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

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

3. 3 Motivation Characterization of very smal magnetic objects (≤ 10 nm) Necessity of very short wavelengths X-ray magnetooptics XMCD: X-ray Magnetic Circular Dichroismus predicted1975 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. 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“ 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

5. 5 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 ≠

6. 6 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 rulesOrbital moment L -> L±1 ΔM L = 0, ±1,

7. 7 L-edge iron spectrum

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

9. 9 Comparison: ELNES and XANES XANES ELNES

10. 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 two coherent, mutually perpendicular, phase shifted electron beams (preferably the phase shift = π /2)

11. 11 EMCD

12. 12 EMCD Differential cross section Mixed dynamical form factor

13. 13 Mixed dynamic form factor (MDFF)

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

15. 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 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

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

17. 17 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“

18. 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 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

19. 19 Results First result: EMCD: L edge of iron XMCDEMCDCalculation 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. 20 Results of simulation: dichroic maps Dependence of the amplitude of dichroism on detector position fcc Ni q x, q y, ~ θ x, θ y determine the angle of incoming electron beam qyqy qxqx

21. 21 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 %

22. 22 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

23. 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 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

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

25. 25 Thanks to the CHIRALTEM project and to all present for their attention