1. Nuclear Resonant Scattering of Synchrotron Radiation Dénes Lajos Nagy Thin Films as Seen by Local Probes ERASMUS Intensive Programme Frostavallen (Höör), Sweden, 2-12 May, 2002 KFKI Research Institute for Particle and Nuclear Physics and Eötvös Loránd University, Budapest, Hungary

2. Outline  Synchrotron Radiation (SR) - History - The machine - SR sources - Properties of SR

3. Outline  Nuclear Resonant Scattering of SR: Theory - Conventional Mössbauer spectroscopy - Nuclear resonant forward scattering  Nuclear Resonant Scattering of SR: Experiment - The experimental setup - The transverse coherence length - Nuclear resonant inelastic scattering  Problems

4. Synchrotron radiation: History  SR: polarised electromagnetic radiation produced in particle accelerators or storage rings when relativistic electrons or positrons are deflected in magnetic fields  Elder et al. (1947): first observation of SR at a 70-MeV synchrotron  Tomboulian, Hartman (1956): first spectroscopic studies at a 300-MeV machine  First-generation SR sources (  1965-1980): machines built for particle physics, SR produced at bending magnets is used in parasitic regime

5. Synchrotron radiation: History  Second-generation SR sources (  1970-1990): machines dedicated to the applications of SR, radiation produced at bending magnets  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 - APS (Argone, USA): 7 GeV - SPring8 (Harima, Japan): 8GeV  The future: x-ray free-electron lasers (XFEL)

6. X-ray beams: past, present and future

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

8. ESRF, Grenoble

10. ELETTRA, Trieste

11. DORIS (HASYLAB), Hamburg

12. APS, Argonne

13. SPring8, Harima

14. acceleration electron orbit acceleration electron orbit non-relativistic electronsrelativistic electrons v/c << 1 v/c  1   E/m 0 c 2 Radiation field of radially accelerated electrons

15. 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.

16. Technical aspects (example: ESRF)  Critical wavelength of SR: c = (4  /3)(R/  3 ), i.e., c [Å] = 5.59 (R[m]/E[GeV] 3 ) where R is the radius of the electron orbit in the bending magnet or in the insertion device.  Spectral brilliance of a SR source (bending magnet or insertion device): photons/s/mm 2 /mrad 2 /0.1 % energy bandwidth

17. 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: . Horizontal beam divergence >> 1/ .

18. Technical aspects (example: ESRF)  Undulators: weak magnetic field, narrow-band radiation from the individual poles is coherently added at the undulator maxima. Intensity:  2. Horizontal beam divergence  1/ .

19. Bending magnet

20. Wiggler / undulator

21. Undulator (ESRF)

22. Brilliance of an undulator (U23 of ID18 at ESRF)

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

24. Conventional (energy-domain) MS

25.  Only one transition is excited at the same time, therefore the resultant spectrum is the incoherent sum of the indivitual transitions (the intensities are added).

26. I e =3/2 I g =1/2 3/2, +3/2 3/2, -3/2 3/2, +1/2 3/2, -1/2 1/2, -1/2 1/2, +1/2 isomer shift electric quadrupole splitting electric quadrupole splitting and magnetic dipole perturbation Hyperfine splitting of the 57 Fe nuclear levels

27. Hyperfine splitting of nuclear levels  neV E hf  neV E   keV 57 Fe

28. 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, - suppression of electronic scattering by using electronically forbidden Bragg reflections (out of date), - fast detectors and electronics.

29. Nuclear resonant scattering of SR: Mössbauer effect with SR  Bergmann et al. (1994): 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 indivitual transitions (the amplitudes are added).

30. Nuclear resonant scattering of SR: Mössbauer effect with SR  Not only the different transitions of the same nucleus but also transitions of different nuclei within the coherence length are excited simultaneously and the scattering takes place coherently.  The longitudinal coherence length of the resonant radiation is c  n  42 m for 57 Fe.

31. 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 (e.g. magnetic field) is reflected in the frequency/frequencies of the quantum beats.  The orientation of the magnetic field and of the electric field gradient is reflected in the intensities of the different frequency components and in the depth of the beating.

32. Nuclear resonant scattering of SR: Mössbauer effect with SR  Due to the full linear polarisation of SR, the nuclear resonant scattering of SR is extremely sensitive to the orientation of the hyperfine magnetic field.

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

34. Spin-crossover transition in Fe(tpa)(NCS) 2 The transition invokes a change in the quadrupole interaction.

35. H. Grünsteudel Orientation of the EFG axis a) time-domain patterns, b) energy-domain spectra with linear polarised radiation, c) energy-domain spectra with unpolarised radiation

36. H. Grünsteudel Orientation of the EFG axis (CN 3 H 6 ) 2 [(Fe(CN) 5 NO] single crystal

37. 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”)

38. O. Leupold

39. 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 within the longitudinal coherence length.

40. 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

41. H. Grünsteudel Effect of the finite absorber thickness: the dynamic beats

42. H. Grünsteudel Channel-cut monochromator

43. H. Grünsteudel Asymmetric reflection The acceptance for incoming and outgoing beam is different.

44. H. Grünsteudel High-resolution monochromators

45. H. Grünsteudel High-heat-load premonochromator and high-resolution nested monochromator

46. x-ray hole electron depletion region avalanche region abc H. Grünsteudel Principle of the avalanche photo diode (APD)

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

48. H. Grünsteudel Setup of the fast timing electronics for nuclear resonant scattering experiments

49. 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

51. The Doppler shift depends on z s only. For point-like source and detector: The transverse coherence length

52. For finite source and detector there exists an effective transverse coherence length L c  /2  with Typical values at ESRF ID18:  0 = 120  m, S = 41 m,  d = 500  m, D = 2.5 m  L c  300 Å. With appropriate slits (e.g. of 15  m height, one 10 cm behind the sample, another 4 cm in front of the detector) L c  3  m. The transverse coherence length

53. Measured time responses with slits (a, 95 Hz: without slits) A.Q.R. Baron et al. The transverse coherence length

54. Measured time responses divided by the fit to the response at rest. A.Q.R. Baron et al. The transverse coherence length

55. H.F. Grünsteudel et al. Domain structure in iron at the    transition 3  m 57 Fe foil at 15 GPa.  –Fe: ferromagnetic,  –Fe: paramagnetic. Solid line: incoherent sum using the coherent time responses of  –Fe (21%),  –Fe (38%) and the coherent sum of both. The effective transverse coherence length was L c  10 Å.

56.  –Fe response  –Fe response coherent sum of 50%  – Fe and 50%  –Fe incoherent sum of 50%  – Fe and 50%  –Fe H.F. Grünsteudel et al. Domain structure in iron at the    transition

57. NRS vs. conventional MS  NRS is not just a repetition of conventional energy-domain Mössbauer spectroscopy; the two methods are complementary. It should be applied when unique properties of SR are used: - small solid angle is available (e.g., at grazing-incidence experiments in thin films), - small samples are available (small single crystals, high- pressure experiments, biological samples), - linear polarised radiation is advantageous (determination of the hyperfine field direction), - etc.

58. H. Grünsteudel Setup for a nuclear inelastic scattering experiment

59. Nuclear inelastic scattering experiment  The pulsed SR beam is monochromatized to a meV energy band with the high-resolution monochromator before it penetrates the ionization chamber (IC) and the sample.  The radiative decay of the resonant nuclei in the sample is measured with two APD detectors: one in forward direction (NFS), which collects data only from a small solid angle (top) and one at 90  (NIS) which collects data in a large solid angle (bottom).

60. Nuclear inelastic scattering experiment  At exact resonance energy (E   ) the NFS detector collects the time-depending NFS.  During scanning the energy of the incident beam by detuning the HRM the time-integrated signal of the NFS detector shows a sharp peak at E   which represents the energy resolution of the monochromator system.

61. Nuclear inelastic scattering experiment  The time-integrated signal of the NIS detector shows for the same energy scan a high central peak at E   and peaks apart from the resonance energy, depending on the sample. This energy spectrum represents the probability of resonance absorption with recoil overlapped by the signal at E   produced by subsequent processes of the internal conversion. The time dependence of the NIS signal shows an exponential decay after excitation, since the data are collected angle-integrated.

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

63. Inelastic x-ray scattering with nuclear resonant anayser

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

65. E. Gerdau, H. de Waard (eds.), Nuclear Resonant Scattering of Synchrotron Radiation, special volumes 123/124 and 125 of Hyp. Int.Reference

66. Problems 1.Bunch modes at ESRF:  uniform filling: 992 bunches uniformly distributed in the storage ring,  1/3 filling: 331 bunches filling 1/3 of the ring,  single-bunch filling: 1 bunch in the ring,  16-bunch filling: 16 bunches uniformly distributed in the storage ring,  hybrid filling: 331 bunches filling 1/3 of the ring + 1 bunch in front of the 331 bunches. Which modes are suitable for nuclear resonant forward scattering experiments on 57 Fe (nuclear lifetime of the resonant level: 141 ns)? And for inelastic scattering experiments on the same nucleus?

67. Problems 2.Explain qualitatively, why no quantum beats but an exponential decay is observed when the axially symmetric EFG axis is perpendicular both to k and E. (1/2  3/2 transition). 3.A 57 Fe foil is randomly vibrating along the photon beam with an average frequency = 10 Hz and an amplitude a = 5 mm. Describe qualitatively the conventional energy- domain Mössbauer spectrum as compared with the case of the static foil! Do the same for the nuclear resonant forward scattering of SR!

68. Problems 4.A resonant photon beam is passing two subsequent 57 Fe foils. Both foils are magnetised to saturation in high magnetic fields perpendicular to the sample plane, i.e., along the photon beam. Both energy- and time-domain Mössbauer experiments are performed for a) parallel b) antiparallel magnetisations of the two foils. Describe qualitatively the results of both pairs of experiments!