nuclear resonant scattering with synchrotron radiation fileinstitute for synchrotron radiation /...

KIT – University of the State of Baden-Württemberg and National Laboratory of the Helmholtz Association

Institute for Synchrotron Radiation / ANKA / - Karlsruhe Institute of Technology

www.kit.edu

Nuclear Resonant Scattering with Nuclear Resonant Scattering with

Synchrotron RadiationSynchrotron Radiation

Svetoslav Stankov

[email protected] School of Synchrotron Radiation, 31.1-4.2.2011, Liptovsky Jan, Slovakia

Outlook:Outlook:

I.I. The MThe Möössbauer effect.ssbauer effect.

II.II. Nuclear forward scattering. Comparison with Nuclear forward scattering. Comparison with

the classical Mthe classical Möössbauer spectroscopy.ssbauer spectroscopy.

III.III. Nuclear inelastic scattering.Nuclear inelastic scattering.


Nucleus of 57Fe:

E0 = 14.413 keV

τ = 141.1 ns; Γ Γ Γ Γ = 4.66 neV:

Resolving power E0 /ΓΓΓΓ = ~1x1012

Ee

Eg

E0

The MThe Möössbauer effect:ssbauer effect:

Nuclear resonant recoilless absorption/emission of Nuclear resonant recoilless absorption/emission of γ γ γ γ γ γ γ γ –– rays.rays.

ge EEE −=0


vR

vx

γ -ray

( )

22)(

2

1

2

1Rxgxe

Rxx

vvMEEMvE

vvMc

EMv

−++=+

−+=

γ

γ

meVMc

EMvE RR 2

22

12

2

2 ≅==γ

Nucleus of 57Fe:

E0 = 14.413 keV

τ = 141.1 ns; Γ Γ Γ Γ = 4.66 neV:


Ee

Eg

E0 ge EEE −=0

E0



Recoil energy:


vR

vx

γ -ray

Nucleus of 57Fe:

E0 = 14.413 keV

τ = 141.1 ns; Γ Γ Γ Γ = 4.66 neV:


Ee

Eg

E0 ge EEE −=0

the Mössbauer effect:



( )

22)(

2

1

2

1Rxgxe

Rxx

vvMEEMvE

vvMc

EMv

−++=+

−+=

γ

γ

meVMc

EMvE RR 2

22

12

2

2 ≅==γ

Recoil energy:


0––2 E - E0

S(E

)

Einstein model of a solid

ωhωhωh ωh 2

vR

vx

γ -ray

Nucleus of 57Fe:

E0 = 14.413 keV

τ = 141.1 ns; Γ Γ Γ Γ = 4.66 neV:


Ee

Eg

E0 ge EEE −=0

Atoms bound in a crystal lattice



( )

22)(

2

1

2

1Rxgxe

Rxx

vvMEEMvE

vvMc

EMv

−++=+

−+=

γ

γ

meVMc

EMvE RR 2

22

12

2

2 ≅==γ

Recoil energy:


( )

22)(

2

1

2

1Rxgxe

Rxx

vvMEEMvE

vvMc

EMv

−++=+

−+=

γ

γ

0––2 E - E0

S(E

)


ωhωhωh ωh 2

)/42(222

12

2

2smmmeV

Mc

EMvE RR ≅==

γ

Prize motivation:"for his researches concerning the resonanceabsorption of gamma radiation and his discoveryin this connection of the effect which bears his name"

The Nobel Prize in Physics 1961Robert Hofstadter, Rudolf Mössbauer

vR

vx

γ -ray

Nucleus of 57Fe:

E0 = 14.413 keV

τ = 141.1 ns; Γ Γ Γ Γ = 4.66 neV:


Ee

Eg

E0 ge EEE −=0

Atoms bound in a crystal lattice




laboratory setup




laboratory setup

ESRF(France)

APS (USA)Spring8 (Japan)

PETRA III (Germany)




( )22)0()0()0( sae Ψ−Ψ=∆ρ

Hyperfine interactions in the nucleus of Hyperfine interactions in the nucleus of 5757Fe (EFe (Ee e = 14.4 keV, = 14.4 keV, τ τ τ τ τ τ τ τ = 141ns)= 141ns)

I. Isomer (chemical) shift:

II. Electric quadrupole interaction:

III. Magnetic dipole interaction:

2)0()(

3

2rezSzEE SA ∆∆′=−= ρ

πδ

gerrr

222 −=∆

+=∆

31

2

2ηzzQ

eQVE

( )zzyyxx VVV −=η

BIgBH NM ⋅−=⋅−= µµ NM gmBE µ−=


50 100 150 200 250 300

Mössbauer spectrum in the

time domain(nuclear forward scattering)

Time, ns Time, ns Time, ns

50 100 150 200 250 300 50 100 150 200 250 300

Comparison between MComparison between Möössbauer and nuclear forward scattering spectrassbauer and nuclear forward scattering spectra

Mössbauer spectrum in the energy domain(classical Mössbauer spectroscopy)

Hyperfine interactions

in the nucleus of 57Fe


R. Röhlsberger „Nuclear Condensed Matter Physics with Synchrotron Radiation“ Springer 2004

Nuclear Exciton Nuclear Exciton

Quantum beats Quantum beats

Simultaneous, phased in time, collective excitation of all hyperfine levels of the

excited state of resonant nuclei in the sample. It propagates through the sample

predominantly in spatially coherent channels (forward or Bragg direction).

The coherent superposition of waves

emitted from various hyperfine split levels.

time


Dynamic beats Dynamic beats

Nuclear forward scattering spectra of (NH4)2Mg57Fe(CN)6

for various effective thicknesses taU. Van Bürck, Hyperfine Interactions 123/124 483 (1999)

dnft ALMa 0σ= effective thickness

0σ

LMf

An

d

maximal cross-section for nuclear resonant absorption

Avogadro’s number

Lamb-Mössbauer factor

Sample thickness

Lattice dynamics: 22 xk

LM ef−

=



Polarization dependence of the nuclear resonant scatteringPolarization dependence of the nuclear resonant scattering

Synchrotron σ

k0

EFG

Vzz

Vxx

Vyy

ΘΘΘΘ

φφφφ

x

y

z




Electric quadrupole interactions

H. Grünsteudel et al., Hyperfine Interact. 122, 345 (1999)

Nitropruside anion:Fe(CN)5NO

Vzz

GuNP

NFS spectra of (CN3H6)2[57Fe(CN)5NO] recorder at the

indicaated single-crystal orientations and thicknesses.

100 200 300 400

Time, ns




a) Electric quadrupole interactions b) Magnetic dipole interactions


∆E ≅ 0.5 meV

timingmode

∆E ≅ 3 eV

high heat load mono

high resolution mono

16 bunch mode

176 ns

time, ns

ESRF revolver undulator

CRL

CRL

sample

0 50 100 150 200 250 300

100

1000

10000

100000

nuclear signal

electronic signal

Co

unts

time, ns

Nuclear forward scattering spectrum

(Mössbauer spectrum in the time domain)

Instrumentation for nuclear resonant scattering experimentsInstrumentation for nuclear resonant scattering experiments

R. Rüffer and A.I. Chumakov, Hyperfine Interact. 97–98, 589 (1996)

laboratory setup


6 – cirkle diffractometer

Can accomodate:

Continuous flow cryo:300 K – 5 K

Furnace: 300 K – 1200 K

∆E ≅ 0.5 meV

timingmode

∆E ≅ 3 eV

high heat load mono


16 bunch mode

176 ns

time, ns


CRL

CRL




Cryo-magnet system:

Temp. range: 300 K-2 K

Magnetic field: 0 T -8 T

∆E ≅ 0.5 meV

timingmode

∆E ≅ 3 eV

high heat load mono


16 bunch mode

176 ns

time, ns


CRL

CRL




S. Stankov et al., Rev. Sci. Instr. 79, 045108 (2008)

Ultrahigh vacuum system

∆E ≅ 0.5 meV

timingmode

∆E ≅ 3 eV

high heat load mono


16 bunch mode

176 ns

time, ns


CRL

CRL




Noncollinear Magnetization Structure at the ThicknessNoncollinear Magnetization Structure at the Thickness--Driven Driven

SpinSpin--Reorientation Transition in Epitaxial Fe Films on W(110)Reorientation Transition in Epitaxial Fe Films on W(110)

T. Slezak et al., Phys. Rev. Lett. 105, 027206 (2010)

The magnetization structure during the thickness-

induced SRT for the Fe/W(110) system NFS time spectra measured in-situ at the

indicated film thicknesses.

T. Slezak et al.,J. Phys. Conf. Series 217, 012090 (2010)


0– Eph Eph–2Eph2Eph E - E0

S(E

)

R. Röhlsberger „Nuclear Condensed Matter Physics with Synchrotron Radiation“


1 - phonon 2 - phonon

0 - phonon

E0 ±∆E

Nuclear inelastic XNuclear inelastic X--ray scatteringray scattering

meVEphon ~.

eVEhf µ~

The partial phonon density of states

of 159Tb in TbOx (E = 58keV).

H. Weiss and H. Langhoff, Phys. Lett. 69A, 448 (1979)

Eg

Ee


( ) ( )( )TkEEEgEES BR −−= exp1)(1

-60 -40 -20 0 20 40 60

E - E0 , meV

0– Eph Eph–2Eph2Eph E - E0

S(E

)

R. Röhlsberger „Nuclear Condensed Matter Physics with Synchrotron Radiation“


1 - phonon 2 - phonon

0 - phonon

E0 ±∆E

Nuclear inelastic XNuclear inelastic X--ray scatteringray scattering

meVEphon ~.

eVEhf µ~ S0Sn

S1

( ) ( )

+= ∑

∞

ESEfEW nLM

1

)( δ

( ) ( )∫∞

∞−

−′′−′= EdEESES

nES nn 11

1)(

Quasiharmonic approximation

(harmonic interaction between the atoms)

Eg

Ee


∫∞

=0

2

2),(~)( dEEkEg

MkV γγ

r

h

r

∫∞

−

+=

01

1),(~

4

1)( dE

e

eEkEgkT

E

E

β

β

γγ

rr

( )∫∞

−

−−

−

+=

0

2/2/ln

1

1

2)(3 dEee

e

eEEgkS

EE

E

E

B

ββ

β

ββ

( )∫∞

−=

0

2

2

)1()(3 dE

e

eEEgkC

E

E

BV β

ββ

∫∞

−

+=

01

1)(

2

3dE

e

eEEgU

E

E

β

β

0 10 20 30 40 500,00

0,02

0,04

0,06

DO

S, m

eV

-1

Energy, meV

Phonon DOS of α - Fe

� Vibrational contribution to the internal energy

� Lattice specific heat at constant

volume/pressure

� Vibrational entropy

� Mean kinetic energy and

force constant

−=

dT

dTCC VP

ν

ν

11

Phonon DOS determines the Phonon DOS determines the

vibrational thermodynamics of the solidvibrational thermodynamics of the solid

� Velocity of sound332

2

2

~)(

Dnv

E

m

mEg

hπ

=

� Mean square atomic displacement 2

2 ln

γk

fx LM−=


-60 -40 -20 0 20 40 60

∆E ≅ 0.5 meV

timingmode

∆E ≅ 3 eV

high heat load mono


16 bunch mode

176 ns

time, ns


CRL

CRL

sample

Instrumentation for nuclear inelastic scattering experimentsInstrumentation for nuclear inelastic scattering experiments


E - E0 , meV

-60 -40 -20 0 20 40 60

E - E0 , meV


Fe/W(110)

a model system for investigation of

structure, diffusion and magnetic

properties of nanostructures.

S. Stankov et al., Phys. Rev. Lett. 99, 185501 (2007)

Fe

W

misfit parameter: ε = (aFe-aW)/aW = - 9.4 %

Phonons in Fe: from bulk to a monolayerPhonons in Fe: from bulk to a monolayer

1 ML = 0.2 nm


Summary:Summary:

� Simultaneous access to electronic, magnetic properties and lattiSimultaneous access to electronic, magnetic properties and lattice ce

dynamicsdynamics

�� Partial (element and isotope Partial (element and isotope -- specific) infomrationspecific) infomration

�� Access to buried layersAccess to buried layers

�� SensitiveSensitive to 1 atomic layer of materialto 1 atomic layer of material

�� The number of accessible isotopes is continiously increasing:The number of accessible isotopes is continiously increasing:

5757Fe, Fe, 119119Sn, Sn, 149149Sm, Sm, 151151Eu, Eu, 161161Dy, Dy, 8383Kr, Kr, 125125Te, Te, 121121Sb ( Sb ( 127127I,I,129129I, I, 6161Ni, Ni, 169169Tm ... )Tm ... )

�� Nuclear resonance beamlines worldwide:Nuclear resonance beamlines worldwide:

Grenoble Grenoble -- ESRF (ID18) Argonne ESRF (ID18) Argonne -- APS(3APS(3--ID)ID)

Hamburg Hamburg -- Petra III (P01) Kouto Petra III (P01) Kouto -- SpringSpring--8(BL09XU)8(BL09XU)

nuclear resonant scattering with synchrotron radiation fileinstitute for synchrotron radiation /...

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