Abstract
We report application of hole-free phase plate (HFPP) to imaging of magnetic skyrmion lattices. Using HFPP imaging, we observed skyrmions in FeGe, and succeeded in obtaining phase contrast images that reflect the sample magnetization distribution. According to the Aharonov-Bohm effect, the electron phase is shifted by the magnetic flux due to sample magnetization. The differential processing of the intensity in a HFPP image allows us to successfully reconstruct the magnetization map of the skyrmion lattice. Furthermore, the calculated phase shift due to the magnetization of the thin film was consistent with that measured by electron holography experiment, which demonstrates that HFPP imaging can be utilized for analysis of magnetic fields and electrostatic potential distribution at the nanoscale.
Highlights
We discuss a simplified image formation model by deriving an expression of the Zernike type phase plate, i.e. in case of the additional phase shift η is applied by the hole-free phase plate (HFPP) to the electron wave in the close vicinity of the unscattered electron beam
The electron wave ψ0 is described by the axial electron wave which is comprised of the unscattered wave traveling through the sample, and the wave scattered by a phase object φobj: Ψ0(x, y) = exp[iφ(x, y)] = Aref exp[iφref(x, y)] + Aobj exp[iφobj(x, y)], (1)
Even though the HFPP phase shift is not known and different from -π/2, the fact that the magnetic phase shift is weak suffices to obtain a linear relation between the image contrast and the magnetic phase shift, see Eq (4)
Summary
If we can detect the phase shift derived from the skyrmion lattice, the magnetic field distribution can be measured. This phenomenon is referred to as the Aharonov-Bhom (AB) effect.[20] The magnetization distribution can be extracted from the phase plate images that exhibit the contrast linear with the phase shift. The magnetic field can be obtained by differentiation of the image contrast as follows: B(x, y)
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