Polarization, strain induced phase transitions and dielectric response in ultrathin PbTiO3 nanowires

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  • 1. Polarization, strain induced phase transitions and dielectric response in ultrathin PbTiO3 nanowires G. Pilania and R. Ramprasad Chemical, Materials & Biomolecular Engineering Institute of Materials Science University of Connecticut APS March Meeting 2012, Boston, MASession J32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Domain Structures and Switching Tuesday, February 28, 2012 http://www.ims.uconn.edu/~rampi/
  • 2. Ferroelectric Nanostructures: Applications! Information Storage Energy Storage 1 2 Emax = εEB 2 Polymer matrix!J. M. Gregg, Nature Nanotech. 3, 380 - 381 (2008) ! Ferroelectric nanoparticles!W. Lee et al. Nature Nanotech. 3, 402–407 (2008)! Kim et al. ACS Nano, 3, 2581–2592, 2009!
  • 3. Ultrathin PbTiO3 Nanowires Do Have Sharp {001} Facets! Surface Energies ! BaTiO3 nanorod! PbTiO3 nanorod! (in eV per surface cell)! Urban et al. Am. Chem. H. Deng et al., J. Mater. Chem.!R. I. Eglitis, D. Vanderbilt, PRB 76, 155439 (2007)! Soc. 2002, 124, 1186! 2009, 19, 976–982!
  • 4. Ultrathin PbTiO3 Nanowires: Model Details ! (2x2) PbO-terminated ! Nanowire! c! c! [001]! (2x2) TiO2-terminated ! Nanowire! G. Pilania and R. Ramprasad, Phys. Rev. B 82, 155442 (2010)!
  • 5. Ground State Polarization in PbTiO3 Nanowires c tetragonal Bulk Fa c! Fa Fa Fa acubic Bulkc (Å) P Fv c! P P Fa=Ferroelectric (axial)! P=Paraelectric! Fv=Ferroelectric (vortex)! (1x1)! (2x2)! (3x3)! (4x4)!
  • 6. (4x4) TiO2-terminated PbTiO3 Nanowire: " A vortex ground state Ti O(3) O(2)Pb O(1)
  • 7. Effect of axial strain! G. Pilania and R. Ramprasad, Phys. Rev. B 82, 155442 (2010)!
  • 8. Effect of axial strain
  • 9. Effect of axial strainPbTiO3 nanowires display switchable rectilinear (axial)and non-rectilinear (vortex) polarization configurations!
  • 10. Dielectric Permittivity" PbTiO3 Nanowires !(4x4) TiO2-terminated ! (4x4) PbO-terminated ! Nanowire! Nanowire! Vacuum + Nanowire Composite G. Pilania and R. Ramprasad, J. Materials Science 2012 (Special issue: Recent Advances in First Principles Computations in Materials Research )
  • 11. A hybrid approach:" DFPT + Effective Medium Theory! α cell = ηV α wire ε ii − 1 α= Polarizability !∝ 1+ (ε ii − 1)Pi AcellVcell 1 Awire Vwire Pz = 0 Px,y = 2 Axial Off-axis ⎛ ε ii − 1 ⎞ ⎛ ε ii − 1 ⎞ wire (ε ii − 1) = ηV (ε − 1) ⎜ ε + 1 ⎟ = ηV ⎜ ε wire 1 ⎟ wire ii ⎝ ii ⎠ ⎝ ii + ⎠
  • 12. DFPT + Effective Medium Theory ηV ηV Vary volume fraction occupied by wire in the supercell by changing size of the supercell!
  • 13. Planar-averaged screening charge density
  • 14. Dielectric Permittivity PbTiO3 Nanowires System! Optical! Static! "∞xx/yy! "∞zz! "0xx/yy! "0zz! Bulk (cubic)! 8.85 (8.70)1! 8.85 (8.70) 1! 23.26! 23.26! Bulk (Tetragonal)! 8.00 (7.27) 2! 7.47 (7.20) 2! 170.9 (125) 3! 33.73 (30.4) 3! Nanowires! ! ! ! ! ! (4x4) PbO-terminated 6.29! 28.92! 10.73! 58.77! rectilinear polarization! ! ! ! ! ! (4x4) TiO2-terminated 5.60! 27.16! 12.98! 80.29! vortex polarization!1. PRB 26, 2707, 1982 2. APL 20, 135, 1972) 3. Helv. Phys. Acta 49, 1, 1976
  • 15. Summary!Polarization States in PbTiO3 Nanowires u  Ultra-thin PbTiO3 nanowires display switchable rectilinear (axial) and non- rectilinear (vortex) polarization configurations.! u  PbO-termination and axial tensile strain favor axial polarization state.! u  TiO2-termination and axial compressive strain favor axial polarization state.!Dielectric Permittivity of PbTiO3 Nanowires u  Static and optical dielectric permittivity along the axial direction gets enhanced significantly.! u  Permittivity along the off-axis directions is reduced, owing to the depolarizing field.! u  Nanowires with exotic vortex polarization states are expected to have a larger dielectric permittivity.!