Designer oxides that work

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Designer oxides that work

• Karin M. Rabe
• Theory-driven search for new functional materials
• first principles methods atomic scale
  investigation of the rich phase diagrams of
  complex oxides
• closing the loop in the laboratory

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Outline

• Functional materials
• First principles methods
• New ferroelectrics via epitaxial strain
• first principles predictions experimental
  confirmation in thin films and superlattices
• Predicting novel phases of functional oxides from
  first principles future prospects

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Functional materials

• Defining characteristic
• Some useful macroscopic property has high
  sensitivity
• to an external perturbation (e.g. applied field
  or stress)
• For example, electric polarization P has high
  sensitivity
• to applied electric field E

Electric dipole moment per volume (electrical
analog of magnetization)
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electric polarization P is controlled by applied
electric field E Dielectrics P ? E (small E)
e(E) with nonlinear P(E) Ferroelectrics P ? 0
in zero E Switchable to another orientation by
applied E Piezoelectricity in
ferroelectrics Polarization-strain
coupling Elastic deformation induced by applied E
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• Electric-field-controlled functional materials
  applications
• Electric-field-tunable dielectrics for microwave
  applications
• Piezoelectric actuators/sensors
• ultra-precise motion control systems
• SONAR
• medical ultrasound
• energy harvesters
• Ferroelectrics
• Nonvolatile information storage FeRAM
• Programmable electronics FeFETs
• New materials higher performance/new regimes
• Novel functionality ? novel devices multiferroics

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Origin of macroscopic polarization at the
microscopic (atomic) leveldirectly linked to
the crystal structure

• Polarization of an ionic insulator is produced by
  relative displacement of positively charged
  cations and negatively charged anions
• Displacement in response to applied field
  dielectrics
• Displacement in absence of applied field
  ferroelectrics

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Simple ionic insulator NaCl
electron
Cl1-
Na1
simple, symmetric structure Preferred
cation-anion spacing a0 can be adjusted so that
all spacings have ideal value
not a functional material
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More complexity Perovskite oxides ABO3
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Perovskite oxides ABO3
Preferred AO and BO spacings a0 CANNOT be
adjusted so that all spacings have ideal value ?
frustrated, prone to distortion Too-small
rattling B ? unstable to uniform
displacement polarization Ps ferroelectric induce
d strain piezoelectric
A
a0
up
down
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Outline

• Functional materials
• High sensitivity to external perturbations
• Ferroelectrics and piezoelectrics
• Macroscopic microscopic why complex oxides?
• First principles methods
• New ferroelectrics via epitaxial strain
• first principles predictions experimental
  confirmation in thin films and superlattices
• Predicting novel phases of perovskites from first
  principles future prospects

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Solid as a physical system of interacting
electrons and nuclei fully described by the
theory of quantum mechanics
The underlying physical laws necessary for the
mathematical theory of a large part of physics
and the whole of chemistry are thus completely
known Proceedings of the Royal Society of
London. Series A, Vol. 123, No. 792 (Apr. 6,
1929)
P.A.M. Dirac in 1934
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Solid as a physical system of interacting
electrons and nuclei fully described by the
theory of quantum mechanics
The underlying physical laws necessary for the
mathematical theory of a large part of physics
and the whole of chemistry are thus completely
known, and the difficulty is only that the exact
application of these laws leads to equations much
too complicated to be soluble. It therefore
becomes desirable that approximate practical
methods of applying quantum mechanics should be
developed, which can lead to an explanation of
the main features of complex atomic systems
without too much computation. Proceedings of the
Royal Society of London. Series A, Vol. 123, No.
792 (Apr. 6, 1929)
P.A.M. Dirac in 1934
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How to predict equilibrium atomic positions in a
molecule or crystal? Total energy of nuclei and
electrons within adiabatic approximation
electrons in ground state corresponding to fixed
nuclei
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Introduction to first principles methods
Example diatomic molecule
E
electrons in ground state for nuclei fixed at
separation R
R
rectangular space group pm compute energy wrt
a, c, u and minimize to predict structural
parameters
Example simple crystal with 2 atoms/unit cell
c
optic phonon
u
a
u
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Starting structure Positions and atomic s
Formalism approximations algorithms
software
Hardware cycles/memory
Energy and forces (first derivatives of energy)
Optimized structural parameters
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Softwarehomespun
Formalism density functional theory (local
density approx) pseudopotentials Direct matrix
diagonalization
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Softwarehomespun
Formalism density functional theory (local
density approx) pseudopotentials Direct matrix
diagonalization
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If I had to choose between the algorithms of
1980 and the computers of today, and the
computers of 1980 and the algorithms of today, I
would choose the latter Jim Chelikowsky, U
Texas Austin March meeting symposium 2005
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first principles calculations after 25 years
Formalism density functional theory
extensions (new functionals, LSDAU and
DMFT) pseudopotentials, PAW Car-Parinello
molecular dynamics Density functional
perturbation theory Modern theory of polarization
Software VASP, ABINIT, PWscf, SIESTA,
Optimized structure Energy and forces higher
derivatives of energy (response
functions) Polarization, magnetic
ordering Optical and transport properties
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first principles calculations after 25 years
Formalism density functional theory
extensions (new functionals, LSDAU and
DMFT) pseudopotentials, PAW Car-Parinello
molecular dynamics Density functional
perturbation theory Modern theory of polarization
Software VASP, ABINIT, PWscf, SIESTA,
Hardware Cray XT5, IBM Blue Gene/P gt 1
PFLOPS RUPC (Rutgers U Parallel Computer) ? 1.5
TFLOPS
Wide range of material systems, including complex
oxides
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First-principles results (circa 1995)
SrTiO3 and BaTiO3 ideal cubic
ferroelectric tetragonal 5-atom cell a, c, zTi,
zA, zO SrTiO3 cubic structure stable a
3.863 A (3.905 A)
c
a
BaTiO3 atoms displace from ideal
positions calculated Ps 0.25 C/m2 (0.26
C/m2) a 3.945 A (3.992 A) tetragonal strain c/a
1.011 (1.011)
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Tremendous advances in complex oxide synthesis
characterization atomic scale control
(LaTiO3)1(SrTiO3)n
Ohtomo, Muller, Grazul, Hwang, (2002)
(PbTiO3)3(SrTiO3)3
Dawber, Lichtensteiger, Cantoni, Veithen,
Ghosez, Johnston, Rabe, Triscone (2005)
(BaTiO3)n(SrTiO3)m(CaTiO3)k
Lee, Christen, Chisholm, Rouleau Lowndes (2005)
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First principles and experiments
quantitative first principles calculations for
superlattices and nanocheckerboards, thin films
with subtrate interfaces free
surfaces Intrinsic properties of ideal
structures Atomic-scale information complementary
to expt Predictiveidentify systems for exptl
study Rewarding experimental-theoretical
dialogue
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Joint theoretical-experimental search for new
functional oxides
First principles at Rutgers Jun Hee Lee,
postdoc Carl-Johan Eklund, student Lucia Palova,
student Craig Fennie, now at Cornell Jeff
Neaton, now at LBNL David Vanderbilt
Support from ONR, NSF-NIRT/MRSEC (Penn
State), Intel, and ARO-MURI (Caltech)
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Joint experimental-theoretical search for new
functional oxides
Experimental collaborators Charles Ahn, Yale
Matt Dawber, SUNY Stony Brook Ho-Nyung Lee,
ORNL R. Ramesh, Berkeley Darrell Schlom,
Cornell Jim Scott, U. Cambridge Ichiro Takeuchi,
U. Maryland Venkat Gopalan, Penn State
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Outline

• Functional materials
• First principles methods
• Methods hardware ? realistic complex oxides
• Experimental-theoretical dialogue
• New ferroelectrics via epitaxial strain
• first principles predictions experimental
  confirmation in thin films and superlattices
• Predicting novel phases of perovskites from first
  principles future prospects

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Compressive epitaxial strain on (001) square
substrate
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Compressive epitaxial strain on (001) square
substrate
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Compressive epitaxial strain on (001) square
substrate
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Compressive epitaxial strain on (001) square
substrate
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Compressive epitaxial strain on (001) square
substrate
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Compressive epitaxial strain on (001) square
substrate
Isolate effect of epitaxial stain by imposing
epitaxial strain constraints on lattice
parameters in infinite bulk strained bulk
calculation
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First-principles results
SrTiO3 and BaTiO3 ideal cubic
ferroelectric tetragonal 5-atom cell a, c, zTi,
zA, zO SrTiO3 cubic structure stable
energy
c
a
displacement
BaTiO3 atoms displace from ideal positions
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Energy landscape from first principles
Construct matrix of 2nd derivatives ?2E
?uia?ujb 5x315 dimensional lots of
symmetry SrTiO3 cubic structure stable all
eigenvalues nonnegative
c
a
BaTiO3 cubic structure unstable one 3-fold
degenerate negative eigenvalue polar distortion
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Strain couples strongly to the lowest polar
mode polarization-strain coupling (Cohen,
1992) in ferroelectrics ? piezoelectricity in
paraelectric ? epitaxial-strain-induced
ferrroelectricity
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Epitaxial strain-induced ferroelectricity in
SrTiO3
z
w2
Paraelectric ground state
0
x,y
c
p
aa
compressive
tensile
Landau theory Pertsev, PRL 2000 First
principles Antons, Neaton, Rabe Vanderbilt 2004
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Experimental observation of strain-induced
ferroelectricity in SrTiO3 epitaxial thin films
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Epitaxial-strain-induced ferroelectricity in
superlattices
BT8/ST4 on DyScO3, GdScO3, NdScO3, SmScO3,
SrTiO3 Tenne, Eom, Schlom et al unpublished
BT/ST on ST orthorhombic relaxed about
1 Jiang, Rios and Scott 2003, 2004 Johnston,
Huang, Neaton, Rabe, 2005
SrTiO3
BaTiO3
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q p/a(111) qp/a(110) oxygen octahedron
rotations
q 0 polar
Classification of distorted perovskite
structures Low symmetry structures generated by
freezing in an unstable mode or coupled group of
modes
See table in Stokes, 1994
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negative ? double well for corresponding
distortion

• Instabilities at q?0 do not contribute to bulk
  phase
• coupling to polar mode suppresses them in FE
  phases
• q?0 alternative phases freeze in one or more
  modes
• low energy, but in this case not lowest

from Ghosez, Waghmare, Cockayne Rabe, PRB 1999
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Epitaxial-strain-induced ferroelectricity in
CaTiO3
(C.J. Eklund, C. J. Fennie KMR, PRB 2009)
Paraelectric orthorhombic structure Octahedral
rotations and tilts
(Cockayne Burton, PRB 2000)
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Epitaxial-strain-induced ferroelectricity in
CaTiO3
(C.J. Eklund, C. J. Fennie KMR, PRB 2009)
Paraelectric orthorhombic structure generated by
R110 and M001
(Cockayne Burton, PRB 2000)
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Epitaxial Pnma CaTiO3
Rotations two epitaxial orientations Str
ain changes polar mode, rotations, polar mode
couples to rotations as well
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(001) epitaxial strain Ferroelectric for tensile
strain above 2 No strain-induced
ferroelectricity in compressive strain
R110 and M001 G110 P 0.45 mC/cm2
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Epitaxial strain induced ferroelectricity in
CaTiO3 experiment
Charles Brooks, Effie Vlahos, Darrell Schlom,
Venkat Gopalan
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Ferromagnetic ferroelectric multiferroic Magn
etism a new level of functionality multiple
functionality electric, magnetic
H
E
M
P
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• Ferromagnetic ferroelectric multiferroic
• Magnetism a new level of functionality
• multiple functionality electric, magnetic
• novel functionality electromagnetic coupling
• Control magnetization with electric field
• Control polarization with magnetic field

H
E
M
P
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Epitaxial-strain-induced multiferroicity
Spin phonon coupling mechanism in PE/AFM
EuTiO3 Fennie Rabe, PRL 97, 267602 (2006)
Polar phonon in FM is lower frequency than AFM
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SHG of Strained EuTiO3 / (110) DyScO3
Venkat GopalanPenn State University
Magneto-optical Kerr Effect measurements
Ezekiel Johnston-HalperinOhio State University
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Outline

• Functional materials
• First principles methods
• Methods hardware ? realistic complex oxides
• Experimental-theoretical dialogue
• New ferroelectrics via epitaxial strain
• first principles predictions experimental
  confirmation in thin films and superlattices
• SrTiO3, CaTiO3, and multiferroicity in EuTiO3
• Predicting novel phases of perovskites from first
  principles future prospects

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SrMnO3
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Spin phonon coupling at G in SrMnO3
Observed structure cubic G-AFM, TN260K
VASP, LSDAU, frozen phonon
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Spin phonon coupling at G in SrMnO3
Observed structure cubic G-AFM, TN260K
VASP, LSDAU, frozen phonon EFM-EAFM 80 meV/f.u.
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Polar distortions in SrMnO3
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Polar distortions in SrMnO3
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Epitaxial SrMnO3 phase diagram
PE/G-AFM FE/G-AFM FE/C-AFM FE/A-AFM --
FE/FM
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Outline/summary

• Functional materials
• High sensitivity to external perturbations
• Ferroelectrics and piezoelectrics
• Macroscopic microscopic why complex oxides?
• First principles methods
• Methods hardware ? realistic complex oxides
• Experimental-theoretical dialogue
• New ferroelectrics via epitaxial strain
• first principles predictions experimental
  confirmation
• in thin films and superlattices
• SrTiO3, CaTiO3, and multiferroicity in EuTiO3
• Predicting novel phases of perovskites from first
  principles future prospects
• material surveys
• SrMnO3

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A few last comments
Advances in techniquehardware Accurate
calculations for complex structures Results
complement experiments Conceptual framework
based on first principles results Challenges sol
id solutions A1-xAxBO3 real materials
defects, microstructure Better simulations /
better physical understanding
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With ABINIT Lebedev, Phys. Sol. State
2009 Ground state I4/mcm (R25)
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Overview/big picture

• Functional materials
• fundamental science and technological
  applications
• complex oxides
• enormous progress in synthesis, characterization
  theory
• complexity is key to desirable functional
  properties
• high sensitivity to fields stresses
• instabilities and competing low-energy states
• phase transitions to novel non-bulk phases
• First principles

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Outline

• Functional materials
• Ferroelectrics piezoelectrics why complex
  oxides?
• First principles methods
• How we compute and what we learn
• New ferroelectrics via epitaxial strain
• first principles predictions experimental
  confirmation in thin films and superlattices
• Predicting novel phases of functional oxides from
  first principles future prospects

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