full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors...

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Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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Page 1: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

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

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.

?

Page 4: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

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

Page 6: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

● 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

Page 8: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 9: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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).

Page 10: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

Nat = Nx · 40 atoms

Building the cell: replicating the paraelectric structure

• Nx repetitions in [100] direction.

• The energies of these cells as references.

Page 11: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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.

Page 12: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 13: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 14: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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)

Page 15: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 16: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 17: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 18: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

Changing the electrode, the ground state of PbTiO3 changes from monodomain to polydomain

Lichtensteiger, Triscone, Junquera, Ghosez.

Lichtensteiger, et al.

Page 19: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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

Page 20: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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]

[email protected]

Page 21: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

More information …

Page 22: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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)

Page 23: Full first-principles simulations on 180º stripe domains in realistic ferroelectric capacitors Pablo Aguado-Puente Javier Junquera

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