Cubic Perovskite

Distortions ocuring in perovskites: • Tilting of the octahedra • Cation displacements • Jahn-Teller distortions

Electronic, magnetic and dielectric properties depend on the details of such distortions

Ferroelectric ABO3 oxides PbTiO3

Pb

Ti

O

Ferroelectric materials exhibit electric dipole in the absence of electric field

Cubic Paraelectric Phase

Tetragonal Ferroelectric Phase

PS

PS

E

E

C. Lichtensteiger et al., Phys. Rev. Lett. 94, 047603 (2005)

Reduction of polarization for film thicknesses < 20 nm

Indirect measurement of polarization

Reduction of tetragonality

94 96 98 100 102 104 1062Theta/Omega (°)

100

1K

unts/s

6.96 nm 12.89 nm 16.06 nm 25.30 nm

PTO(004)

STO(004)

XRD Results

0 10 20 30 40 50

1.02

1.03

1.04

1.05

1.06

Tetra

gona

lity

(c/a

)

Thickness (nm)

Tetragonality of bulk PTO

• Reduce electrostatic energy by formation of domains

• Domains provide direct evidence of ferroelectricity

+ + + - - - + + + - - - + + + - - -

- - - + + + - - - + + + - - - + + +

STO

PTO

Poly-domain state Mono-domain state + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - -

STO

PTO

Direct measurement of polarization PbTiO3 on insulating STO substrate

X-ray diffraction intensities are sensitive to relative Ti and Pb positions

Pb

Ti

Basic physics for domain periodicities

20wdU

wF γ−==

∂∂

21

2

dw

Udw

∝

= γ

Under equilibrium conditions:

d

w 180o domains

Layer thickness

Domain width

wdUwF γ+=

Electrostatic energy of a free surface

Domain wall energy

General property of ferroic domains of any kind: • Ferromagnetic Kittel, 1946 • Ferroelectric Mitsui and Furuichi, 1953 • Ferroelastic Roytburd, 1976

-4200 -4100 -4000 -3900 -3800 -3700Qx*10000(rlu)

5400

5450

5500

5550

5600

5650

5700

5750

5800

5850

0000(rlu)

Omega 78.269002Theta 86.69400

Phi 0.20Psi -0.51

X 2.00Y 2.50Z 8.170

PTO_stripes_XCL_35.xrdml

0.2

0.9

2.1

3.6

5.7

8.2

11.2

14.6

18.5

22.8

27.6

32.8

38.5

44.7

51.3

58.4

65.9

73.9

82.3

91.2

100.6

Reciprocal space maps PTO(203)

-4200 -4100 -4000 -3900 -3800 -3700Qx*10000(rlu)

5400

5450

5500

5550

5600

5650

5700

5750

5800

5850

0000(rlu)

Omega 78.274002Theta 86.73000

Phi 0.61Psi -1.05

X 1.00Y 38.00Z 8.170

PTO_stripes_XCL_34.xrdml

0.3

1.0

2.3

4.1

6.4

9.2

12.6

16.4

20.8

25.6

31.0

36.9

43.3

50.2

57.7

65.6

74.1

83.1

92.5

102.5

113.1

Sample cooled in oxygen t = 12.89 nm

Sample cooled in vacuum t = 17.83 nm

STO PTO

(002)

(203)

Stripe Domain Observation at Room Temperature

~1/Λ

thickness fringes

Kα1 Kα2

H

L

Stripe domains are observed for films of 1.6 to 25nm thickness at RT

PTO (203)

A. Schilling et al., Phys. Rev. B 74, 024115 (2006) S.K. Streiffer et al., Science 304, 1650 (2004) T. Mitsui et al., Physical Review 90, 193 (1953) R. Meyer et al., submitted to Phys. Rev. B

21

dw ∝

100 101 102 103 104 105 106 107100

101

102

103

104

Dom

ain

perio

dicit

y (n

m)

Film thickness (nm)

Domains in Ferroelectrics

- lab source - synchrotron source