Mapping vibrational surface and bulk modes in a single nanocube

Abstract

Imaging of vibrational excitations in and near nanostructures is essential for developing low-loss infrared nanophotonics1, controlling heat transport in thermal nanodevices2,3, inventing new thermoelectric materials4 and understanding nanoscale energy transport. Spatially resolved electron energy loss spectroscopy has previously been used to image plasmonic behaviour in nanostructures in an electron microscope5,6, but hitherto it has not been possible to map vibrational modes directly in a single nanostructure, limiting our understanding of phonon coupling with photons7 and plasmons8. Here we present spatial mapping of optical and acoustic, bulk and surface vibrational modes in magnesium oxide nanocubes using an atom-wide electron beam. We find that the energy and the symmetry of the surface polariton phonon modes depend on the size of the nanocubes, and that they are localized to the surfaces of the nanocube. We also observe a limiting of bulk phonon scattering in the presence of surface phonon modes. Most phonon spectroscopies are selectively sensitive to either surface or bulk excitations; therefore, by demonstrating the excitation of both bulk and surface vibrational modes using a single probe, our work represents advances in the detection and visualization of spatially confined surface and bulk phonons in nanostructures.

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Figure 1: STEM Imaging and EELS spectra of MgO cubes.
Figure 2: Spatially dependent EELS scattering acquired along the [110] direction of a 150-nm MgO cube.
Figure 3: Experimental and simulated maps of surface and bulk vibrational EELS scattering on the edge of a single 100-nm MgO cube.
Figure 4: Size effects on the excitation of surface modes.

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Acknowledgements

P.E.B. and M.J.L. acknowledge the financial support of US Department of Energy, Office of Science, Basic Energy Sciences under award number DE-SC0005132. U.H. and A.T. acknowledge the support of the Austrian Science Fund FWF under project P27299-N27 and the SFB F49 NextLite (F4906-N23). We acknowledge O. Krivanek, N. Dellby, T. Lovejoy, M. Saharan and C. Meyer for discussions on the microscope instrumentation/operation and for help with the software development for microscopy data acquisition.

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Contributions

M.J.L. initiated the project and conceived the experiments. M.J.L. prepared the samples and conducted the EELS-STEM experiments. M.J.L. and P.E.B. performed the data analysis and interpretation. U.H. and A.T. developed the theoretical model and performed the theoretical calculations. M.J.L. and P.E.B. wrote the manuscript. All authors read and commented on the manuscript.

Corresponding author

Correspondence to Maureen J. Lagos.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks C. Colliex, P. Rez and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Excitation of corner, face and edge SPhP modes in approximately 150-nm MgO cubes.

The excitation occurs in the aloof geometry and the probe positions are indicated by dots in the ADF images (see insets of a, c and e). a, c, e, Experimental EELS spectra for cubes oriented along the [001], [111] and [110] directions, respectively. b, d, f, Simulated EELS probabilities (dotted lines) corresponding to the configurations shown in a, c and e, respectively. The continuous lines are theoretical curves that correspond to the convolution of the dotted lines with a Gaussian function with a width of 10 meV, which accounts for the instrument response. Excitation of the corner mode (red curves) shows up as a peak at approximately 69 meV (vertical dashed red lines in a, c and e). The face-mode excitation (green curves) appears as an asymmetric peak at approximately 78 meV (vertical dashed green line in a). This asymmetry is introduced by low-energy contributions of the corner and edge modes. The edge-mode excitation (blue curves) appears as an asymmetric peak at approximately 72 meV (vertical dashed blue line in e). Good agreement between the theoretical convoluted curves (b, d, f) and the experimental results (a, c, e) is obtained. Source data

Extended Data Figure 2 Scattering coupling factor between the swift electron and the phonon modes of a bulk MgO crystal.

See Methods. The phonon dispersions (light grey curves) were determined using the rigid-ion approach and most of the calculated phonon frequencies exhibit excellent agreement with the experimental data. The dispersion curves exhibit the typical optical (LO, TO) and acoustic (LA, TA) modes across the first Brillouin zone. The strength of the coupling is represented by the size of the red circles (proportional to qFλ(q)), which are superposed over the light grey phonon dispersion lines, with larger circles indicating stronger coupling. The swift electron can couple very efficiently to the LO and LA modes, while the transverse modes display weak coupling. An effective coupling can occur with short-wavelength phonons close to the Brillouin zone boundaries through high-angle scattering events. Source data

Extended Data Figure 3 Simulated EELS probabilities for cubes of different sizes, considering an electron probe in the aloof geometry in the middle of the cube face (5 nm away from the surface).

At this location, the probe is able to excite corner, edge and face SPhP modes with different probabilities, as shown in Extended Data Fig. 1b (green curve). The probabilities were normalized with respect to the intensity maximum of the corner resonance (about 71 meV). For the small cubes, the corner mode dominates the excitation spectrum, resulting in small probabilities of face-mode excitations. Source data

Supplementary information

Phonon Mapping 100nm MgOcube

Video showing experimental phonon EELS maps acquired on the edge of a suspended 100 nm MgO cube. Each snapshot represents a phonon map generated at certain energy. Note the surface phonon modes (~ 70 and 77 meV) are highly localized close to corner and face of the cube, respectively. Their scattering intensities can extend towards the vacuum. The bulk modes (~ 40, 50 and 88 meV) remain confined within the cube. The dotted line indicated the edge of the nanocube. (MP4 1118 kb)

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Lagos, M., Trügler, A., Hohenester, U. et al. Mapping vibrational surface and bulk modes in a single nanocube. Nature 543, 529–532 (2017). https://doi.org/10.1038/nature21699

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