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, MA
Session 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 Bulk
c (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 strain
PbTiO3 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
Acell
Vcell
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.!