The vibrational excitations of nanostructures have been mapped using state-of-the-art electron microscopy. The results improve our understanding of these excitations, which will aid the design of nanostructures. See Letter p.529
When matter is heated, its atoms vibrate around their equilibrium positions. As a consequence of the interactions between the individual atoms, their motion is generally collective. The quantum-mechanical descriptions of the vibrational excitations (modes) of an atomic lattice are called phonons. These phonons are key to understanding energy exchange and transfer in these lattices — and, consequently, the thermodynamic properties of materials. On page 529, Lagos et al.1 report experimental maps that show the response of phonons in nanometre-scale magnesium oxide cubes to a narrow beam of high-energy electrons. These maps reveal details about the energy and spatial distribution of vibrational modes in such nanostructures, enhancing our fundamental understanding of phonons.
The properties of phonons have been investigated for decades, both experimentally and theoretically. Scattering experiments that use X-rays, neutrons or infrared light have provided a comprehensive view, revealing phonons' dispersion curves — the relationship between their energy and momentum — and the existence of different types of vibrational mode, including acoustic, optical, transverse and longitudinal. However, this knowledge derives mostly from experiments on bulk materials. These experiments generally use broad beams, and generate information on extended surfaces or collections of nanoparticles. A detailed investigation of phonon modes in a nanoscale object, involving a characteristic vibrational response of the object's surface atoms, has been difficult to achieve.
In an ionic crystal, an optical phonon is the quantum of elastic energy associated with the mechanical oscillation of oppositely charged ions. These oscillations induce electric polarization waves that can strongly couple to an electromagnetic wave, resulting in a 'quasiparticle' called a surface phonon polariton that propagates on the surface of the crystal. Such quasiparticles are analogous to the more commonly studied surface plasmon polaritons, which are produced when oscillations of free electrons (plasmons) are coupled to an electromagnetic wave.
However, there are two main differences. First, surface plasmon polaritons are produced in the ultraviolet to near-infrared energy range (typically 1–3 electronvolts) in metals such as silver or gold2, whereas those of phonons manifest in the infrared range (usually 10–100 meV) in ionic or semiconducting materials3. Second, plasmon modes are damped by electron scattering on a timescale of tens of femtoseconds2 (1 fs is 10−15 seconds), whereas optical phonon modes decay through much weaker phonon–phonon interactions on a picosecond timescale3 (1 ps is 10−12 s). The combination of these two factors means that surface phonon polaritons are much more difficult to investigate than their plasmonic counterparts. In this respect, Lagos and colleagues' work is truly impressive. They obtain detailed information on the energy and spatial distribution of surface phonon polaritons on nanoscale cubes of magnesium oxide.
Lagos et al. use a mapping technique called electron energy-loss spectroscopy (EELS) spectrum imaging. First, they expose the nanocube to a narrow beam of high-energy electrons in a state-of-the-art scanning transmission electron microscope (developed by the authors of ref. 4). As electrons scatter off the cube, they lose energy. Lagos and colleagues measure this energy loss using an electron spectrometer and use the data to generate an EELS spectrum (Fig. 1a). They then record spectra when the electron beam is at different positions (typically separated by a few nanometres) in the bulk of the cube, or outside and parallel to its external faces and edges. This allows the authors to produce EELS maps that show the intensity of electron scattering for a given value of the energy loss (Fig. 1b).
Lagos and colleagues find that surface phonon polaritons are produced for electron energy losses in the range 40–100 meV, which the authors probe with a resolution of about 10 meV. Their spectacular set of EELS spectra and experimental set-up clearly demonstrate the improvement in instrumental performance that is required to move from the plasmonics to the phononics field. A similar study5 that identified the 3D distribution of plasmon modes on the faces, edges and corners of a silver nanocube required EELS spectra in the energy range 1–4 eV, recorded with a resolution of 170 meV.
One of Lagos and collaborators' most spectacular results is the level of detail recorded in the EELS maps for energy losses of 70 and 77 meV (Fig. 1b), which correspond to the excitation energies of the corner and face surface phonon polaritons, respectively. The authors' work also demonstrates the excellent agreement between experimental observations and the results of simulations realized using the MNPBEM toolbox6 — a computer program developed by two of the co-authors that can simulate EELS spectra for many plasmonic and phononic systems.
Lagos and collaborators' work has historical interest because it revisits an old subject, namely phonons in small (nanoscale) magnesium oxide particles. More than 40 years ago, these phonons were measured by EELS on particles of a similar compound (lithium fluoride)7 and on magnesium oxide cubes extracted from the smoke of a burnt magnesium ribbon8. Moreover, theoretical developments were made around this time to calculate the optical absorption of small ionic-crystal cubes9. In particular, several absorption peaks had been identified that could be attributed to different spatial distributions of surface charges on the cubes. Thanks to Lagos et al., the identification of phonons in these nanostructures is now fully resolved. Furthermore, the authors' advanced microscopy technique could be applied to more-complex situations, potentially giving rise to nanoscale optical devices that work at infrared frequencies and offer greater sensitivity than current devices. Footnote 1
Lagos, M. J., Trügler, A., Hohenester, U. & Batson, P. E. Nature 543, 529–532 (2017).
Colliex, C., Kociak, M. & Stéphan, O. Ultramicroscopy 162, A1–A24 (2016).
Sangster, M. J. L., Peckham, G. & Saunderson, D. H. J. Phys. C 3, 1026–1036 (1970).
Krivanek, O. L. et al. Nature 514, 209–212 (2014).
Nicoletti, O. et al. Nature 502, 80–84 (2013).
Hohenester, U. & Trügler, A. Comput. Phys. Commun. 183, 370–381 (2012).
Boersch, H., Geiger, J. & Stickel, W. Phys. Rev. Lett. 17, 379–381 (1966).
Geiger, J. J. Phys. Soc. Japan 36, 615 (1974).
Fuchs, R. Phys. Rev. B 11, 1732–1740 (1975).