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