Nuclear Resonant Nuclear Resonant Scattering of Scattering of Synchrotron Synchrotron

Radiation Radiation

Dénes Lajos Nagy

KFKI Research Institute for Particle and Nuclear Physics

and Loránd Eötvös University, Budapest, Hungary

Short Course on Physical Characterization of Short Course on Physical Characterization of NanostructuresNanostructures

Leuven, Belgium, 8–13 May 2011Leuven, Belgium, 8–13 May 2011

OutlineOutline

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

Synchrotron radiation: HistorySynchrotron 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

Synchrotron radiation: HistorySynchrotron 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)

radi

o w

aves

fm - r

adio

mic

row

aves

infr

ared

visi

ble

light

ultr

avio

let

x-ra

ys

g - ra

ys

cosm

ic r

ays

cell

viru

s

prot

ein

mol

ecul

eat

om

nucl

eus

prot

on

1 m

eter

SR in the electromagnetic SR in the electromagnetic spectrumspectrum

ESRF, GrenobleESRF, Grenoble

Radiation field of radially accelerated Radiation field of radially accelerated electronselectrons

acceleration

electron orbit

acceleration

electron orbit

Maxwell (1864), Hertz (1886) Veksler (1945)

v/c << 1 v/c 1

1/ = E/m0c2

Polarisation

E

Technical aspects (example: Technical aspects (example: ESRF)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.

Technical aspects (example: Technical aspects (example: ESRF)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/.

Technical aspects (example: Technical aspects (example: ESRF)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

electronbeam

synchrotronradiation

Energy bandwidth, monochromatorsEnergy bandwidth, 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

Bragg monochromators

High-heat-loadmonochromator

High-resolution monochromator

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

U23 at ID18 (ESRF)

Properties of SRProperties of SR

Tunable energy

High degree of polarisation

High brilliance

Small beamsize

Small beam divergence

Pulsed time structure

Hyperfine splitting of nuclear levelsHyperfine splitting of nuclear levels

5 neV

Ehf 100 neV

Ehf 100 neV

Eg 14.4 keV

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,

- fast detectors and electronics.

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

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

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

Diffraction and quantum beatsDiffraction 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. RöhlsbergerR. Röhlsberger

undulatorx-ray beam

electron storage ringwith one electron bunch

detectorssample

measured data

fast electronicsbunch clock

ICM HRM

H. H. GrünsteudelGrünsteudel

Principle of a nuclear resonant Principle of a nuclear resonant scattering experimentscattering experiment

sample detectort

t t

beamtime

H. H. GrünsteudelGrünsteudel

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

Temporal beats

14.4 keV

57Fe

R. RöhlsbergerR. Röhlsberger

Energy- and time-domain Mössbauer Energy- and time-domain Mössbauer spectraspectra

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 Quantum-beat patterns for pure electric quadrupole interactionelectric quadrupole interaction

H. H. GrünsteudelGrünsteudel

The time spectra sensitively depend on the orientation of the

Magnetization M

relative to the

Photon wave vector k0

R. RöhlsbergerR. Röhlsberger

Orientation of the hyperfine fieldOrientation of the hyperfine field

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. O. LeupoldLeupold

Orientation of the hyperfine fieldOrientation of the hyperfine field

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.

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

time after excitation / ns

coun

ts

time after excitation / ns

100

101

102

103

100

101

102

103

H. H. GrünsteudelGrünsteudel

Measurement of the isomer shiftMeasurement of the isomer shift

Fe2+O2(SC6HF4)(TPpivP)

single-line reference:K4Fe(CN)6

sample

p,k

source

', pk

detector

sample

p,,II kk

source detector

',,II p kk

Reflection geometry: depth selectivity mrad101θ

X-ray and Mössbauer reflectometryX-ray and Mössbauer reflectometry

na

1

2

i

n1

n2

ni

ns

d1

d2

di

z

Relation between scattering amplitude and index of refraction:

nN

kf 1

22

X-ray and Mössbauer reflectometry:X-ray and Mössbauer reflectometry:the scattering amplitudesthe scattering amplitudes

f E f f Eph phel

phnuc( ) ( )

f Zr iphel 0

electron densityphotoabsorptio

nf E

kV

hcf

I

a

E E E iphnuc

LMg

( )( ),

1

2 12

hyperfine energies

hyperfine matrix elements

Mössbauer reflectometry: why at Mössbauer reflectometry: why at synchrotrons?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 106 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.

0.00 0.05 0.10 0.15 0.20 0.25 0.300

50

100

150

200

coun

ts

qz [Å]

/2-scan: qz-scan

d = 2/qz

-scan: qx-scan

= 1/ qx-4 -2 0 2 4

0

20

40

60

80

100

coun

ts (

norm

alis

ed)

qx [10-4 Å]

Arrangement of an SMR experimentArrangement of an SMR experiment

2or

Hex

t

x

yz

k

APD

from the high-resolutionmonochromator

E

Depth selective phase analysis with Depth selective phase analysis with SMRSMR

[mrad] d [nm]

5 40.5

4 20.5

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:

0 20 40 60 80 100 120 140 160

10100

1000

10100

1000

10100

1000

10100

1000

10100

1000

10100

1000

10100

1000

10100

1000

0 20 40 60 80 100 120 140 160

5.2

20 nm 57Fe on float glass, 170 oC, 4 h, in air

time after excitation [ns]

4.7

4.2

3.7

non-resonant penetration depth [nm]

3.1

coun

ts

2.6

40

20

3.5

2.0

2.1

= 1.6 mrad

0 20 40 60 80 100 120 140

0.1

1

10

100

5.6

4.2

2.8

1.4

40

204.0

2.0

dept

h [n

m]

20 nm 57Fe on float glass, 170 oC, 4 h, air

time [ns] [m

rad]

de

laye

d y

ield

Depth selective phase analysis with Depth selective phase analysis with SMRSMR

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 Direction of the magnetisation in a Co/Fe/Co trilayerCo/Fe/Co trilayer

0 50 100 150

100

101 1

Gerjesztés után eltelt idõ [ns]

100

101

7

100

101

102

3

10010

1

4

Be

üté

sszá

m

10 -1100101102

6

5

100

10110

2103

57Fe

56Fe

7 6 5 4 3 2 1

CuCo

Fe

Co

Time after excitation (ns)

Cou

nts

Antiferromagnetic coupling in a Fe/Cr Antiferromagnetic coupling in a Fe/Cr multilayermultilayer

Cr

Fe

Fe

Cr

Cr

Fe

CrLayer magnetisations:

Fe

Patch domains in AF-coupled Patch domains in AF-coupled multilayersmultilayers

Layer magnetisations:

The ‘magnetic field lines’ are shortcut by the AF structure the stray field is reduced no ‘ripple’ but ‘patch’ domains are formed.

The off-specular scattering widthThe off-specular scattering width

The off-specular (diffuse) scattering width around an AF reflection stems only from the magnetic roughness.

The diffuse scattering width Qx at an AF reflection is inversely proportional to the correlation length of the layer magnetisation:

= 1/ Qx

At an AF reflection, is the average domain size!

ESRFID18

Correlation length: = 1/qx

370 nm 800 nm

Domain ripening: off-specular SMR, hard Domain ripening: off-specular SMR, hard directiondirection

MgO(001)[MgO(001)[5757Fe(26Å)/Cr(13Å)]Fe(26Å)/Cr(13Å)]2020

22 @ AF reflection @ AF reflection

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

H. GrünsteudelH. Grünsteudel

Nuclear resonant inelastic scatteringNuclear resonant inelastic scattering

-60 -40 -20 0 20 40 600

200

400

600

Counts

Relative energy [meV]

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

Phonon excitation probability of Fe under Phonon excitation probability of Fe under extreme conditionsextreme conditions

J. F. Lin et al.

The sound velocity inside the Earth can be estimated!

B.K. Rai et al.

The peaks of the vibrational density

of states can be well assigned to certain

normal modes involving 57Fe.

Nuclear resonance vibrational spectroscopy Nuclear resonance vibrational spectroscopy of of 5757Fe in in Fe in in

(Nitrosyl)iron(II)tetraphenylporphyrin(Nitrosyl)iron(II)tetraphenylporphyrin

Nuclear resonance vibrational spectroscopy Nuclear resonance vibrational spectroscopy of of 5757Fe in in Fe in in

(Nitrosyl)iron(II)tetraphenylporphyrin(Nitrosyl)iron(II)tetraphenylporphyrin

B.K. Rai et al.

Phenyl in-plane and out-of-plane vibrations of 57Fe

can be well distinguished providing an

improved model for the role of iron atom dynamics in

the biological functioning of

hemeproteins.

Inelastic x-ray scattering with a Inelastic x-ray scattering with a nuclear resonant analysernuclear resonant analyser

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

Inelastic x-ray scattering with a Inelastic x-ray scattering with a nuclear resonant analysernuclear resonant analyser

E. Gerdau and H. de Waard (eds.)

Nuclear Resonant Scattering ofSynchrotron Radiation

special volumes 123/124 and 125 ofHyperfine Interactions

(1999-2000)

ReferenceReference