Ele c tron magnetic cir c ul a r dichroism

1. Electron magnetic circular dichroism Pavel Novák Institute of Physics ASCR, Prague, Czech Republic

2. Scope • Motivation • Short history • XMCD –X-ray magnetic circular dichroism • EMCD – electron magnetic circular dichroism • Modelling of experiment • Results • Outlook • Conclusions

3. Motivation Characterization of verysmal magnetic objects (≤ 10 nm) Necessity of veryshortwavelengths 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

4. 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 support 2004 –project approved within program NEST 6 „Adventure“ Our group:Ján Rusz, Pavel Novák, Jan Kuneš, Vladimír Kamberský 2005 – experimental verification, microscopic theory, first workshop 2006 –paper in Nature, second workshop 2007 –sensitivity increased by order of magnitude planned: third workshop, closing the project

5. Circular magnetic dichroism ≠ Circular dichroism: absorption spectrum of polarizedlight is different for left and right helicity Symmetry with respect to time inversion must be broken: magnetic field magnetically ordered systems Microscopic mechanism: inelastic diffraction oflight, electric dipol transitions coupling of light and magnetism – spin-orbit interaction X-ray circular dichroism:circular dichroism in theX-rayregion

6. XANES and XMCD XANES – X-ray near edge spectroscopy Transition of an electron from the corelevel of an atomto an empty state Crosssection of XANES polarization vector XMCD – X-ray magnetic circular dichroism difference of XANES spectrafor left and right helicity , Selection rules Orbital moment L -> L±1 ΔML = 0, ±1

7. L-edge iron spectrum

8. 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 Diferentialcross section ELNES XANES polarization vector (ELNES) (XANES) is equivalent to

9. Comparison: ELNES and XANES XANES ELNES

10. 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 twocoherent, mutually perpendicular, phaseshifted electron beams (preferably the phase shift =π/2)

11. EMCD

12. EMCD Differential cross section Mixed dynamical form factor

13. Mixed dynamic form factor (MDFF)

14. Coherent electron beams: first way (Dresden) External beam splitter:possibility to studyarbitrary object

15. Coherent electron beams: second way (Vienna) crystal as a „beam splitter“:limitation – single crystals Electron source incoming electron beam-plane wave wave vector k incrystal Σ(Bloch state), in k, k±G, k±2G …………. incrystal Σ(Bloch state), out outcoming electron beam-planewaves k, k±G, k±2G …….. detector

16. Coherent electron beams: second way Two positions A, B of detector in the diffraction plane

17. Modelling the experiment: crystal as a „beam splitter“ 1/ Microscopic calculation of MDFF • Program package based on WIEN2k • calculation of theband structure • matrix elements • Brillouin zone integration, summation 2/ Electron optics originally program package „IL5“ (M. Nelhiebel, 1999) new program package„DYNDIF“

18. Modelling the experiment: crystal as a „beam splitter“ Electron optics • more general (eg. it includes higher order Laue zones ) • more precise potentials, possibility to useab-initio potentials • can be used for all type of ELNES DYNDIF • DYNDIF includes experimental conditions • angle of incident electron beam • detector position, thicknessof the sample • results depend on the structure and • composition of the system

19. 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)

20. Results of simulation: dichroic maps Dependence of the amplitudeof dichroismon detector position fcc Ni qx, qy, ~θx, θy determine the angle of incoming electron beam qy qx

21. Results: dependence on the thickness of the sample bcc Fe ELNES(1) ELNES(2) EMCD= ELNES(1)-ELNES(2) hcp Co EMCD % * * * Exp. EMCD % fcc Ni

22. New way of EMCD measurement withorder of magnitude increased signal/noise ratio hcp Co, thickness 18 nm Dichroic signal asa function of the diffraction angle (in units of G)

23. 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 DYNDIFafter „user friendly“ modificationpart of the • WIEN2k package • sum rulesfor EMCD (determination of spin and orbital moment) • Using the princip ofEMCD for electron holography

24. Conclusion EMCD:new spectroscopic method with potentially largeimpact in nanomagnetism Computer modelling: increasingly important part of the solid state physics

25. Thanks to the CHIRALTEMproject and to all present for their attention