Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors...
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![Page 1: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera.](https://reader030.fdocuments.net/reader030/viewer/2022032704/56649d5d5503460f94a3cad0/html5/thumbnails/1.jpg)
Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors
Pablo Aguado-Puente
Javier Junquera
![Page 2: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera.](https://reader030.fdocuments.net/reader030/viewer/2022032704/56649d5d5503460f94a3cad0/html5/thumbnails/2.jpg)
Technological applications: ABO3 perovskites oxides, promising candidates for NV-FRAM
metal (SrTiO3-Nb, SrRuO3,Pt)
perovskite oxide(PZT,BST)
The use as a NV-FRAM depends on the existence of a polar ground state …
… is there a fundamental limit?
![Page 3: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera.](https://reader030.fdocuments.net/reader030/viewer/2022032704/56649d5d5503460f94a3cad0/html5/thumbnails/3.jpg)
PTO: PbTiO3
PZT: Pb(Zr,Ti)O3
BTO: BaTiO3
TGS: tryglycine sulphate
PVDF: Ferroelectric polymer
Bun
e et
al.
(PV
DF
)
Ph. Ghosez and J. Junquera, First-Principles Modeling of Ferroelectric Oxide Nanostructures,Handbook of Theoretical and Computational Nanotechnology, Vol. 9, Chap. 13, 623-728 (2006)
(http://xxx.lanl.gov/pdf/cond-mat/0605299)and references therein.
Courtesy of H. Kohlstedt
Fundamental motivation: what’s the most stable phase for epitaxial ferroelectric ultrathin films?
• Long time question.
•Hot field.
?
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PbTiO3
SrTiO3
(insulator)
d
a
PbTiO3
Nb-SrTiO3
(metal)
d
PbZr0.2Ti0.8O3
SrRuO3
SrRuO3
SrTiO3
PbTiO3
SrTiO3
(insulator)
d
D. D. Fong et al. (2004)S. K. Streiffer et al. (2002)
C. Lichtensteiger et al. (2005)A. T. J. van Helvoort et al. (2005)
D. D. Fong et al. (2005) V. Nagarajan et al. (2006)
Experimentally: small changes in boundary conditions, great changes in ground state
![Page 5: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera.](https://reader030.fdocuments.net/reader030/viewer/2022032704/56649d5d5503460f94a3cad0/html5/thumbnails/5.jpg)
Mechanical
Electrostatic
Surface
Finite conductivity
Defects(vacancies, misfit dislocations…)
Chemistry
Many effects might alter the delicate balance between long and short range forces
Experimental measures,
global result
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Mechanical
Electrostatic
Surface
Finite conductivity
Defects(vacancies, misfit dislocations…)
Chemistry
First-principles calculations allow to isolate their respective influence
![Page 7: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera.](https://reader030.fdocuments.net/reader030/viewer/2022032704/56649d5d5503460f94a3cad0/html5/thumbnails/7.jpg)
● Uniform reduction of the polarization
real electrode
real electrode
P’Ed
real electrode
real electrode
Junquera and Ghosez, (2003)Umeno et al. (2006)
Present work
Until today, monodomain studies, goal of this work: ab initio multidomain simulations
● Break down into domains
• Full first-principles simulation using
• Explicitly included electrodes.
P
bulk
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Ferroelectric layer: fundamental parameters of the simulations
Nx = domain period
FE layer: Nx repetitions in [100] direction and m cells in [001] direction
m = layer thickness
• Nx from 2 to 8 cells
• m from 2 to 4 cells
• FE layer made of BaTiO3.
• Domain wall in BaO and TiO2
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Building the cell: the paraelectric unit cell
m =
2 u
nit
cells
Sr
Ru
O
Ti
BaBaTiO3
SrRuO3
SrRuO3
SrTiO3
Short-circuit boundary conditions
Mirror symmetry plane
[100]
[001]
Nat = 40 atoms
a = aSrTiO3
• Building the reference cell following the scheme of
Junquera and Ghosez (2003).
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Nat = Nx · 40 atoms
Building the cell: replicating the paraelectric structure
• Nx repetitions in [100] direction.
• The energies of these cells as references.
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Nat = Nx · 40 atoms
Building the cell: inducing a polarization by hand
• Chosing a domain wall.
• Inducing a polarization by hand in the FE layer displacing the atoms a percentage of the bulk soft mode.
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Forces smaller than 0.01 eV/Å
No constraints impossed on the atomic positions
Relaxing all the atomic coordinates coordinates, both in the FE layer and the electrodes
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Results: multidomain phases more stable than paraelectric structure for Nx > 4
1 2 3 4 5 6 7 8 9-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Ba-wall
Ti-wall
Nx cells
(E-E
par
a)/N
x (m
eV)
2-unit-cells thick BaTiO3 layer
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Nx = 4
BaO domain walls
C. Kittel (1971)
Ferromagnetic domains
Results: multidomain phases more stable than paraelectric structure for Nx > 4
Nx = 4
BaO domain walls
1 2 3 4 5 6 7 8 9-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Ba-wall
Ti-wall
Nx cells
(E-E
par
a)/N
x (m
eV)
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Nx=4
BaO wall
TiO2 wall TiO2 wall
BaO wall
Nx=6
Results: multidomain phases more stable than paraelectric structure for Nx > 4
1 2 3 4 5 6 7 8 9-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Ba-wall
Ti-wall
Nx cells
(E-E
par
a)/N
x (m
eV)
2-unit-cells thick BaTiO3 layer
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Resulting phases show in-plane displacements and small polarization
Nx = 4
BaO domain walls Small polarization inside the domains.
-10 -5 0 5 10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
TiO2-wall distance from domain wall (Bohr)
(B
ohr)
Nx = 2bulk
capacitor
About 1/10 of bulk soft-mode polarization
Sr
Ru
O
Ti
Ba
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In-plane displacements are essential to get polarization domains
-10 -5 0 5 10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
TiO2-wall distance from domain wall (Bohr)
(B
ohr)
Nx = 2bulk
capacitor
-10 -5 0 5 10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
TiO2-wall distance from domain wall (Bohr)
(B
ohr)
Nx = 2bulk
capacitor
In-plane displacements: ON In-plane displacements: OFF
When in-plane coordinates are fixed, structure goes back to the paraelectric phase
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Changing the electrode, the ground state of PbTiO3 changes from monodomain to polydomain
Lichtensteiger, Triscone, Junquera, Ghosez.
Lichtensteiger, et al.
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Transition from vortices to standard 180º domains. 4-unit-cell thick layer, great increase in polarization
-15 -10 -5 0 5 10 15
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
TiO2-wall distance from domain wall (Bohr)
(B
ohr)
Nx = 4bulk
capacitor
Displacements 10 times bigger than in the 2-cells thick layer
m = 4, Nx = 4
TiO2 domain walls
Sr
Ru
O
Ti
Ba
(E-Epara)/Nx < -16.6 meV
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Conclusions
• The chemical interaction through the interface is an essential factor since it affects the in-plane mobility of the atoms.
• There are stable multidomain phases in ultrathin FE films.
1 2 3 4 5 6 7 8 9-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Ba-wall
Ti-wall
Nx cells
(E-E
par
a)/N
x (meV
)
• Closure domains in FE capacitors are predicted.
-10 -5 0 5 10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
TiO2-wall distance from domain wall (Bohr)
(B
ohr)
Nx = 2bulk
capacitor
Slides available at: http://personales.unican.es/junqueraj
Contact: [email protected]
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More information …
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Method: Computational details
First-principles calculations withinKohn-Sham Density Functional Theory (DFT)
Exchange-correlation functional : LDA, fit to Ceperley-Alder dataNorm conserving pseudopotentials: Ti, Sr, Ba, Ru: semicore in
valenceBasis set:
NAO: valence: Double- + Polarization ; semicore: Single-Real-space grid cutoff : 400 Ryk-point grid : equivalent to 12x12x12 for simple cubic perovskiteSupercell geometry
: Numerical Atomic Orbital DFT code.
http://www.uam.es/siesta
J. M. Soler et al., J. Phys. Condens. Matter 14, 2745 (2002)
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Very small energy differences, very accurate simulations needed
m=2, Nx = 4
BaO domain walls
Structure Total Energy (eV)
Paraelectric -138326.083054
Multidomain -138326.084463
(E-Epara)/Nx = -0.00035 eV