Research ArticleCONDENSED MATTER PHYSICS

Subunit cell–level measurement of polarization in an individual polar vortex

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Science Advances  01 Nov 2019:
Vol. 5, no. 11, eaav4355
DOI: 10.1126/sciadv.aav4355
  • Fig. 1 Structural characterization of (SrTiO3)10/(PbTiO3)10 superlattices.

    (A) Low-magnification STEM image of (PbTiO3)10/(SrTiO3)10 with the zone axis [010] of PbTiO3. (B) Out-of-plane strain εyy and (C) in-plane strain εxx calculated from GPA based on a STEM image. (D) High-angle annular dark-field (HAADF) STEM image overlapped with the polar vectors of a single vortex-antivortex pair in the PbTiO3 layer sandwiched between two SrTiO3 layers, showing a continuous rotation of electric dipole vectors. (E) Atomically resolved iDPC image with inverted contrast for clarity of purpose. (F) Five enlarged unit cells (left, right, top, bottom, and middle) are portrayed to depict the direction of polarization based on the atomic displacement of oxygen with respect to the cations.

  • Fig. 2 Quantitative measurements of polarization distribution for a single vortex-antivortex pair based on the cation-anion atomic positions in the iDPC image.

    (A) An iDPC image overlapped with the polarization vectors that are calculated from the displacements between cations and anions. The unit cell–mapped (B) out-of-plane (Pz) and (C) in-plane (Px). The plot of polarization for (D) the horizontally marked outline region in (B) and the vertically traced outline region in (C). Black dashed lines in (D) and (E) denote the bulk value of polarization. (F) Distribution of magnitude of polarization for out-of-plane and in-plane in PbTiO3 layer having vortex configuration.

  • Fig. 3 Quantitative analysis of the out-of-plane and in-plane lattice constant along with calculation of tetragonality for the PbTiO3/SrTiO3 superlattice.

    Color magnitude map for lattice constant (A) out-of-plane and (B) in-plane. (C) Illustration of magnitude mapping for tetragonality (c/a ratio). The consecutive marked regions (in Fig. 2C) indicate upward (away from substrate) and downward (toward substrate) polarization (>50 μC cm−2). (D) Distribution of magnitude of polarization for upward (red data) and downward (green data) directed polar vectors in the PbTiO3 layer having vortex configuration. The average value for downward (green data) and upward (red data) polarization magnitude is ~77.0 and ~69.6 μC cm−2, respectively.

  • Fig. 4 Subunit scale level of polarization distribution.

    Color magnitude map of out-of-plane (Pz) polarization distribution obtained separately for (A) SrO/PbO atomic planes, (B) TiO2 atomic planes, and (C) contribution ratio of P(SrO/PbO) to P(TiO2). Color magnitude map of in-plane (Px) polarization distribution obtained separately for (D) SrO/PbO atomic planes, (E) TiO2 atomic planes, and (F) contribution ratio of P(SrO/PbO) to P(TiO2). (G) Plot for the horizontally marked rectangular region in (C). (H) Plot for the horizontally marked rectangular regions in (A) and (B), at both PbO atomic planes (purple data) and TiO2 atomic planes (orange data).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaav4355/DC1

    Fig. S1. GPA of PbTiO3/SrTiO3 superlattices.

    Fig. S2. Bond length analysis for polar vortex.

    Fig. S3. An iDPC image of (SrTiO3)10/(PbTiO3)10 superlattices with illustrated PbTiO3 and SrTiO3 layers.

    Fig. S4. Atomically resolved iDPC images of PbTiO3/SrTiO3 thin films.

    Fig. S5. Polarization measurement based on cation-cation atomic positions in the HAADF image.

    Fig. S6. Quantification of polarization distribution for PbTiO3/SrTiO3 thin films based on the cation-anion atomic positions in the iDPC image.

    References (3338)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. GPA of PbTiO3/SrTiO3 superlattices.
    • Fig. S2. Bond length analysis for polar vortex.
    • Fig. S3. An iDPC image of (SrTiO3)10/(PbTiO3)10 superlattices with illustrated PbTiO3 and SrTiO3 layers.
    • Fig. S4. Atomically resolved iDPC images of PbTiO3/SrTiO3 thin films.
    • Fig. S5. Polarization measurement based on cation-cation atomic positions in the HAADF image.
    • Fig. S6. Quantification of polarization distribution for PbTiO3/SrTiO3 thin films based on the cation-anion atomic positions in the iDPC image.
    • References (3338)

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