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Oxide Interfaces: Perspectives & New Physics
Sashi Satpathy
University of Missouri,
Columbia
Seminar, University of Illinois
September 24, 2007
Funding: DOE, AFOSR, PRF, MURB, DFGFunding: DOE, AFOSR, PRF, MURB, DFG
http://www.missouri.edu/~satpathys
““One should not work with semiconductors, that is a filthyOne should not work with semiconductors, that is a filthy mess; who knows if they really exist. mess; who knows if they really exist.”” ---- ---- Pauli Pauli 19311931
History of semiconductor physics
A picture of the first transistor ever assembled, invented in Bell Labs in 1947. Itwas called a point contact transistor because amplification or transistor action occurredwhen two pointed metal contacts were pressed onto the surface of the semiconductormaterial. The contacts, which are supported by a wedge shaped piece of insulatingmaterial, are placed extremely close together so that they are separated by only a fewthousandths of an inch. The contacts are made of gold and the semiconductor isgermanium. The semiconductor rests on a metal base.
First Semiconductor Transistor (1947)
Bardeen, Brattain, and ShockleyBell Labs (1947)
High Quality Oxide Interfaces
High-resolution scanning electron microscopyimage of a lattice-matched SrTiO3/LaTiO3superlattice, grown with pulsed laser deposition.
Ref: Ohtomo et al., Nature 419, 378 (2002)
LaTiO3SrTiO3Examples of systems:
• SrTiO3/LaTiO3 (interfacial 2DEG)
• LaMnO3/SrMnO3 (spin-polarized 2DEG?)
• CaRuO3/CaMnO3 (metal in contact with anantiferromagnet)
• SrTiO3/LaAlO3 (polar heterostructure)
• SrTiO3/LaVO3 (polar heterostructure)
• FM/SC interfaces, etc.
Epitaxial Oxides Credit: Christen, Oak RidgeNational Lab, 12/2006
Theoretical Methods
Density-Functional Theory
Local Density Approximation (LDA, LSDA)
Generalized Gradient approximation (GGA)
LDA/GGA + Hubbard U
Models: Hartree-Fock, Dynamical mean fieldtheory (DMFT)
More accurate methods: exact diagonalization,Quantum Monte Carlo (Limited to small systems)
Electronic structure of solids: Interacting many-body problem
Density-functional Theory
• Key point (Kohn, Sham, Hohenberg, 1965): The ground-state energy of theinteracting electrons can be found by solving a one-particle Schrödingerequation with an effective potential:
Solution of the “mean-field” one-particle equations
• LMTO (Linear muffin-tin orbitals method)– {most physical, computationally fast}
• LAPW (Linear augmented plane waves)– {most accurate}
• Pseudopotential plane waves method– {easiest to formulate}
H =h2
2m2
+Veff (x,y,z)
H i = i i
Different religions, same God.
I. The LaTiO3/SrTiO3 Interface: 2D Electron Gas
Ohtomo et al., Nature 419, 378 (2002)
SrTiO3LaTiO3
Superconducting interface between insulating oxides: 2DEG
Ref: Reyren et al., Science 317, 1196 (2007)
Quantum Hall effect in the 2DEG at the oxide interfaces
Ref: Tsukazaki et al., Science 315, 1388 (2007)
Bulk electronic structure of SrTiO3 and LaTiO3
Ref: Tokura et al, PRL 70, 2126 (1993)
FIG: Resistivity data indicating theMetal-Insulator transition as asmall number of holes are dopedvia Sr substitution
LaTiO3: Mott insulator - Occupied Ti(d1) -
Half-filled Hubbard band - antiferromagnetic insulator
SrTiO3: Band insulator - Empty Ti(d0) band
LaxSr1-xTiO3LaxSr1-xTiO3
The LaTiO3/SrTiO3 Interface: 2D Electron Gas
LaTiO3SrTiO3
• Electronic Structure Calculations• Density-Functional Theory• Methods: LMTO, LAPW
Zoran Popovic Paul Larson
SrTiO3/(LaTiO3)1/SrTiO3: Basic result from DFT
Popovic and Satpathy, PRL 94, 176805 (2005)
The V-shaped potential and theelectron density profile near theinterface from DFT
2DEG
Electron density profile from EELS
Theory
Experiment
Ti(+3)
One layer of LaTiO3
Two layers
Ref: Ohtomo et al., Nature 419, 378 (2002)
Electron confinement at the interface: No lattice relaxation
Electron charge-densitycontours
2DEG
Effect of lattice relaxation
Ti and O atoms relax to generate a dipolemoment that screens the interface electric field
SrTiO3Single LaTiO3Interfacelayer
Ti(+)O(-)
+
+
+
+
+LaO (Positivelycharged plane)
TiO2 TiO2TiO2SrO SrO SrO
LAPW results: Larson et al, unpublished
Lattice Relaxation screens the electric field
unrelaxed
relaxed
Screening in solids: Electronic + lattice
SrTiO3 is close to a ferroelectrictransition, with very large dielectricconstant.
DFT: Static dielectric constant ~ 23 (electrons only) unrelaxed
~ 70 (electrons + lattice) relaxed
The 2DEG at the interface
30 Å
Interface Subbands
FIG: Electric fields calculated from DFT
GaN/AlxGa1-xN Interface: Highest-density 2DEG in thesemiconductor system
2DEG at the GaN/AlxGa1-xN Interface (Expt vs. Theory)
Al concentration x
~ 1012 cm-2 (semiconductor
interface)
~ 1 x 1013 cm-2 (GaN/AlGaN)
~ 3 x 1014 cm-2 (LaTiO3/SrTiO3 interface)
Density of the 2DEG
SS, Popovic, Mitchel, JAP 95, 5597 (2004)
Schematics of the 2DEG formed at the oxideinterface. The charged La atom forms a positivesheet charge, localizing a 2DEG in its neighborhood.
Jellium model for the 2DEG at the Oxide Interface
Ref: Thulasi, Ph. D. thesis (MU, 2006); Thulasi and Satpathy, PRB (2006)
Sunita Thulasi
V-shaped external potential:
Problem: Study the ground-state properties usingHartree-Fock and DFT methods.
Two-Dimensional Airy electron gas
in the jellium model
H = Hke + Hee + Hext + Heb =h2
2m* i2
i
+e2
2| zi |+Hee
i=1
N
h2
2m
d2
dz2+V (z) = , V (z) = F | z |
|F > = ar k n
+ | vac >r k n
occ
EHF = < F |H |F >
One-particle states are the Airyfunctions in the V-shaped potential well
Hartree-Fock:
| k n >=1
Aei
r k .
r r ||
n (z)
DFT Calculation of the 2DEG
Use von Barth-Hedin expressionfor Vxc and solve self-consistently
Ground-state Energy
Potential and electron density
Kohn-Sham equations
Calculated density profile of the 2DEG, compared to the EELS data.Expt: Ohtomo et al., Nature (2002)
Spatial extent of the 2DEG: Jellium model vs. Expt
(Jellium DFT)
CaRuO3
M ~ 0.85 μBper interfaceatom
Mag
neti
zati
on p
erin
terf
ace
atom
(μ
B)
AFM insulator
Para metal
CaMnO3
II. CaRuO3/CaMnO3: A metal-on-magnetic insulator interface
Ref: Tokura et al. (2006), Takahashi (2001)
Q. Is the suppressed magnetic moment due to the formation ofmagnetic domains or something more interesting might be going on atthe interface?
FerroMagnetism exists atInterface Only
CaMnO3/CaRuO3 Interface
Q. What is the origin of thesuppressed magnetization at theinterface?
Q. Can we control the interfacemagnetism by controlling the leakedmetallic electrons?
Expt: K. S. Takahashi, M. Kawasaki, and Y.Tokura, Appl. Phys. Lett. 79, 1324 (2001)
Ranjit Nanda
V (z) ={1 exp[ (z z0)]} /[2 (z z0)], z > z0U0 /{Aexp[ B(z0 z)]+1}, z < z0
Exponential leakage of electron gas similar to a Jellium surface Potential is similar to that of metal-vacuum interface
W surface: Jones, Jennings, and Jepsen, PRB (1984)
Lang and Kohn, PRB (1970)
Potential barrier and charge leakage at the interface
DFT Results
Charge leakage from the metallic to the insulator side
Lang and Kohn, PRB (1970)
Interface Dipole moment Exponential leakage of electron gas similar to a
Jellium surface
Energetics (LSDA results)
AFM FM FM-II
Minimum energy structure
DFT Results: Electron distribution at the interface
interface
Leaked electrons
Mn (d) electron states in the solid
Mn (d)
t 2g
eg
itinerant
electron
Magnetic Interactions: Superexchange and Double Exchange
• Superexchanget
U
Mn core
spins
Hopping allowed
t 2g
eg
Mn
t 2g
eg
Mn
t 2g
eg
Mn
t 2g
eg
Mn
Hopping forbidden
• Double Exchange (Anderson, Hasegawa, Zener, De Gennes, 1950s)
Xt
Canting angle of the Mn core spins
Simple model: Anderson-Hasegawa (1950) =>
Canting does survive in a lattice andalso Coulomb does not kill the canting
Results of exact diagonalization
Ref: Mishra, SS, Gunnarsson, PRB 55, 2725 (1997)
Two-site model: Anderson-Hasegawa (1950) ==>
Buridan’s ass is the common name for the thought experiment which
states that an entirely rational ass, placed exactly in the middle between
two stacks of hay of equal size and quality, will starve since it cannot
make any rational decision to start eating one rather than the other.
=)()(
)()(
kk
kkH
k
(k) = 2t sin( /2) f (k)
(k) = 2t cos( /2) f (k)
f (k) = cos kxa + cos kya
Q. How are the competing interactions accommodated at the interface layer?Ans: A spin-canted state forms.
A single MnO2 plane at theinterface
Compute canting angle byminimizing total energy:t2g
eg
No. of electrons in eg level = x
• First layer: electron concentration x ~ 0.1=> canted state
• Second layer: x ~ 0.01=> AFM state remains unchanged
Expt: Mag. Mom. at theinterface is 0.85 B=> 1150 canting
Canted State in the interfacial CaMnO3 layer
FIG: Dependence of canting onelectron concentration (x) in the layer
AFM
FM
canted
Conclusion: Canted antiferromagnet at the interface.
Nanda, SS, Springborg,PRL (2007)
III. Spin polarized 2DEG: The LaMnO3/SrMnO3 system
Potential V(z) seen by electrons near the interface
Spin-up
Spin-down
Spin-polarized 2DEG
Control of interface magnetism by strain
Double exchange ~ t (Ferro)Superexchange ~ -t2/U (Anti-ferro)
t
Mag
neti
c ex
chan
ge a
cros
s th
e in
terf
ace
Bhattacharya/ Ecksteinstructure grown on SrTiO3
Expt: Yamada, APL 89, 052506 (2006)
strain
tensilecompressive
IV. Polar Interfaces
Coulomb divergence (Harrison 1978)
Ge GaAs
-+
Coulomb divergence solved by atomic diffusion at theinterface. But does that really happen or do we have“electronic reconsruction”?
LaAlO3/SrTiO3
2DEG
2DHG
Thiel et al, Science (2006)
Q. What is the origin of the 2DEG at theinterface? (polarity issues)
Q. How much of the effect is intrinsic to theinterface and how much is extrinsic, such asoxygen vacancy?
Q. Why is 2DEG metallic, while 2DHG is insulating?
Q. Is the 2DEG any different from that in thesemiconductor interfaces? (correlated system)
Eckstein, Nat. Mater. July 2007
Reyren et al., Science317, 1196 (2007)
Superconducting2DEG
Conclusion
• New class of perovskite oxide interfaces -- New physics of 2DEG?
• Examples:
• SrTiO3/LaTiO3/SrTiO3 (High density 2DEG at interface)
• CaMnO3/CaRuO3 (Interfacial magnetism controlled by leaked
electrons)
• LaMnO3/SrMnO3/LaMnO3 (spin polarized 2DEG --new system
ever? )
• LaAlO3/SrTiO3 (how does polarity affect interface states)
• Rapid progress in growth of high-quality, lattice-matched oxide
interfaces is poised to bring in a new era
• Potential for new physics and new device applications
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