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

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 two coherent, mutually perpendicular, phase shifted 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 study arbitrary 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 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 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 the band 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 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 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 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 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 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 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 Conclusion EMCD: new spectroscopic method with potentially large impact in nanomagnetism Computer modelling: increasingly important part of the solid state physics

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