Site-Selective Holographic Imaging of Iron Arrangements in Magnetite

Complex $\gamma$-ray holograms were recorded by tuning to the nuclear absorption lines of ${}^{57}\mathrm{Fe}$ in magnetite corresponding to different hyperfine fields. The numerical reconstruction of the holograms to real space provided three-dimensional images of local iron arrangements in octahedral and tetrahedral sublattices of magnetite. This direct site-selective imaging of atomic structure was performed using a tabletop experimental setup.

Figure 1

Acquisition of complex $\gamma$-ray holograms for ${}^{57}\mathrm{Fe}_3{\mathrm{O}}_4$. (a) Conversion electron Mössbauer spectrum of ${}^{57}\mathrm{Fe}_3{\mathrm{O}}_4$ epitaxial film recorded before experiment. The spectrum consists of two Zeeman sextets corresponding to ${\mathrm{Fe}}^{3+}$ ions and Fe ions with effective valency $2.5+$, respectively. Points represent measured data; lines are fits to the experimental data. The inset shows an enlarged view of best resolved lines indicated by an arrow. Complex $\gamma$-ray holograms were recorded by detuning below and above exact resonances (as depicted by solid and dashed lines, respectively) to achieve a shift of the scattering phase. (b) The holograms were acquired simultaneously using the velocity signal shown as a dashed line (not to scale). Points represent conversion electron yield recorded for a single sample orientation. The sum of counts in the regions of well-defined constant velocities, indicated by rectangles, were taken as single points of two-dimensional holograms. The spectrum summed over all orientations is represented by a solid line. The left and right horizontal scales refer to points and solid line, respectively

Figure 2

Complex $\gamma$-ray holograms of ${\mathrm{Fe}}_3{\mathrm{O}}_4$. Holograms were extracted from two-dimensional patterns of conversion electron yield dependence measured as the sample was rotated relative to the incident $\gamma$-ray beam direction. The holograms were obtained for nuclear resonances characteristic of ${\mathrm{Fe}}^{3+}$ (a) and ${\mathrm{Fe}}^{2.5+}$ (b) ions. Left: Real holograms (difference of patterns recorded above and below the resonance). Right: Imaginary holograms (sum of patterns recorded above and below the resonance). The intensity scale is normalized to the nuclear resonant background of each transition. All patterns are presented in the $k$-vector space as orthographic projections. The ticks are separated by $k/2$, where $k=2\pi /\lambda =7.29{\AA }^{-1}$. A fourfold symmetrization was applied to all patterns.

Figure 3

Three-dimensional real-space images of iron arrangements in magnetite. For clarity, only single octants of the real space are shown. Images were reconstructed from the holograms recorded for the nuclear resonance characteristic of ${\mathrm{Fe}}^{3+}$ (a) and ${\mathrm{Fe}}^{2.5+}$ ions (b). Each of the reconstructed voxels is represented by a small sphere with diameter and color scale proportional to the square of the reconstructed real-space image. The color bars are shown next to plots. The hot color scale corresponds to images reconstructed from real holograms, while the cold color scale to images reconstructed from imaginary holograms. Coordinates are labeled in units of lattice constant ($a_0=8.396\AA$). The lines join the expected positions of iron nuclei at $A$ and $B$ sites, respectively, assuming a linear combination of two equivalent $A$ and four $B$ sites, which have different orientations. The reference nuclei (not self-imaged) are located at the origins.