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