Boundaries for Efficient Use of Electron Vortex Beams to Measure Magnetic Properties

Ján Rusz and Somnath Bhowmick

Phys. Rev. Lett. 111, 105504 – Published 6 September 2013

Abstract

Development of experimental techniques for characterization of magnetic properties at high spatial resolution is essential for progress in miniaturization of magnetic devices, for example, in data storage media. Inelastic scattering of electron vortex beams (EVBs) was recently reported to contain atom-specific magnetic information. We develop a theoretical description of inelastic scattering of EVBs on crystals and perform simulations for EVBs of different diameters. We show that use of an EVB wider than an interatomic distance does not provide any advantage over an ordinary convergent beam without angular momentum. On the other hand, in the atomic-resolution limit, electron energy loss spectra measured by EVBs are strongly sensitive to the spin and orbital magnetic moments of studied matter, when channeling through or very close to the atomic columns. Our results demonstrate the boundaries for efficient use of EVBs in measurement of magnetic properties.

Received 16 June 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.105504

Authors & Affiliations

Ján Rusz^1,2,* and Somnath Bhowmick^1,3

¹Department of Physics and Astronomy, Uppsala University, Post Office Box 516, 75120 Uppsala, Sweden
²Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague, Czech Republic
³Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur 208016, India

^*jan.rusz@physics.uu.se

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Issue

Vol. 111, Iss. 10 — 6 September 2013

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Images

Figure 1
Evolution of $⟨ {\hat{L}}_{z} ⟩$ of the vortex beam as a function of sample thickness, averaged over different locations of the vortex core within a unit cell. “Error bars” indicate the spread of the angular momenta (minimum and maximum) at a given thickness. The top panel shows that a wide beam with $q_{\max } = 0.1$ has a negligible spread and thus virtually no dependence of angular momentum on the position of the vortex core. For a narrow vortex beam (bottom panel, $q_{\max } = 0.5$ ), there is a large spread of the angular momenta.Reuse & Permissions
Figure 2
Inelastic scattering of a wide vortex beam. The grid of EFDIF patterns shows intensity per hole in a $3 d$ shell and per Bohr magneton of spin magnetization in the $x$ , $y$ , and $z$ directions (columns from left to right) for four different thicknesses, 10, 20, 30, and 40 nm (rows from top to bottom). Range of plots is from $- 2 G$ to $2 G$ , where $G = (100)$ . The color ranges are from 0 to 3.0 (blue to red) for the first column and $- 0.0625$ to 0.0625 (black to yellow) for the second to fourth columns, respectively.Reuse & Permissions
Figure 3
Inelastic scattering of a narrow vortex beam with angular momentum $⟨ {\hat{L}}_{z} ⟩ = + ℏ$ , calculated for a sample thickness of 20 nm. Figure displays a grid of calculated EFDIF patterns normalized per hole in a $3 d$ shell (right-bottom triangle) and per Bohr magneton of magnetization in the $z$ direction (left-top triangle), representing the nonmagnetic and magnetic signals, respectively. The color ranges are from 0 to 1.2 (dark blue to red) and $- 0.025$ to 0.025 (black to yellow), respectively. The range of plots is from $- 5 G$ to $5 G$ in both the $x$ and $y$ directions, where $G = (100)$ . The maps in the lower-left corner correspond to a vortex core passing through an atom at the origin of the unit cell, while the maps in the right-top corner describe a vortex passing through a column of atoms in the centers of the body-centered cubic unit cells. The bottom panel shows the diffraction patterns (nonmagnetic and magnetic parts) for a vortex passing through an atomic column (left) and in between columns (right).Reuse & Permissions
Figure 4
High-resolution energy-filtered images for a beam of zero angular momentum (top panel) and $⟨ {\hat{L}}_{z} ⟩ = ℏ$ (bottom panel). Individual rows correspond to thicknesses of 10, 20, 30, and 40 nm, respectively, and columns refer to signal contributions normalized per hole or per $1 μ_{B}$ of spin magnetization along the $x$ , $y$ , and $z$ directions, respectively. Each pattern covers one unit cell.Reuse & Permissions

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