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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