1. Nuclear Resonant Scattering of Synchrotron Radiation Dénes Lajos Nagy KFKI Research Institute for Particle and Nuclear Physics and Loránd Eötvös University, Budapest, Hungary Short Course on Physical Characterization of Nanostructures Leuven, Belgium, 8–13 May 2011

2. Outline  Synchrotron Radiation (SR)  Nuclear Resonant Scattering of SR: Theory  Nuclear Resonant Scattering of SR: Experiment: applications in physics, chemistry and materials sciences  Thin film applications  Nuclear Resonant Inelastic Scattering of SR: applications in geology and biology

3. Synchrotron radiation: History  SR: polarised electromagnetic radiation produced in particle accelerators or storage rings by relativistic electrons or positrons deflected in magnetic fields  First-generation SR sources (  1965- 1980): machines built for particle physics, SR produced at bending magnets is used in parasitic regime  Second-generation SR sources (  1970- 1990): machines dedicated to the applications of SR, radiation produced at bending magnets

4. Synchrotron radiation: History  Third-generation SR sources (  1990-): machines dedicated to the applications of SR, radiation produced both at bending magnets and at insertion devices - ESRF (Grenoble, France): 6 GeV - PETRA III (Hamburg, Germany): 6 GeV - APS (Argonne, USA): 7 GeV - SPring-8 (Harima, Japan): 8 GeV  The future: x-ray free-electron lasers (XFEL)

5. radio waves fm - radio microwaves infrared visible light ultraviolet x-rays g - rays cosmic rays cell virus protein molecule atom nucleus proton 1 meter SR in the electromagnetic spectrum

6. ESRF, Grenoble

7. Radiation field of radially accelerated electrons acceleration electron orbit acceleration electron orbit Maxwell (1864), Hertz (1886) Veksler (1945) v/c << 1 v/c  1 1/   = E/m 0 c 2 Polarisation E

8. Technical aspects (example: ESRF)  Pre-accelerators: - LINAC: 100 keV electron gun  200 MeV - booster synchrotron: 200 MeV  6 GeV  The storage ring: - circumference: 845 m; - number of electron buckets: up to 992; - electron bunch length: 6 mm  pulse duration: 20 ps and 100 ps at bending magnets and insertion devices, respectively; - re-acceleration power at I = 100 mA: 650 kW.

9. Technical aspects (example: ESRF)  Insertion devices: wigglers and undulators. These are two arrays of N permanent magnets above and below the electron (positron) beam. The SR is generated through the sinusoidal motion of the particles in the alternating magnetic field.  Wigglers: strong magnetic field, broad- band radiation from the individual poles is incoherently added. Intensity: ~ N. Horizontal beam divergence >> 1/ .

10. Technical aspects (example: ESRF)  Undulators: weak magnetic field, narrow- band radiation from the individual poles is coherently added at the undulator maxima. Intensity: ~ N 2. Horizontal beam divergence ~ 1/ . Wigglers, undulators electron beam synchrotron radiation

11. Energy bandwidth, monochromators Bragg monochromators High-heat-load monochromator High-resolution monochromator U23 at ID18 (ESRF)

12. Properties of SR  Tunable energy  High degree of polarisation  High brilliance  Small beamsize  Small beam divergence  Pulsed time structure

13. Hyperfine splitting of nuclear levels  5 neV E hf  100 neV E g  14.4 keV 57 Fe

14. Nuclear resonant scattering of SR: Mössbauer effect with SR  E. Gerdau et al. (1984): first observation of delayed photons from nuclear resonant scattering of SR (at beamline F4 of HASYLAB).  Basic problem: huge background from prompt non-resonant photons. The solution: - monochromatisation of the primary SR, - fast detectors and electronics.

15. Nuclear resonant scattering of SR: Mössbauer effect with SR  Hastings et al. (1991): first observation of delayed photons from nuclear resonant forward scattering of SR.  The bandwidth of SR is much larger than the hyperfine splitting.  All transitions are excited at the same time. Therefore the resultant time response is the coherent sum of the individual transitions (the amplitudes are added).

16. Nuclear resonant scattering of SR: Mössbauer effect with SR  Not only the different transitions of the same nucleus but also transitions of different nuclei (longitudinally within any distance and transversally within the transverse coherence length) are excited simultaneously and the scattering takes place coherently.

17. Nuclear resonant scattering of SR: Mössbauer effect with SR  The temporal interference of the amplitudes scattered from different hyperfine-split transitions leads to quantum beats. The strength of the hyperfine interaction is reflected in the frequency of the beating.  The orientation of the hyperfine field is reflected in the intensities of the different frequency components and in the depth of the beating.

18. Diffraction and quantum beats Diffraction pattern Time spectrum Illumination by a spatially extended beam Illumination by an energetically extended beam Array of slits A(x) Array of resonances A(E) Position x Energy E Momentum transfer q Time t Intensity |A(t)| 2 Intensity |A(q)| 2 R. Röhlsberger

19. H. Grünsteudel Principle of a nuclear resonant scattering experiment

20. H. Grünsteudel The pulsed SR (left side, pulses separated by  t) penetrates the sample and reaches the detector. The decay of the nuclear excited states, which takes place in the time window  t (right side), reflects the hyperfine interactions of the resonant nuclei. Setup for a nuclear resonant forward scattering experiment

22. Energy- and time-domain Mössbauer spectra

23. Quantum-beat patterns for pure electric quadrupole interaction H. Grünsteudel

24. The time spectra sensitively depend on the orientation of the Magnetization M relative to the Photon wave vector k 0 R. Röhlsberger Orientation of the hyperfine field

25. x y z k E B 1 2 3 4 5 6 x y z B E k x y z B E k Orientation of the hyperfine field (the ”Smirnov figures”)

26. O. Leupold Orientation of the hyperfine field

27. Measurement of the isomer shift  The NRS time response depends only on the differences of the resonance line energies. Therefore the isomer shift has no influence to the quantum-beat pattern.  The isomer shift can be measured by inserting a single-line absorber to the photon beam.

28. H. Grünsteudel Measurement of the isomer shift Fe 2+ O 2 (SC 6 HF 4 )(TP piv P) single-line reference: K 4 Fe(CN) 6

29. sample source detector

30. sample source detector Reflection geometry: depth selectivity

31. X-ray and Mössbauer reflectometry Relation between scattering amplitude and index of refraction:

32. X-ray and Mössbauer reflectometry: the scattering amplitudes  electron density photoabsorption hyperfine energies hyperfine matrix elements

33. Mössbauer reflectometry: why at synchrotrons?  Due to the small (1-2 cm) size of the sample and the small (1-10 mrad) angle of grazing incidence, the solid angle involved in a Mössbauer reflectometry experiment is 10 -5  only 1 photon from 10 6 is used in a conventional source experiment. In contrast, the highly collimated SR is fully used.  The linear polarisation of the SR allows an easy determination of the magnetisation direction.

34.  /2  -scan: q z -scan d = 2  /q z  -scan: q x -scan  = 1/  q x Arrangement of an SMR experiment 22  or  H ext x y z k APD from the high-resolution monochromator E

35. Depth selective phase analysis with SMR  [mrad]d  [nm] 540.5 420.5 3 3.5 0 1.3 Close to the critical angle of electronic total reflection, the penetration depth of hard x- rays strongly depends on the angle of grazing incidence. For E = 14.4 keV and iron:

37. Depth selective phase analysis with SMR

38. Monolayer resolution can be achieved by using the resonant isotope marker technique. In a Co/Fe(7ML)/Co trilayer, the magnetisation of the Fe layers at the Co/Fe interface is parallel while that of the internal Fe layers is perpendicular to the plane. (C. Carbone et al, 1999) Direction of the magnetisation in a Co/Fe/Co trilayer Time after excitation (ns) Counts

39. Antiferromagnetic coupling in a Fe/Cr multilayer Cr Fe Cr Fe Cr Layer magnetisations: Fe

40. Patch domains in AF-coupled multilayers Layer magnetisations: The ‘magnetic field lines’ are shortcut by the AF structure  the stray field is reduced  no ‘ripple’ but ‘patch’ domains are formed.

41. The off-specular scattering width  The off-specular (diffuse) scattering width around an AF reflection stems only from the magnetic roughness.  The diffuse scattering width  Q x at an AF reflection is inversely proportional to the correlation length  of the layer magnetisation:  = 1/  Q x At an AF reflection,  is the average domain size!

42. ESRF ID18 Correlation length:  = 1/  q x   370 nm   800 nm Domain ripening: off-specular SMR, hard direction MgO(001)[ 57 Fe(26Å)/Cr(13Å)] 20 2  @ AF reflection

43. H. Grünsteudel Nuclear resonant inelastic scattering

44. Lattice dynamics of an icosahedral Al 62 Cu 25.5 Fe 12.5 quasicrystal (A. Chumakov)

45. Phonon excitation probability of Fe under extreme conditions J. F. Lin et al. The sound velocity inside the Earth can be estimated!

46. B.K. Rai et al. The peaks of the vibrational density of states can be well assigned to certain normal modes involving 57 Fe. Nuclear resonance vibrational spectroscopy of 57 Fe in in (Nitrosyl)iron(II)tetraphenylporphyrin

47. B.K. Rai et al. Phenyl in-plane and out-of-plane vibrations of 57 Fe can be well distinguished providing an improved model for the role of iron atom dynamics in the biological functioning of heme proteins.

48. Inelastic x-ray scattering with a nuclear resonant analyser

49. Chumakov et al., Phys. Rev. Lett. 76, 4258 (1996) Inelastic x-ray scattering with a nuclear resonant analyser

50. E. Gerdau and H. de Waard (eds.) Nuclear Resonant Scattering of Synchrotron Radiation special volumes 123/124 and 125 of Hyperfine Interactions (1999-2000)Reference