Structural imaging of nanoscale phonon transport in ferroelectrics excited by metamaterial-enhanced terahertz fields

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Structural imaging of nanoscale phonon transport in ferroelectrics excited by metamaterial-enhanced terahertz fields

Yi Zhu, Frank Chen, Joonkyu Park, Kiran Sasikumar, Bin Hu, Anoop R. Damodaran, Il Woong Jung, Matthew J. Highland, Zhonghou Cai, I-Cheng Tung, Donald A. Walko, John W. Freeland, Lane W. Martin, Subramanian K. R. S. Sankaranarayanan, Paul G. Evans, Aaron M. Lindenberg, and Haidan Wen

Phys. Rev. Materials 1, 060601(R) – Published 16 November 2017

Abstract

Nanoscale phonon transport is a key process that governs thermal conduction in a wide range of materials and devices. Creating controlled phonon populations by resonant excitation at terahertz (THz) frequencies can drastically change the characteristics of nanoscale thermal transport and allow a direct real-space characterization of phonon mean-free paths. Using metamaterial-enhanced terahertz excitation, we tailored a phononic excitation by selectively populating low-frequency phonons within a nanoscale volume in a ferroelectric $BaTi O_{3}$ thin film. Real-space time-resolved x-ray diffraction microscopy following THz excitation reveals ballistic phonon transport over a distance of hundreds of nm, two orders of magnitude longer than the averaged phonon mean-free path in $BaTi O_{3}$ . On longer length scales, diffusive phonon transport dominates the recovery of the transient strain response, largely due to heat conduction into the substrate. The measured real-space phonon transport can be directly compared with the phonon mean-free path as predicted by molecular dynamics modeling. This time-resolved real-space visualization of THz-matter interactions opens up opportunities to engineer and image nanoscale transient structural states with new functionalities.

Received 13 September 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.060601

Physics Subject Headings (PhySH)

Ballistic transport Ferroelectricity Lattice dynamics Phonons

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yi Zhu¹, Frank Chen^2,3, Joonkyu Park⁴, Kiran Sasikumar⁵, Bin Hu¹, Anoop R. Damodaran^6,7, Il Woong Jung⁵, Matthew J. Highland⁸, Zhonghou Cai¹, I-Cheng Tung¹, Donald A. Walko¹, John W. Freeland¹, Lane W. Martin^6,7, Subramanian K. R. S. Sankaranarayanan⁵, Paul G. Evans⁴, Aaron M. Lindenberg^3,9,10, and Haidan Wen^1,*

¹Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
²Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
³SIMES Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁴Department of Materials Science and Engineering, University of Wisconsin, Madison, Madison, Wisconsin 53706, USA
⁵Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁶Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720, USA
⁷Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁸Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁹Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
¹⁰PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

^*wen@aps.anl.gov

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Issue

Vol. 1, Iss. 6 — November 2017

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Images

Figure 1
Schematic of the experiment. The vertically polarized THz pulses are focused onto the sample surface. The THz field is enhanced near the horizontal gold gaps (red-colored ellipses) of the split-ring resonators shown by the gold color. An x-ray beam is focused by a Fresnel zone plate to probe locally in the vicinity of the field-enhanced regions and the diffracted x-ray beam is collected by an area detector. The inset shows the unit cell of $BaTi O_{3}$ .
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Figure 2
(a) Static x-ray diffraction intensity map of the sample around the SRR gap without THz excitation. (b) The radial scans of BTO 002 x-ray reflection in the gap and under the gold surface, corresponding to the positions shown by the color dots in (a). (c) The THz-induced shift of the 002 diffraction peak of the BTO thin film. The blue arrow indicates the diffraction angle $θ = 16 . 09^{\circ}$ at which (a) and (d) plots were acquired. (d) The diffraction intensity change and the calibrated strain as a function of delay between THz and x-ray pulses.
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Figure 3
(a) The THz-induced strain map obtained by subtracting the diffraction intensity map measured before THz excitation from the one measured at 100 ps after THz excitation. Two-dimensional smooth was applied. The magenta-overlaid area shows the gold metamaterial profile extracted from the intensity maps of the gold diffraction. (b) Strain profiles along the dashed line in (a) measured at different delays. The inset at the bottom of the plot shows a cross-sectional view of the sample. The THz field distribution is calculated along the dashed red line.
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Figure 4
(a) The spectrum of the incident THz field. (b) The calculated THz field distribution in the BTO layer around a split-ring resonator. The color bar shows the field enhancement factor. The white rectangular box across the gap shows the regime of 1D x-ray scanning probe along the $x$ axis. (c) The line profiles of the THz field across the gap along the $x$ axis in the BTO layer, simulated with different incident THz frequencies. The profile at 0.2 and 2 THz was scaled by a factor of 0.47 and 2.3 to compare with the profile at 0.6 THz. (d) Measured (dots) and simulated (solid curves) strain profile based on the diffusive model at 100 ps. (e) Fitted (black) and simulated (other colors) temperature profiles inside BTO thin film based on diffusive thermal transport model.
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Figure 5
The calculated phonon mean-free path as a function of frequency. The green overlay around 0.2 to 1.7 THz shows the spectral region that is covered by the pump THz pulse. Select phonon modes, longitudinal acoustic (LA) vs transverse acoustic (TA) along three Brillouin zone (BZ) branches, are color-coded as appropriate. Γ refers to the origin of the BZ, $X$ is (0.5,0,0), $M$ is (0.5,0.5,0), and $R$ is (0.5,0.5,0.5).
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