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

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

http://www.ims.uconn.edu/~rampi/

APS March Meeting 2012, Boston, MA

Session J32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Domain Structures and Switching

Tuesday, February 28, 2012

Ferroelectric Nanostructures: Applications!Information Storage

W. Lee et al. Nature Nanotech. 3, 402–407 (2008)!

J. M. Gregg, Nature Nanotech. 3, 380 - 381 (2008) !

Emax =12εE2

B

Energy Storage

Kim et al. ACS Nano, 3, 2581–2592, 2009!

Ferroelectric nanoparticles!

Polymer matrix!

R. I. Eglitis, D. Vanderbilt, PRB 76, 155439 (2007)!

Surface Energies !(in eV per surface cell)!

BaTiO3 nanorod!

Urban et al. Am. Chem. Soc. 2002, 124, 1186!

PbTiO3 nanorod!

H. Deng et al., J. Mater. Chem.! 2009, 19, 976–982!

Ultrathin PbTiO3 Nanowires Do Have Sharp {001} Facets!

G. Pilania and R. Ramprasad, Phys. Rev. B 82, 155442 (2010)!

c!

(2x2) PbO-terminated !Nanowire!

(2x2) TiO2-terminated !Nanowire!

c!

Ultrathin PbTiO3 Nanowires: Model Details!

[001]!

Ground State Polarization in PbTiO3 Nanowires

c tetragonal Bulk

acubic Bulk c (Å)

Fa

Fa

Fa Fa

Fv

P

P

P

(1x1)! (2x2)! (3x3)! (4x4)!

Fa=Ferroelectric (axial)!P=Paraelectric!Fv=Ferroelectric (vortex)!

c!

c!

(4x4) TiO2-terminated PbTiO3 Nanowire: "A vortex ground state

Pb O(1)

O(2) O(3) Ti

Effect of axial strain!

G. Pilania and R. Ramprasad, Phys. Rev. B 82, 155442 (2010)!

Effect of axial strain

Effect of axial strain PbTiO3 nanowires display switchable rectilinear (axial) and non-rectilinear (vortex) polarization configurations!

Dielectric Permittivity "PbTiO3 Nanowires!

Vacuum + Nanowire Composite

G. Pilania and R. Ramprasad, J. Materials Science 2012 (Special issue: Recent Advances in First Principles Computations in Materials Research )

(4x4) PbO-terminated !Nanowire!

(4x4) TiO2-terminated !Nanowire!

A hybrid approach:"DFPT + Effective Medium Theory!

Acell

Awire

VcellVwire

∝ ε ii −11+ (ε ii −1)Pi

Polarizability !α =

α cell =ηVαwire

Px,y =12

Pz = 0

ε ii −1ε ii +1

⎛⎝⎜

⎞⎠⎟=ηV

ε wireii −1

ε wireii +1

⎛⎝⎜

⎞⎠⎟

Off-axis

(ε ii −1) =ηV (εwireii −1)

Axial

DFPT + Effective Medium Theory

Vary volume fraction occupied by wire in the supercell by changing size of the supercell!

ηVηV

Planar-averaged screening charge density

Dielectric Permittivity PbTiO3 Nanowires System! Optical! Static!

ε∞xx/yy! ε∞zz! ε0xx/yy! ε0

zz!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

rectilinear polarization!

!6.29!

!28.92!

!10.73!

!58.77!

!(4x4) TiO2-terminated

vortex polarization!

!5.60!

!27.16!

!12.98!

!80.29!

1. PRB 26, 2707, 1982 2. APL 20, 135, 1972) 3. Helv. Phys. Acta 49, 1, 1976

Summary!Polarization States in PbTiO3 Nanowires

Dielectric Permittivity of 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.!

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.!