1. Magnetism in Complex Systems 2009
Magnetic Neutron Scattering
Martin Rotter, University of Oxford
Martin Rotter
Magnetism in Complex Systems 2009

2. Magnetism in Complex Systems 2009
Contents
Introduction: Neutrons and Magnetism
Elastic Magnetic Scattering
Inelastic Magnetic Scattering
Martin Rotter
Magnetism in Complex Systems 2009

3. 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
Hall
Probe
VSM
SQUID
MOKE
MFM
NMR
FMR
SR NS
Micromagnetism:
Domain Dynamics,
Hysteresis
MFM image
Micromagnetic simulation.
Atomic Magnetism:
Instrinsic Magnetic
Properties
Martin Rotter
Magnetism in Complex Systems 2009

4. Single Crystal Diffraction E2 – HMI, Berlin
neutrons: S=1/2 μNeutron= –1.9 μN
τ = 885 s (β decay)
k=2π/ λ E=h2/2Mnλ2=81.1meV/λ2[Å2] k Q O
Martin Rotter
Magnetism in Complex Systems 2009

5. Magnetism in Complex Systems 2009
Atomic Lattice
Magnetic Lattice
ferro
antiferro
Martin Rotter
Magnetism in Complex Systems 2009

6. 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 some atoms point up and some point down).

7. Magnetic Structure from Neutron Powder Diffraction
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0)
Magnetic Structure from
Neutron Powder Diffraction
Experimental data D4, ILL
Calculation done by McPhase
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
Martin Rotter
Magnetism in Complex Systems 2009

8. Magnetic Structure from Neutron Powder Diffraction
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0)
Magnetic Structure from
Neutron Powder Diffraction
Experimental data D4, ILL
Calculation done by McPhase
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
Martin Rotter
Magnetism in Complex Systems 2009

9. Magnetic Structure from Neutron Powder Diffraction
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0)
Magnetic Structure from
Neutron Powder Diffraction
Experimental data D4, ILL
Calculation done by McPhase
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
Martin Rotter
Magnetism in Complex Systems 2009

10. Magnetic Structure from Neutron Powder Diffraction
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0)
Magnetic Structure from
Neutron Powder Diffraction
Experimental data D4, ILL
Calculation done by McPhase
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
Martin Rotter
Magnetism in Complex Systems 2009

11. Magnetic Structure from Neutron Powder Diffraction
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0)
Magnetic Structure from
Neutron Powder Diffraction
Experimental data D4, ILL
Calculation done by McPhase
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
Martin Rotter
Magnetism in Complex Systems 2009

12. Magnetic Structure from Neutron Powder Diffraction
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0)
Magnetic Structure from
Neutron Powder Diffraction
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
Martin Rotter
Magnetism in Complex Systems 2009

13. 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)
Martin Rotter
Magnetism in Complex Systems 2009

14. Magnetism in Complex Systems 2009
M neutron mass
k wavevector
|sn> Spin state of
the neutron
Psn Polarisation
|i>, |f> Initial-,final-
state of the
targets
Ei, Ef Energies of –‘‘-
Pi thermal
population
of state |i>
Hint Interaction
-operator
S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984
(follows from Fermi`s golden rule)
Martin Rotter
Magnetism in Complex Systems 2009

15. Interaction of Neutrons with Matter
Martin Rotter
Magnetism in Complex Systems 2009

16. Magnetism in Complex Systems 2009
Magnetic Diffraction
Difference to nuclear scattering:
Formfactor no magnetic signal at high angles
Polarisationfactor only moment components
normal to Q contribute
Martin Rotter
Magnetism in Complex Systems 2009

17. Magnetism in Complex Systems 2009
Formfactor Q=
Dipole Approximation (small Q):
Martin Rotter
Magnetism in Complex Systems 2009

18. 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
Martin Rotter
Magnetism in Complex Systems 2009

19. Magnetism in Complex Systems 2009
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, 79 (2009) R140405
Calculation done by McPhase
Martin Rotter
Magnetism in Complex Systems 2009

20. Measuring Spin Density Distributions
polarized neutron beam
sample in magnetic field to induce ferromagnetic moment
-> magnetic intensity on top of nuclear reflections
-> nuclear-magnetic interference term:
PnB
Pn B
Nuclear Magnetic
Structure Factor
Forsyth, Atomic Energy Review 17(1979) 345
“Flipping Ratio”:
nuclear structure factor has to be known with high accuracy
only for centrosymmetric structure (no phase problem)
spin density measurements are made in external magnetic field,
comparison to results of ab initio model calculations desirable !
Martin Rotter
Magnetism in Complex Systems 2009

21. Inelastic Magnetic Scattering
Dreiachsenspektometer – PANDA
Dynamik magnetischer Systeme:
Magnonen
Kristallfelder
Multipolare Anregungen
Martin Rotter
Magnetism in Complex Systems 2009

22. Three Axes Spectrometer (TAS)k‘ k q Q
Ghkl
constant-E scans
constant-Q scans
Martin Rotter
Magnetism in Complex Systems 2009

23. PANDA – TAS for Polarized Neutrons at the FRM-II, Munich
beam-channel
monochromator- shielding with platform
Cabin with computer work-places and electronics
secondary spectrometer
with surrounding radioprotection,
15 Tesla / 30mK Cryomagnet
Martin Rotter
Magnetism in Complex Systems 2009

24. Magnetism in Complex Systems 2009
Martin Rotter
Magnetism in Complex Systems 2009

25. Magnetism in Complex Systems 2009
Movement of Atoms [Sound, Phonons]
Brockhouse
The Nobel Prize in Physics 1994 E Q
π/a
Phonon Spectroscopy: 1) neutrons
2) high resolution X-rays
Martin Rotter
Magnetism in Complex Systems 2009

26. Magnetism in Complex Systems 2009
Movement of Spins - Magnons
153
MF - Zeeman Ansatz
(for S=1/2)
T=1.3 K
Martin Rotter
Magnetism in Complex Systems 2009

27. Magnetism in Complex Systems 2009
Movement of Spins - Magnons
153
T=1.3 K
Bohn et. al.
PRB 22 (1980) 5447
Martin Rotter
Magnetism in Complex Systems 2009

28. Magnetism in Complex Systems 2009
Movement of Spins - Magnons
153 a
T=1.3 K
Bohn et. al.
PRB 22 (1980) 5447
Martin Rotter
Magnetism in Complex Systems 2009

29. Movement of Charges - the Crystal Field Concept+
charge density
of unfilled shell E Q
Hamiltonian
Neutrons change the magnetic moment in an inelastic scattering process: this is correlated to a change in the charge density by the LS coupling …”crystal field excitation”
Martin Rotter
Magnetism in Complex Systems 2009

30. Magnetism in Complex Systems 2009
Movements of Atoms [Sound, Phonons]
Movement of Spins [Magnons]
? Movement of Orbitals [Orbitons] a a
τorbiton
τorbiton
Description: quadrupolar
(+higher order) interactions
Martin Rotter
Magnetism in Complex Systems 2009

31. Magnetism in Complex Systems 2009
PrNi2Si2
bct ThCr2Si2 structure
Space group I4/mmm
Pr3+ (4f2) J=4
-CF singlet groundstate
-Induced moment system
-Ampl mod mag. structure
TN=20 K
q=( ), M=2.35 μB/Pr
10meV
Blancoet. al. PRB 45 (1992) 2529
Martin Rotter
Magnetism in Complex Systems 2009

32. Magnetism in Complex Systems 2009
PrNi2Si2 excitations
Neutron Scattering Experiment
Blanco et al. PRB 56 (1997) 11666
Blanco et al. Physica B 234 (1997) 756
Calculations done by McPhase
Martin Rotter
Magnetism in Complex Systems 2009

33. Magnetism in Complex Systems 2009
Calculate Magnetic Excitations and the Neutron Scattering Cross Section
Linear Response Theory, MF-RPA
.... High Speed (DMD) algorithm: M. Rotter Comp. Mat. Sci. 38 (2006) 400
Martin Rotter
Magnetism in Complex Systems 2009

34. Magnetism in Complex Systems 2009
Summary
Magnetic Diffraction
Magnetic Structures
Caveat on using the Dipole Approx.
Magnetic Spectroscopy
Magnons (Spin Waves)
Crystal Field Excitations
Orbitons
Martin Rotter
Magnetism in Complex Systems 2009

35. Epilogue
How much does an average European citizen spend on Neutron Scattering per year ?
NESY- Fachausschuss “Forschung mit Neutronen und Synchrotron-strahlung” der Oesterr. Physikalischen Gesellschaft,
CENI – Central European Neutron Initiative (Austria, Czech Rep., Hungary) – membership at ILL (Institute Laue Langevin)
Funding is strongly needed to build the ESS, the European Spallation Source

36. Magnetism in Complex Systems 2009
Martin Rotter, University of Oxford
Martin Rotter
Magnetism in Complex Systems 2009

37. McPhase - the World of Magnetism
McPhase is a program package for the calculation of magnetic properties
! NOW AVAILABLE with INTERMEDIATE COUPLING module !
          Magnetization                       Magnetic Phasediagrams
    Magnetic Structures            Elastic/Inelastic/Diffuse                                               Neutron Scattering                                              Cross Section
Martin Rotter
Magnetism in Complex Systems 2009

38. Magnetism in Complex Systems 2009
Crystal Field/Magnetic/Orbital Excitations
McPhase runs on Linux & Windows it is freeware
Magnetostriction 
and much more....
Martin Rotter
Magnetism in Complex Systems 2009

39. Thanks to …… ……. and thanks to you !
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 NdCu2 Appl. 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 (2004) 481
    M. Doerr, M. Loewenhaupt, TU-Dresden
R. Schedler, HMI-Berlin   P. Fabi né Hoffmann, FZ Jülich
  S. Rotter, Wien
M. Banks, MPI Stuttgart
Duc Manh Le, University of London
J. Brown, B. Fak, ILL, Grenoble
A. Boothroyd, Oxford
P. Rogl, University of Vienna
E. Gratz, E. Balcar, G.Badurek
TU Vienna
J. Blanco,Universidad Oviedo
University of Oxford
Thanks to ……
……. and thanks to you !
Martin Rotter
Magnetism in Complex Systems 2009

40. Bragg’s Law in Reciprocal Space (Ewald Sphere)
Incoming
Neutron
τ=Q q 2q
Scattered k k‘ O
2/l a* c*

41. Unpolarised Neutrons - Van Hove Scattering function S(Q,ω)
for the following we assume that there is no nuclear order - <I>=0:
Splitting of S into elastic and inelastic part

42. Magnetism in Complex Systems 2009
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)
Martin Rotter
Magnetism in Complex Systems 2009

43. Neutron – Diffraction Lattice G with basis B: Latticefactor
Structurefactor |F|2
„Isotope-incoherent-Scattering“
„Spin-incoherent-Scattering“
Independent of Q:
one element(NB=1):

44. Three Axes Spectrometer (TAS)k Q
Ghkl k‘ q
Martin Rotter
Magnetism in Complex Systems 2009

45. Magnetism in Complex Systems 2009
Arrangement of Magnetic Moments in Matter
Paramagnet
Ferromagnet
Antiferromagnet
And many more ....
Ferrimagnet, Helimagnet, Spinglass ...collinear, commensurate etc.
Martin Rotter
Magnetism in Complex Systems 2009

46. NdCu2 Magnetic Phasediagram (Field along b-direction)
Martin Rotter
Magnetism in Complex Systems 2009

47. Magnetism in Complex Systems 2009
Complex Structures
μ0Hb=2.6T
AF1
μ0Hb=1T
μ0Hb=0 Q=
Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499
Martin Rotter
Magnetism in Complex Systems 2009

48. Magnetism in Complex Systems 2009
Complex Structures
μ0Hb=2.6T F1
μ0Hb=1T
μ0Hb=0 Q=
Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499
Martin Rotter
Magnetism in Complex Systems 2009

49. Magnetism in Complex Systems 2009
Complex Structures
μ0Hb=2.6T F2
μ0Hb=1T
μ0Hb=0 Q=
Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499
Martin Rotter
Magnetism in Complex Systems 2009

50. NdCu2 Magnetic Phasediagram H||b
F1   
F3  c
F1  b a
AF1 
Lines=Experiment
Colors=Theory
Calculation done by McPhase
Martin Rotter
Magnetism in Complex Systems 2009

51. 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
Martin Rotter
Magnetism in Complex Systems 2009

52. Magnetism in Complex Systems 2009
NdCu2 - 4f Charge Density
T=100 K
T=40 K
T=10 K
Martin Rotter
Magnetism in Complex Systems 2009

53. NdCu2
F3 
F3: measured dispersion was fitted to get exchange constants J(ij)
F1 
AF1 
Calculations done by McPhase

54. Magnetism in Complex Systems 2009
E. Balcar
M. Rotter & A. Boothroyd
2008
did some calculations
Martin Rotter
Magnetism in Complex Systems 2009

55. Magnetism in Complex Systems 2009
Calculation done by McPhase
Comparison to
experiment
(|FM|2-|FMdip|2)/ |FMdip|2 (%)
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
Goodness of fit:
Rpdip=15.6%
Rpbey=8.4 %
(Rpnuc=7.3%)
M. Rotter, A. Boothroyd, PRB, submitted
Martin Rotter
Magnetism in Complex Systems 2009