devices

10-1m

10-3m

10-5m

10-7m

10-9m

10-11m

MFM image

Micromagnetic simulation.

Micromagnetism:

Domain Dynamics,

Hysteresis

Atomic Magnetism:

Instrinsic Magnetic

Properties

Hall

Probe

VSM

SQUID

MOKE

MFM

NMR

FMR

SR

NS

NESY Winter School 2009

slide4

2/l

k

2q

τ=Q

k‘

q

Incoming

Neutron

Scattered

Neutron

Bragg’s Law in Reciprocal Space (Ewald Sphere)

O

a*

c*

the scattering cross section
The Scattering Cross Section

Scattering Cross Sections

Total

Differential

Double Differential

Scattering Law S .... Scattering function

Units: 1 barn=10-28 m2 (ca. Nuclear radius2)

NESY Winter School 2009

slide7

(follows from Fermis golden rule)

M neutron mass

k wavevector

|sn>Spin state of

the neutron

Psn Polarisation

|i>,|f> Initial-,final-

state of the

targets

Ei,EfEnergies of –‘‘-

Pi thermal

population

of state |i>

Hint Interaction

-operator

S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984

NESY Winter School 2009

slide10

A short

Excursion

to Fourier

and Delta

Functions ....

it follows by extending the range of x to more than –L/2 ...L/2 and

going to 3 dimensions (v0 the unit cell volume)

NESY Winter School 2009

neutron diffraction

Lattice G with basis B:

Latticefactor

Structurefactor

Independent ofQ:

„Isotope-incoherent-Scattering“

„Spin-incoherent-Scattering“

one element(NB=1):

Neutron – Diffraction
magnetic diffraction

Difference to nuclear scattering:

Formfactor ... no magnetic signal at high angles

Polarisationfactor ... only moment components

normal to κ contribute

Magnetic Diffraction

NESY Winter School 2009

slide13

Atomic Lattice

Magnetic Lattice

ferro

antiferro

NESY Winter School 2009

slide14

Atomic Lattice

Magnetic Lattice

ferro

antiferro

NESY Winter School 2009

slide15

Atomic Lattice

Magnetic Lattice

ferro

antiferro

NESY Winter School 2009

formfactor
Formfactor

Q=

Dipole Approximation (small Q):

NESY Winter School 2009

slide17

The Nobel Prize in Physics 1994

In 1949 Shull showed the magnetic structure of the MnO crystal, which led to the discovery of antiferromagnetism (where the magnetic moments of someatoms point up and some point down).

slide18

Arrangement of Magnetic Moments in Matter

Paramagnet

Ferromagnet

Antiferromagnet

And many more ....

Ferrimagnet, Helimagnet, Spinglass ...collinear, commensurate etc.

NESY Winter School 2009

gdcu 2
GdCu2

TN= 42 K M [010]

TR= 10 K q = (2/3 1 0)

Magnetic Structure from

Neutron Scattering

Experimental data D4, ILL

Calculation done by McPhase

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

NESY Winter School 2009

gdcu 220
GdCu2

TN= 42 K M [010]

TR= 10 K q = (2/3 1 0)

Magnetic Structure from

Neutron Scattering

Experimental data D4, ILL

Calculation done by McPhase

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

NESY Winter School 2009

gdcu 221
GdCu2

TN= 42 K M [010]

TR= 10 K q = (2/3 1 0)

Magnetic Structure from

Neutron Scattering

Experimental data D4, ILL

Calculation done by McPhase

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

NESY Winter School 2009

gdcu 222
GdCu2

TN= 42 K M [010]

TR= 10 K q = (2/3 1 0)

Magnetic Structure from

Neutron Scattering

Experimental data D4, ILL

Calculation done by McPhase

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

NESY Winter School 2009

gdcu 223
GdCu2

TN= 42 K M [010]

TR= 10 K q = (2/3 1 0)

Magnetic Structure from

Neutron Scattering

Experimental data D4, ILL

Calculation done by McPhase

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

NESY Winter School 2009

gdcu 224
GdCu2

TN= 42 K M [010]

TR= 10 K q = (2/3 1 0)

Magnetic Structure from

Neutron Scattering

Rpnuc= 4.95%

Rpmag= 6.21%

Experimental data D4, ILL

Calculation done by McPhase

Goodness of fit

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

NESY Winter School 2009

slide25

NdCu2 Magnetic Phasediagram

(Field along b-direction)

NESY Winter School 2009

slide26

Complex Structures

μ0Hb=2.6T

AF1

μ0Hb=1T

μ0Hb=0

Q=

Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499

NESY Winter School 2009

slide27

Complex Structures

μ0Hb=2.6T

F1

μ0Hb=1T

μ0Hb=0

Q=

Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499

NESY Winter School 2009

slide28

Complex Structures

μ0Hb=2.6T

F2

μ0Hb=1T

μ0Hb=0

Q=

Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499

NESY Winter School 2009

ndcu 2 magnetic phasediagram h b
NdCu2 Magnetic PhasediagramH||b

F1   

F3 

c

F1 

b

a

AF1 

Lines=Experiment

Colors=Theory

Calculation done by McPhase

NESY Winter School 2009

a caveat on the dipole approximation
A caveat on the Dipole Approximation

Dipole Approximation (small Q):

E. Balcar derived accurate formulas for the

S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984

Page 241-242

NESY Winter School 2009

slide31

M. Rotter & A. Boothroyd

2008

did some calculations

E. Balcar

NESY Winter School 2009

slide32

Comparison to

experiment

(σ-σdip)/σdip(%)

Goodness of fit:

Rpdip=15.6%

Rpbey=8.4 %

(Rpnuc=7.3%)

Calculation done by McPhase

CePd2Si2

bct ThCr2Si2 structure

Space group I4/mmm

Ce3+ (4f1)J=5/2

TN=8.5 K

q=(½ ½ 0), M=0.66 μB/Ce

M. Rotter, A. Boothroyd, PRB, submitted

NESY Winter School 2009

slide33

NdBa2Cu3O6.97

superconductor TC=96K

orth YBa2Cu3O7-x structure

Space group Pmmm

Nd3+ (4f3)J=9/2

TN=0.6 K

q=(½ ½ ½), M=1.4 μB/Nd

... using the dipole approximation may lead to a wrong magnetic structure !

M. Rotter, A. Boothroyd, PRB, submitted

Calculation done by McPhase

NESY Winter School 2009

inelastic magnetic scattering
Inelastic Magnetic Scattering
  • Dreiachsenspektometer – PANDA
  • Dynamik magnetischer Systeme:
        • Magnonen
        • Kristallfelder
        • Multipolare Anregungen

NESY Winter School 2009

three axes spectrometer tas
Three Axes Spectrometer (TAS)

k

Q

Ghkl

k‘

q

NESY Winter School 2009

panda tas for polarized neutrons at the frm ii munich37
PANDA – TAS for Polarized Neutrons at the FRM-II, Munich

beam-channel

monochromator-shielding with platform

Cabin with computer work-placesand electronics

secondary spectrometer

with surrounding radioprotection,

15 Tesla / 30mK Cryomagnet

NESY Winter School 2009

slide38

The Nobel Prize in Physics 1994

E

Q

Movement of Atoms [Sound, Phonons]

Brockhouse 1950 ...

π/a

Phonon Spectroscopy: 1) neutrons

2) high resolution X-rays

NESY Winter School 2009

slide39

Movement of Spins - Magnons

153

MF - Zeeman Ansatz

(for S=1/2)

T=1.3 K

NESY Winter School 2009

slide40

Movement of Spins - Magnons

153

T=1.3 K

Bohn et. al.

PRB 22 (1980) 5447

NESY Winter School 2009

slide41

Movement of Spins - Magnons

153

a

T=1.3 K

Bohn et. al.

PRB 22 (1980) 5447

NESY Winter School 2009

movement of charges the crystal field concept

+

+

+

+

+

+

+

+

+

+

E

Hamiltonian

Q

Movement of Charges - the Crystal Field Concept

4f –charge density

NESY Winter School 2009

ndcu 2 crystal field excitations
NdCu2 – Crystal Field Excitations

orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ion

Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297

NESY Winter School 2009

ndcu 2 4f charge density

T=100 K

T=40 K

T=10 K

NdCu2 - 4f Charge Density

NESY Winter School 2009

calculate magnetic excitations and the neutron scattering cross section

Linear Response Theory, MF-RPA

Calculate Magnetic Excitations and the Neutron Scattering Cross Section

.... High Speed (DMD) algorithm: M. Rotter Comp. Mat. Sci. 38 (2006) 400

NESY Winter School 2009

ndcu 2

F3 

F1 

AF1 

NdCu2

F3: measured dispersion was fitted to get exchange constants J(ij)

Calculations done by McPhase

slide47

Movements of Atoms [Sound, Phonons]

1970 Movement of Spins [Magnons]

? Movement of Orbitals [Orbitons]

a

a

τorbiton

τorbiton

Description: quadrupolar

(+higher order) interactions

NESY Winter School 2009

summary
Magnetic Diffraction

Magnetic Structures

Caveat on using the Dipole Approx.

  • Magnetic Spectroscopy
  • Magnons (Spin Waves)
  • Crystal Field Excitations
  • Orbitons
Summary

NESY Winter School 2009

slide50

McPhase-theWorldofRareEarthMagnetism

McPhase is a program package for the calculation of

magnetic properties of rare earth based systems.

Magnetization Magnetic Phasediagrams

Magnetic StructuresElastic/Inelastic/Diffuse                                              Neutron Scattering                                             Cross Section

NESY Winter School 2009

slide51

Crystal Field/Magnetic/Orbital Excitations

McPhase runs on Linux & Windows it is freeware

www.mcphase.de

Magnetostriction

and much more....

NESY Winter School 2009

slide52

Important Publications referencing McPhase:

  • M. Rotter, S. Kramp, M. Loewenhaupt, E. Gratz, W. Schmidt, N. M. Pyka, B. Hennion, R. v.d.Kamp Magnetic Excitations in the antiferromagnetic phase of NdCu2Appl. Phys. A74 (2002) S751    
  • M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu2 Compounds using McPhase J. of Applied Physics 91 (2002) 8885
  • M. Rotter Using McPhase to calculate Magnetic Phase Diagrams of Rare Earth Compounds J. Magn. Magn. Mat. 272-276 (2004) 481

Thanks to ……

  • M. Doerr,M. Loewenhaupt, TU-Dresden
  • R. Schedler, HMI-Berlin P. Fabi né Hoffmann, FZ Jülich
  • S. Rotter, Wien, Austria
  • M. Banks, MPI Stuttgart
  • Duc Manh Le, University of London
  • J. Brown, B. Fak, ILL, Grenoble
  • Boothroyd, Oxford
  • P. Rogl, University of Vienna
  • E. Gratz, E. Balcar TU Vienna

University of Oxford

…….and thanks to you !

NESY Winter School 2009