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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
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