nuclear resonant scattering of synchrotron radiation dénes lajos nagy thin films as seen by local...

Nuclear Resonant Scattering of Nuclear Resonant Scattering of Synchrotron Synchrotron RadiationRadiation

Dénes Lajos Nagy

Thin Films as Seen by Local ProbesThin Films as Seen by Local ProbesERASMUS Intensive ProgrammeERASMUS Intensive Programme

Frostavallen (Höör), SwedenFrostavallen (Höör), Sweden, , 2-2-1122 MayMay, 2002, 2002

KFKI Research Institute for Particle and Nuclear Physicsand

Eötvös Loránd University , Budapest, Hungary

Outline Outline

Synchrotron Radiation (SR)

- History

- The machine

- SR sources

- Properties of SR

OutlineOutline

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

Synchrotron radiation: HistorySynchrotron 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

Synchrotron radiation: HistorySynchrotron 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)

X-ray beams: past, present and futureX-ray beams: past, present and future

radi

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aves

fm - r

adio

mic

row

aves

infr

ared

visi

ble

light

ultr

avio

let

x-ra

ys

- ra

ys

cosm

ic r

ays

cell

viru

s

prot

ein

mol

ecul

eat

om

nucl

eus

prot

on

1 m

eter

SSR in the eletromagnetic spectrumR in the eletromagnetic spectrum

ESRF, GrenobleESRF, Grenoble

ELETTRA, TriesteELETTRA, Trieste

DORIS (HASYLAB), HamburgDORIS (HASYLAB), Hamburg

APS, ArgonneAPS, Argonne

SSPring8, HarimaPring8, Harima

acceleration

electron orbit

acceleration

electron orbit

non-relativistic electrons relativistic electrons

v/c << 1 v/c 1

E/m0c2

RRadiationadiation field of radially accelerated electrons field of radially accelerated electrons

Technical aspects (example: ESRF)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.


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/mm2/mrad2/0.1 % energy bandwidth


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/.


Undulators: weak magnetic field, narrow-band radiation from the individual poles is coherently added at the undulator maxima. Intensity: 2. Horizontal beam divergence 1/.

Bending magnetBending magnet

Wiggler / undulatorWiggler / undulator

Undulator (ESRF)Undulator (ESRF)

12,0 12,5 13,0 13,5 14,0 14,5 15,0

1015

1016

1017

1018

brill

ianc

e /

pho

tons

/s m

m2 m

rad2 0

.1%

energy / keV

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

Properties of SRProperties of SR

Tunable energy

High degree of polarisation

High brilliance

Small beamsize

Small beam divergence

Pulsed time structure

Conventional (energy-domain) MSConventional (energy-domain) MS

Conventional (energy-domain) MSConventional (energy-domain) MS

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).

Ie=3/2

Ig=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

electricquadrupole

splitting

electric quadrupolesplitting and magnetic

dipole perturbation

Hyperfine splitting of the Hyperfine splitting of the 5757Fe nuclear levelsFe nuclear levels

Hyperfine splitting of nuclear levelsHyperfine splitting of nuclear levels

neV

EhfneV

EhfneV

EkeV

57Fe

Nuclear resonant scattering of SR:Nuclear resonant scattering of SR:Mössbauer effect with SRMössbauer 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.


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).


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 cn 42 m for 57Fe.


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.


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.

0 100 200 300 400 500100

102

104

106

108 E

q=0.8 mm/s

Eq=0.5 mm/s

calc. inten

sity / a.u.

time after excitation / ns

40

60

80

100

teff/line = 1

-15 -10 -5 0 5 10 15

40

60

80

100

teff/line = 1

tran

smission

/ %

relative energy / 0

100

102

104

106

108 E

q=0 mm/s

Eq=0.8 mm/s

a

b

c

d

Quantum-beat patterns for pure electric Quantum-beat patterns for pure electric quadrupole interactionquadrupole interaction

H. GrH. Grünsteudelünsteudel

0 100 200 300 400

100

101

102

103

100

101

102

103

100

101

102

103

0 100 200 300 400

100

101

102

103

0 100 200 300 400

0 100 200 300 400

100

101

102

103

T = 107 K

T = 103 K

T = 102 KT = 102 K

T = 83 K

T = 133 K

T = 107 K

T = 103 K

forw

ard

scat

tere

d in

tens

ity / a

.u.

time / ns H. GrH. Grünsteudelünsteudel

Spin-crossover Spin-crossover transition in Fe(tpa)transition in Fe(tpa)(NCS)(NCS)22

The transition invokes a change in the quadrupole interaction.


Orientation of the EFG axisOrientation of the EFG axis

a) time-domain patterns, b) energy-domain spectra with linear polarised radiation, c) energy-domain spectra with unpolarised radiation

100

101

102 experiment fit

coun

ts /

a.u.

100 200 300 400

100

101

102

coun

ts /

a.u.


a || beam

c || beam


Orientation of the EFG axisOrientation of the EFG axis

(CN3H6)2[(Fe(CN)5NO] single crystal

xyz

k

E

B

0 50 100 150 200

Inte

nsi

ty (

arb

. u

nits

, lo

g.

sca

le)

Time after excitation (ns)

1 2 3 4 5 6

xyz

B

E

k

xyz BE

k

Orientation of the hyperfine fieldOrientation of the hyperfine field(the ”Smirnov figures”)(the ”Smirnov figures”)

O. LeupoldO. Leupold

Measurement of the isomer shiftMeasurement 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.

0 50 100 150

100

101

102

103

0 50 100 150

100

101

102

103

with referencewith reference

dc

a b

T=110 K

T=110 K

T=4.2 K

T=4.2 K


coun

ts


100

101

102

103

100

101

102

103


Measurement of the isomer shiftMeasurement of the isomer shift

Fe2+O2(SC6HF4)(TPpivP)

single-line reference:K4Fe(CN)6

0

20

40

60

80

100

0 500 1000 1500100

102

104

106

108 Eq=2 mm/s

Eq=0 mm/s

calc. inten

sity / a.u.

time after excitation / ns-30 -20-10 0 10 20 30

0

20

40

60

80

100

teff / line=25

tran

smission

/ %

relative energy / 0

100

102

104

106

108 teff=1

teff=25

ab

cd


Effect of the finite absorber thickness:Effect of the finite absorber thickness:the dynamic beatsthe dynamic beats


Channel-cut monochromatorChannel-cut monochromator

cut

2 = B - cut

h22

h11

1 = B + cut


Asymmetric reflectionAsymmetric reflection

The acceptance for incoming and outgoing beam is different.

Si(4 2 2)b=-0.1

Si(4 2 2)b=-10

Si(4 2 2)b=-10

Si(4 2 2)b=-0.1

Si(9 7 5)b=-1

Si(9 7 5)b=-1

Si(9 7 5)b=-0.21

Si(9 7 5)b=-4.7

Si(9 7 5)b=-20

Si(9 7 5)b=-0.05

Si(12 2 2)b=-1

Si(12 2 2)b=-1

E=6.4 meV E=4.4 meV

E=0.8 meVE=1.7 meV

ba

c d

Ge(3 3 1)b=-1


High-resolution monochromatorsHigh-resolution monochromators

high heat loadmonochromator

high resolutionmonochromatorSi (1 1 1)

Si (1 1 1)

Si (4 2 2)

Si (4 2 2)

Si (12 2 2)Si (12 2 2)

E: 300 eV 3 eV 6 meV


High-heat-load premonochromator and high-High-heat-load premonochromator and high-resolution nested monochromatorresolution nested monochromator

x-ray

hole

electron

depletion region

avalanche region

a b c H. GrH. Grünsteudelünsteudel

Principle of the avalanche photo diode (APD)Principle of the avalanche photo diode (APD)

undulatorx-ray beam

electron storage ringwith one electron bunch

detectorssample

measured data

fast electronicsbunch clock

ICM HRM


Principle of a nuclear resonant scattering Principle of a nuclear resonant scattering experimentexperiment

detector(APD)

amplifierCFD

(all events)

TAC MCA

counter(prompt)

counter(delayed)

ADC

gate

star

t

stop

CFD(only delayed

events)bunchclock


Setup of the fast timing electronics for Setup of the fast timing electronics for nuclear resonant scattering experimentsnuclear resonant scattering experiments

sample detectort

t t

beamtime


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 Setup for a nuclear resonant forward scattering experimentscattering experiment

The Doppler shift depends on zs only.

For point-like source and detector:

The transverse coherence lengthThe transverse coherence length

For finite source and detector there exists an effective transverse

coherence length Lc /2 with

Typical values at ESRF ID18: 0 = 120 m, S = 41 m, d =

500 m, D = 2.5 m Lc 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) Lc 3 m.

The transverse coherence lengthThe transverse coherence length

Measured time responses with slits(a, 95 Hz: without slits)

A.Q.R. Baron et al.A.Q.R. Baron et al.

The transverse The transverse coherence lengthcoherence length

Measured time responses divided by the fit to the response at rest.

A.Q.R. Baron et al.A.Q.R. Baron et al.

The transverse The transverse coherence lengthcoherence length

H.F. GrH.F. Grünsteudel et al.ünsteudel et al.

Domain structure in iron at the Domain structure in iron at the transitiontransition

3 m 57Fe 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 Lc 10 Å.

–Fe response

–Fe response

coherent sum of 50% –Fe and 50% –Fe

incoherent sum of 50% –Fe and 50% –Fe

H.F. GrH.F. Grünsteudel et al.ünsteudel et al.

Domain structure in iron at the Domain structure in iron at the transitiontransition

NRS vs. conventional MSNRS 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.

sample

t

t t

NFSE=0

E>0E<0

t t

E=0:

NIS

NFS

NIS

E=0

E>0E<0

beamIC

HRM

time

time

relative energy

relative energy


Setup for a nuclear inelastic scattering Setup for a nuclear inelastic scattering experimentexperiment

Nuclear inelastic scattering experimentNuclear 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).

Nuclear inelastic scattering experimentNuclear 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.

Nuclear inelastic scattering experimentNuclear inelastic scattering experiment

The time-integrated signal of the NIS detector shows for the same energy scan a high central peak at Eand 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.

-60 -40 -20 0 20 40 600

200

400

600

Counts

Relative energy [meV]

Lattice dynamics in an icosahedral Lattice dynamics in an icosahedral AlAl6262CuCu25.525.5FeFe12.512.5 quasicrystal quasicrystal (A. Chumakov)(A. Chumakov)

Inelastic x-ray scattering with nuclear Inelastic x-ray scattering with nuclear resonant anayserresonant anayser

Chumakov et al., Phys. Rev. Lett. 76, 4258 (1996)

Inelastic x-ray scattering with nuclear Inelastic x-ray scattering with nuclear resonant anayserresonant anayser

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

ReferenceReference

ProblemsProblems

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 57Fe (nuclear lifetime of the resonant level: 141 ns)? And for inelastic scattering experiments on the same nucleus?

ProblemsProblems

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 57Fe foil is randomly vibrating along the photon beam with an average frequency = 10 Hz and an amplitudea = 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!

ProblemsProblems

4. A resonant photon beam is passing two subsequent 57Fe 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!

nuclear resonant scattering of synchrotron radiation dénes lajos nagy thin films as seen by local...

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