Vortex beams for atomic resolution dichroism

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
Journal of electron microscopy (Impact Factor: 1.63). 09/2011; 60(5):295-300. DOI: 10.1093/jmicro/dfr069
Source: PubMed


Vortex beams carrying orbital angular momentum have been produced recently with electron microscopy by interfering an incident
electron beam with a grid containing dislocations. Here, we present an analytical derivation of vortex wave functions in reciprocal
and real space. We outline their mathematical and physical properties and describe the conditions under which vortex beams
can be used in scanning transmission microscopy to measure magnetic properties of materials at the atomic scale.

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    ABSTRACT: We report the production of electron vortex beams carrying large orbital angular momentum (OAM) using micro-fabricated spiral zone plates. A series of the spherical waves, focussing onto different positions along the propagating direction of the electron beam, were observed. The nth order vortex beam has an OAM n times larger than that of the first-order vortex beam. We observed an electron vortex with an OAM up to in a high-order diffracted wave. A linear dependence of the diameter of the vortex beam on the OAM was observed, being consistent to numerical simulations.
    Journal of electron microscopy 03/2012; 61(3):171-7. DOI:10.1093/jmicro/dfs036 · 1.63 Impact Factor
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    ABSTRACT: Atomic-size vortex beams have great potential in probing the magnetic moment of materials at atomic scales. However, the limited depth of field of vortex beams constrains the probing depth in which the helical phase front is preserved. On the other hand, electron channeling in crystals can counteract beam divergence and extend the vortex beam without disrupting its topological charge. Specifically, in this article, we report that atomic vortex beams with topological charge ±1 can be coupled to the 2p columnar bound states and propagate for more than 50 nm without being dispersed and losing its helical phase front. We give numerical solutions to the 2p columnar orbitals and tabulate the characteristic size of the 2p states of two typical elements, Co and Dy, for various incident beam energies and various atomic densities. The tabulated numbers allow estimates of the optimal convergence angle for maximal coupling to 2p columnar orbital. We have also developed analytic formulae for beam energy, convergence angle, and hologram-dependent scaling for various characteristic sizes. These length scales are useful for the design of pitch-fork apertures and operations of microscopes in the vortex-beam imaging mode.
    Microscopy and Microanalysis 07/2012; 18(4):711-9. DOI:10.1017/S1431927612000499 · 1.88 Impact Factor
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    ABSTRACT: Electron vortex beam probes offer the possibility of mapping magnetic moments with atomic resolution. In this work we consider using the stray magnetic field produced from a narrow ferromagnetic rod magnetised along its long axis to produce a vortex beam probe, as an alternative to the currently used holographic apertures or gratings. We show through numerical modelling, electron holography observations and direct imaging of the electron probe, that a long narrow ferromagnetic rod induces a phase shift in the wave-function of passing electrons that approximately describes a helix in the regions near its ends. Directing this rod towards the optical axis of a charged-particle beam probe forming system at a limiting aperture position, with the free-end sufficiently close to the axis, is shown to offer a point spread function composed of vortex modes, with evidence of this appearing in observations of the electron probe formed from inserting a micro-fabricated CoFe rod into the beam path of a 300keV transmission electron microscope (TEM). If the rod is arranged to contain the magnetic flux of h/e, thus producing a maximum phase shift of 2π, it produces a simple spiral-like phase contrast transfer function for weak phase objects. In this arrangement the ferromagnetic rod can be used as a phase plate, positioned at the objective aperture position of a TEM, yielding enhanced image contrast which is simulated to be intermediate between comparable Zernike and Hilbert phase plates. Though this aspect of the phase plate performance is not demonstrated here, agreement between our observations and models for the probe formed from an example rod containing a magnetic flux of ~2.35h/e, indicate this phase plate arrangement could be a simple means of enhancing contrast and gaining additional information from TEM imaged weak phase samples, while also offering the capability to produce vortex beam probes. However, steps still need to be taken to either remove or improve the support membrane for the rod in our experiments to reduce any effects from charging in the phase plate.
    Ultramicroscopy 09/2013; 136C:127-143. DOI:10.1016/j.ultramic.2013.08.009 · 2.44 Impact Factor
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