Research ArticlePHYSICAL SCIENCE

Low-energy structural dynamics of ferroelectric domain walls in hexagonal rare-earth manganites

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Science Advances  10 May 2017:
Vol. 3, no. 5, e1602371
DOI: 10.1126/sciadv.1602371
  • Fig. 1 Multimode microscopy on (001) YMnO3.

    (A) Schematic of the experimental setup. The shielded cantilever probe is connected to the SIM electronics via a bias tee, through which a low-frequency ac voltage (95 kHz, 5 V) for PFM or a dc bias (−5 V) for C-AFM can be applied to the tip. The AFM image on the left shows the surface topography of (001) YMnO3. (B) OOP-PFM, C-AFM, SIM-Re, and SIM-Im (f = 1 GHz) images acquired on the same area. Arb. unit, arbitrary unit. Scale bars, 1 μm. (C) SIM-Im (pink) and C-AFM (orange) line profiles across a single DW centered at position 0.0 μm and labeled as dashed lines in (B). The full width at half maximum of 100 nm is comparable to the tip diameter, as shown in the scanning electron microscopy image in the inset. (D) Simulated SIM signals as a function of the effective DW conductivity. The measured DW signals with a ratio of SIM-Re/Im ~0.4 (shaded in red) are consistent with σDW ~400 S/m. The inset shows the tip-sample geometry for the FEA.

  • Fig. 2 SIM experiments on other h-RMnO3.

    (A) Schematic representation of the tip electric fields (pink) and the OOP polarization (blue) on the highlighted (001) ErMnO3 surface. (B) AFM, OOP-PFM, SIM-Re, and SIM-Im (f = 1 GHz) images acquired on (001) ErMnO3. Clear DW contrast can be seen in the SIM data. (C) and (D) are the same as (A) and (B), except that the schematic and the data are for (110) HoMnO3, showing clear domain contrast in the in-plane (IP) PFM but no DW contrast in the SIM images. Scale bars, 1 μm.

  • Fig. 3 Frequency-dependent DW response.

    (A to D) SIM images on (001) YMnO3 at selected frequencies. Scale bars, 1 μm. Simulated SIM signals (E) and SIM-Re/Im ratios for different tip diameters (F), showing weak dependence on the exact tip condition when the Re/Im ratio is calculated. Note that the x axis is σDW/f, that is, the simulation is invariant when σDW is scaled by the frequency. (G) SIM-Re/Im ratio of the DW signals as a function of f in a log-log plot. The constant σDW contours at 10, 30, 100, 300, and 1000 S/m are also plotted in the graph. (H) f-dependent σDW of the (001) YMnO3 DWs. The dash-dot line is a guide to the eyes. The inset shows the same data in the log-log scale.

  • Fig. 4 Periodic DW sliding in the simplified model.

    (A) Ground-state configuration of the simplified Hamiltonian (1), with the DW centered between two Mn sites. (B) High-energy configuration when the DW is centered at a Mn site. The schematics in (A) and (B) show the corresponding on-site energies in the double-well potential. (C) Washboard-like potential when the center of the DW slides across different sites. (D) Phonon spectral function in this simple model, showing the nondispersive sliding mode at the lowest energy, the breathing mode at a higher energy, and the dispersive bulk phonon branch. (E) Mode texture for a lateral shift of the DW position (top) and the corresponding DW sliding mode (bottom). (F) Mode texture for an increase of the DW width (top) and the corresponding DW breathing mode (bottom). (G) Dependence of the DW oscillation frequency on its width.

  • Fig. 5 DW dynamics revealed by first principles–based model calculations.

    (A) Atomistic view of YMnO3 in the (001) plane across the interlocked antiphase boundary and ferroelectric DW. The MnO5 polyhedra are shaded in purple. The displacements of apical oxygen atoms in the down-domain (left), DW (middle), and up-domain (right) regions are displayed by red, green, and blue arrows, respectively. The trimers are indicated by dashed triangles. The black and white double-headed arrows illustrate the amplitudes and directions of the periodic DW sliding. (B) Ground-state configuration of the three order parameters across the DW obtained by minimizing the model Hamiltonian. (C) Phonon spectral function projected to the Q, φ, and P modes. The ripples are due to the finite size (120 sites) of the supercell. The lower panels in the log scale show the spectral intensity of the low-energy nondispersive branch. (D) Real-space oscillation of δQ, δφ, and δP for a regular dispersive phonon at the terahertz range (top) and the localized DW sliding mode at the gigahertz range (bottom).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/5/e1602371/DC1

    section S1. dc conductivity of h-RMnO3

    section S2. SIM electronics and the calibration process

    section S3. FEA of the tip-sample interaction

    section S4. SIM data on polished HoMnO3 samples

    section S5. SIM circuits and impedance match at different frequencies

    section S6. More SIM data at various frequencies

    section S7. Repeated line scans for improving the signal-to-noise ratio

    section S8. Details of the full model calculations

    fig. S1. Measurement of the dc resistivity of YMnO3.

    fig. S2. SIM electronics and the calibration process.

    fig. S3. FEA of the tip-sample interaction.

    fig. S4. SIM data on polished HoMnO3 samples.

    fig. S5. Impedance-match sections at different frequencies.

    fig. S6. SIM images at various frequencies.

    fig. S7. SIM experiments with repeated line scans.

    fig. S8. First principles–based model calculations.

    References (5257)

  • Supplementary Materials

    This PDF file includes:

    • section S1. dc conductivity of h-RMnO3
    • section S2. SIM electronics and the calibration process
    • section S3. FEA of the tip-sample interaction
    • section S4. SIM data on polished HoMnO3 samples
    • section S5. SIM circuits and impedance match at different frequencies
    • section S6. More SIM data at various frequencies
    • section S7. Repeated line scans for improving the signal-to-noise ratio
    • section S8. Details of the full model calculations
    • fig. S1. Measurement of the dc resistivity of YMnO3.
    • fig. S2. SIM electronics and the calibration process.
    • fig. S3. FEA of the tip-sample interaction.
    • fig. S4. SIM data on polished HoMnO3 samples.
    • fig. S5. Impedance-match sections at different frequencies.
    • fig. S6. SIM images at various frequencies.
    • fig. S7. SIM experiments with repeated line scans.
    • fig. S8. First principles–based model calculations.
    • References (52–57)

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