1 electron magnetic circular dichroism pavel novák institute of physics ascr, prague, czech...
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1
Electron magnetic circular dichroism
Pavel Novák
Institute of Physics ASCR, Prague, Czech Republic
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Scope
Motivation
Short history
XMCD –X-ray magnetic circular dichroism
EMCD – electron magnetic circular dichroism
Modelling of experiment
Results
Outlook
Conclusions
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Motivation
Characterization of very smal magnetic objects (≤ 10 nm)
Necessity of very short wavelengths
X-ray magnetooptics
XMCD: X-ray Magnetic Circular Dichroismus
predicted 1975
experimental verification 1987
first possibility to determine separately
spin and orbital magnetic moment
Disadvantage: necessity of synchrotron
Is it possible to obtain analogous information using electron
microscope?Positive answer – in principle study of subnanometric objects possible
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Short history
2003 – Peter Schattschneider et al. (TU Vienna): basic idea of
EMCD EU projektu CHIRALTEM submited
Chiral Dichroism in the Transmission Electron
Microscope
invitation to our group to participate as theoretical
support2004 –project approved within program NEST 6 „Adventure“
2005 – experimental verification, microscopic theory, first workshop
2006 –paper in Nature, second workshop
Our group: Ján Rusz, Pavel Novák, Jan Kuneš, Vladimír Kamberský
2007 –sensitivity increased by order of magnitude
planned: third workshop, closing the project
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Circular dichroism: absorption spectrum of polarized light is different for left and right helicity
Circular magnetic dichroism
X-ray circular dichroism: circular dichroism in the X-ray region
Symmetry with respect to time inversion must be broken:
magnetic field
magnetically ordered systems
Microscopic mechanism:
inelastic diffraction of light, electric dipol transitions
coupling of light and magnetism – spin-orbit interaction
≠
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XANES and XMCD
Crosssection of XANES
polarization vector
XANES – X-ray near edge spectroscopy
Transition of an electron from the core level of an atom to an empty state
XMCD – X-ray magnetic circular dichroism
difference of XANES spectra for left and right
helicity
Selection rules Orbital moment L -> L±1
ΔML = 0, ±1
,
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L-edge iron spectrum
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Comparison: Energy Loss Near Edge Spectroscopy (ELNES) and
X-ray Absorption Near Edge Spectroscopy (XANES)
ELNES: inelastic scattering of the fast electrons
transition from the core state of an atom to an empty state
Diferential cross section
polarization vector
ELNES
XANES
(XANES) is equivalent to (ELNES)
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Comparison: ELNES and XANES
XANES ELNES
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EMCD
Problem of EMCD: how to obtain in the position of an atom the
circularly polarized electric field
Solution (Schattschneider et al. 2003):
it is necessary to use
two coherent,
mutually perpendicular,
phase shifted electron beams (preferably the phase shift
= π/2)
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EMCD
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EMCD
Differential cross section
Mixed dynamical form factor
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Mixed dynamic form factor (MDFF)
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Coherent electron beams: first way (Dresden)
External beam splitter: possibility to study arbitrary object
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Coherent electron beams: second way (Vienna)
crystal as a „beam splitter“: limitation – single crystals
Electron source
incoming electron beam-plane wave
wave vector k
in crystal Σ(Bloch state), in
k, k±G, k±2G ………….
in crystal Σ(Bloch state), out
outcoming electron beam-plane waves
k, k±G, k±2G ……..
detector
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Coherent electron beams: second way
Two positions A, B of detector in the diffraction plane
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Modelling the experiment: crystal as a „beam splitter“
1/ Microscopic calculation of MDFF
Program package based on WIEN2k calculation of the band structure matrix elements Brillouin zone integration, summation
2/ Electron optics
originally program package „IL5“ (M. Nelhiebel, 1999)
new program package „DYNDIF“
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Modelling the experiment: crystal as a „beam splitter“
Electron optics
more general (eg. it includes higher order Laue zones ) more precise potentials, possibility to use ab-initio potentials can be used for all type of ELNES
DYNDIF includes experimental conditions angle of incident electron beam
detector position, thickness of the sample results depend on the structure and
composition of the system
DYNDIF
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Results
First result: EMCD: L edge of iron
XMCD EMCD Calculation
P.Schattschneider, S.Rubino, C.Hébert, J. Rusz, J.Kuneš, P.Novák,
E.Carlino, M.Fabrizioli, G.Panaccione, G.Rossi, Nature 441, 486
(2006)
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Results of simulation: dichroic maps
Dependence of the amplitude of dichroism on detector position
fcc Ni
qx, qy, ~ θx, θy
determine
the angle of
incoming
electron
beam
q
y
qx
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Results: dependence on the thickness of the sample
hcp Co
fcc Ni
bcc Fe ELNES(1)
ELNES(2)
EMCD=
ELNES(1)-ELNES(2)
* * * Exp. EMCD %
EMCD %
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New way of EMCD measurement with order
of magnitude increased signal/noise ratio
Dichroic signal as a function of the diffraction angle (in units of G)
hcp Co, thickness 18 nm
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Outlook
strongly correlated electron systems
band model is inadequate for electron structure determination
necessity to use effective hamiltonian for MDFF calculation
electron optics (DYNDIF) unchanged
program DYNDIF after „user friendly“ modification part of the
WIEN2k package
sum rules for EMCD (determination of spin and orbital moment)
Using the princip of EMCD for electron holography
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Conclusion
EMCD: new spectroscopic method
with potentially large impact in nanomagnetism
Computer modelling:
increasingly important part of the solid state physics
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Thanks to the CHIRALTEM project
and to all present for their
attention
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