Download Lecture I - Columbia Physics

Oxide Interfaces and Heterostructures
A. J. Millis
Department of Physics, Columbia University
Visiting Professor, Ecole Polytechnique
Course made possible by
Columbia-Sorbonne-Science Po-Ecole Polytechnique Alliance
Copyright A. J. Millis 2012
Columbia University
L’Ecole Polytechnique
Acknowledgements
*Satoshi Okamoto*
Chungwei Lin
MJ Han
Hung The Dang
Se Young Park
Hyowon Park
Chris Marianetti
Funding:
US-DOE-BES-ER046169
US-ARO -56032-PH
Copyright A. J. Millis 2012
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L’Ecole Polytechnique
Course schedule
Meetings: Wednesday 1:30-3:20 lecture
3:20-3:45 pause-cafe
3:45-5:00 seminar
1. March 21: Introduction
Seminar: J. Leseur (ESPCI) *seminar starts at 15:30*
2. April 4: Interfaces; magnetism and superconductivity
Seminar: M. Gabay (Orsay)
3. April 11: Quantum Wells and the metal-insulator transition
Seminar: M. Gibert (Geneve)
4. April 18: Nonequilibrium properties and (potential) devices
Seminar: M. Bibes (Thales)
Copyright A. J. Millis 2012
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Oxide Interfaces Web Site
(under construction)
http://www.phys.columbia.edu/~millis/oxideinterfaces.html
Lecture slides
Bibliography (and some downloadable articles)
Links to major research groups
Copyright A. J. Millis 2012
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Modified Schedule
March 21, only
1:30-3:00 Lecture
3:00-3:30 Pause-Cafe
3:30-4:30 Seminar, J. Leseur
Copyright A. J. Millis 2012
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March 21: Introduction
1. Motivation
2. Electronic structure of transition metal oxides
3. Modalities of control: comparison to
semiconductors
4. Synthesis and characterization
5. Systems now being studied
6. (Time permitting): more detailed look at theory
Copyright A. J. Millis 2012
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Motivation
Copyright A. J. Millis 2012
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The first step: (LaTiO3)n(SrTiO3)m
LaTiO3: Ti d1 ‘Mott’ insulator
SrTiO3: Ti d0 `Band’ insulator
Combination of materials
with different (and nontrivial)
electronic properties.
A. Ohtomo, D. A. Muller, J. L. Grazul
and H. Hwang, Nature 419 378 (2002)
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Interesting because transition metal
oxides do interesting things
Manganite
Ruthenate
Organic
Cuprate
In bulk form, materials not easy to control
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Particular case: high temperature
superconductors e.g. YBa2Cu3O7
Wu et. al. PRL 58 908 (1987)
Image from www.tkk.fi/
Copyright A. J. Millis 2012
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Modern electronics
<=>
thin-film semiconductor devices
control (gate voltage) changes
property (conductance)
`Knob’: charge density
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Simple scalar property (carrier density)
is controllable over wide ranges by
tuning parameter (gate voltage)
Basis for control
Physics:
•Poisson equation
•single-particle quantum mechanics
Materials Science
•Monatomic/diatomic
Modulation doped FET
from S. Smirnov thesis, TU Wein
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materials (Si, GaAs)
•traps, defects and surfaces
understood
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(Electronically) correlated oxides
Manganite
High Tc
Mott Transition
Ruthenate
• Many electronic phases: more ‘knobs’ than
just voltage; more responses than just density
• many electronic behaviors: more (potential)
functionalities than just “current on or off”
• =>?wide range of new devices
• =>?wide range of new possibilities for
creating/studying new many-body effects
• =>`materials by design’ challenge to
predictive many-body theory
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Semiconductors: beautiful but boring
Exquisite control over materials
Physics (mostly) well understood
Oxides: interesting but ugly
Materials hard to control
Physics very challenging
Idea: marry control available in
semiconductor devices to the rich
physics of correlated materials
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The Stuart Parkin question:
What do I have to grow to
get a room temperature
superconductor??
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the ‘George Bernard Shaw question’
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the ‘George Bernard Shaw question’
If we combine
•intellectual depth and
varied properties of
correlated electron materials
•control possible in
semiconductor devices
??Whose beauty and whose
brains do we get??
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The fundamental questions: science
• What new (not occurring in bulk in either
component) physics occurs at interfaces
• Can we predict the changes in many-body
phenomena (superconductivity, magnetism,
metal-insulator transition) occurring near
interfaces
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Practical questions: science
• How do we make the materials, know what we
have made and see the behavior of electrons
• How do we characterize and control the
inevitable defects
• What are the concepts we should use to
characterize the spatially varying behavior of
electrons near an oxide interface
• What are the important length and time scales
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A propos of devices:
Goal: put the many-body properties of correlated
electrons: superconductivity, magnetism,
multiferroicity, metal-insulator transitions.....
to practical use.
Herbert Kroemer:
``the interface is the device’’
``the principal applications of any sufficiently
new and innovative technology always have
been--and will continue to be--applications
created by that technology’’
http://www.nobelprize.org/nobel_prizes/physics/
laureates/2000/kroemer-lecture.pdf
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Important variables
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Semiconductors:
control charge by applied fields (from
material design or external leads)
Schematic of High
Electron Mobility
Transistor (HEMT)
gate voltage=>vary
carrier density below
gate=>change sourcedrain conductance
http://www.physorg.com/news142864069.html
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The game in semiconductors:
Put electrons where we want
them, when we want them there
?What lets us do this?
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Electronic Structure: solve many-body
problem.
H=
� −∇2
i
i
2me
+
�
i
1�
e2
Vext (ri ) +
2
|ri − rj |
i�=j
Believed: NP hard.
Certainly no practical solutions available
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Workhorse: density functional band theory
W. Kohn and L Sham, Phys. Rev. 140, A1133 (1965)
�
�
�
−
∇2 + Vions (r) + Vhartree (r) ψn (r)
2m
2
+VXC ({n(r)}) ∗ ψn = En ψn (r)
VXC: exchange correlation potential’ determined by electron
density. Not known exactly but good approximations exist.
Eigenfunctions, eigenvalues in principle no meaning except
Self-consistency: n(r) =
�
En <µ
ψn† (r)ψn (r)
Ground state Eground−state =
�
En
En <µ
In practice: eigenstates often meaningful
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Electrons in semiconductors:
need only a few aspects of band theory
GaAs Crystal Structure
[010]
(001) plane
As
Ga
`Simple’ situations: not
too heavy elements,
monatomic/diatomic
systems; small unit cells
(010) plane
(111) plane
[001]
[100]
Crystal structure for GaAs
1
Eigenstates not too far
from plane waves.
Charge relatively
uniformly distributed
over unit cell
By Eun-Hyeong Yi
http://www.ece.rutgers.edu/~maparker/classes/467-htmlPages/
PresentationECE467-9-28-06.pdf
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Electrons in semiconductors:
need only a few aspects of band theory
Low carrier density:
approx band(s) as
parabola(s)
�2 k 2
E=
2m∗
=>continuum description
atomic-scale details not
important
Band structure for GaAs
(http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/Figs/421.gif)
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(non-mean-field) e-e interactions weak
e2 m ∗
=
π��2 n1/2
Large �, small m∗
rS not too big
In semiconductors, 1<rS<10, far from crystallization
r2D
S
Expt,
2d
Theory
2d
J. Zhu et al PRL 056805 (2003)
Drummond, Needs PRL 102 126402 (2009)
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(non-mean-field) e-e interactions weak
r2D
S
e2 m ∗
=
π��2 n1/2
Large �, small m∗
rS not too big
Main effect of e-e
interactions: self
consistent Coulomb
potential (=>band
bending)
http://www.tf.uni-kiel.de/matwis/amat/semi_en/
kap_2/backbone/r2_2_4.html
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Summary: semiconductors
Continuum (simple plane wave) description;
atomic details unimportant.
No intrinsic scale (if carrier density small
relative to atomic density)
Important variable: charge density (selfconsistently determined)
simple models describe the behavior
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Transition metal oxides
`ABO3 perovskite’: widely
studied material family
crystal structure, cubic phase
A-site. Typically
electrically inert;
choice of A ion
controls valence
of B site
B-site. Where the
action is. Interesting
case: transition
metal with partly
filled d-shell
dont forget oxygen!
http://en.wikipedia.org/wiki/File:Perovskite.jpg
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AQABQB(O2-)3 electron counting:
ionic approximation not bad
O: electronegative. Formal charge 2A: point charge (typically 2+ (e.g. Sr) or 3+ (e.g. La))
=>Charge QB on B-site ion: QB=6-QA typically 4+ or 3+
Change B-charge by alloying on A-site (e.g. La1-xSrxVO3)
--Ionic nature=>strongly polar interfaces
--O vacancies/interstitials add/subtract ~2 electrons=>O
stoichiometry crucial!
--covalency between B-site and O not always negligible
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Transition metals: fill up d-shell
3d
4d
5d
http://www.vertex42.com/Files/pdfs/1/periodic-table_color.pdf
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Oxygens: grab the 2 4s electrons, then
(depending on A-site ion) 1 or 2 from the
d-shell
In perovskite: forget 4s,
have partially filled d
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3d orbitals are small (relative to ABO3 unit cell)
LaTiO3 Lattice constant 3.91A
3.910
Ti0.5 (integrated in z direction ±1Å)
0.1800
Eigenfunctions not
close to plane waves
0.1400
y (Å)
0.1000
0.06000
1.955
0.02000
correlation energy
large (small r in e2/r)
-0.02000
0.000
0.000
1.955
x (Å)
S. Okamoto, N, Spaldin and
AJM PRL 97 056802 (2006)
3.910
Kohn-Sham eigenstates
poor approximation to
spectrum
(4d, 5d orbitals bigger=>weaker correlations
--but spin orbit coupling stronger)
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Minimal Model:
‘Hubbard model’
http://theor.jinr.ru/
~kuzemsky/jhbio.html
One (spin degenerate) orbital per lattice site.
Hopping t between
� sites and on site repulsion
�
H=−
†
ti−j ciσ cjσ
+U
ij
ni↑ ni↓
i
If charging energy ‘U’ is
large, motion is ‘jammed’
=>
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Multi-orbital=>more structure
partly filled d shell; assume weak spin orbit
Fundamental perspective: atom as fully
entangled multielectron system. Eigenstates A
characterized by quantum numbers
Electron number N
Spin Angular momentum S, Sz
Orbital Angular momentum L, Lz
=> Energy EA (N, S, L)
J. C. Slater: Quantum Theory of Atomic Structure
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=>richer structure of interactions
Conventional (Slater-Kanamori) representation
H
= U
�
a
na↑ na↓ + (U − 2J)
+(U − 3J)
�
a�=bσ
�
naσ nbσ
a>b,σ=↑,↓
naσ nbσ̄ − J
�
c†a↑ c†a↓ cb↑ cb↓ + c†a↑ c†b↓ cb↑ ca↓
a�=b
85 interaction terms, determined by 2 parameters
(cubic symmetry; lower symm, more params). Key
interaction: charging energy `U’Nd2
same basic idea: large ‘U’, integer
occupancy=> motion jammed
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Fujimori’s transition metal oxide phase diagram
Variables: intraction strength/bandwidth; d-occupancy
A. Fujimori J Phys Chem Sol 53 (1992)
Insulating phases at integer d-occupancy
incompatible with band theory (in absence of
extra symmetry breaking).
near integer occupancy: interesting physics
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Lifting O(3) rotational symmetry splits
degeneracy of d-level=>electronically important
Rondinelli and Spaldin, Adv. Mater. 23 3363 (2011)
Notes:
--Tm-O bond often rigid: compression=>rotation
--Substrate-induced symmetry breaking=>potentially big
effects
--Distortions from cubic symmetry: big changes to
‘Fujimori’ phase diagram
(see, e.g. Pavarini et. al. PRL 92 176403)
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Summary: oxides
Intrinsic scales relevant
Important variables:
*local charge density
*spin and orbital occupancy (angular
momentum) of d-shell
*Interaction strength/bandwidth
Structure on atomic scales matters
New phenomena: Mott insulator,
magnet, superconductor
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Modalities of control
-chemical dopants (randomly or deliberately
placed)
-interface (attacts carriers)
-quantum well (potential minimum)
-local physics: strain, symmetry lowering...
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Doping:
spatial arrangement
=>device structures
impurities change carrier
count (donate electrons or
holes), also may create
new states
http://www.tf.uni-kiel.de/matwis/amat/
semi_en/kap_2/backbone/r2_2_4.html
http://www.physicsforums.com/
showthread.php?t=164730
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Doping a transition metal oxide
Simple picture: SrTiO3 and LaTiO3
cubic
Mainly d
character
Sr2+ means Ti4+
i.e. Ti d0
La3+ means Ti3+
i.e. Ti d1
µ : LaTiO3
µ : SrTiO3
http://dmft.rutgers.edu/
LDA/lmto/lmto_run.htm
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La in SrTiO3:
controlled dopant array
La3+ donates electron to nearby
Ti site of Sr2+TiO3
Hwang et al Nat. Mat. 11 103 (2012)
A. Ohtomo, D. A. Muller, J. L. Grazul
and H. Hwang, Nature 419 378 (2002)
Length scales ~1nm, brutally short
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Quantum Wells
Length scale: 50AA
=>interface need
not be controlled on
atomic length scale
Difference in
material modelled
as step
http://www.nextnano.de
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Oxide quantum well
3 layers of LaMnO3 in SrTiO3
Length scale: 5AA
=>atomic scale
structure of
interface matters
(a): La (b) Ti
(c) Mn (d) composite
D. Muller Nat. Mat. 9 263 (2009)
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Quantum Well Thickness
Quantum well: Vacuum-LaNiO3--Substrate
Son et al Appl. Phys. Lett. 96 062114 (2010)
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Additional variable: strain
Quantum well: Vacuum-Oxide--Substrate
Son et al Appl. Phys. Lett. 96 062114 (2010)
X-Ray: different substrate-different lattice spacing:
LAO: 1.3% compressive strain
LSAT: 0.8% tensile strain
DSO: 2.5% tensile strain
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TEM: Atoms in LaNiO3 line
up with substrate
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Strain control
Son et al Appl. Phys. Lett. 96 062114 (2010)
LAO: 1.3% compressive strain
LSAT: 0.8% tensile strain
DSO: 2.5% tensile strain
Critical thickness for metalinsulator transition depends on
magnitude and sign of strain
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Modulation-doped interface
(dopant potential<=>charge sheet) set
back from interface
Length scales:
102-104 AA
(Sheet) Carrier densities
1012cm-2 LOW
(~1 per 10-3 atoms inplane)
L. Pfeiffer et al, APL 55 1888 (1989)
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Oxide interface: polar catastrophe
Length scales low (1 nm)
Sheet carrier density high
(1014 /cm-2 in principle!)
Reyren et al, Science 317 1196 (2007)
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the `polar catastrophe’
(better: `polar opportunity’)
Example: ABO3 perovskite along (100) direction
alternating planes:
AO charge QA-2/cell
BO2 charge 2-QA/cell
SrTiO3: planes formally neutral
LaAlO3: charge alternates +/- 1
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Electrostatically unstable as number of
LaAlO3 layers->infinity
Note! E-fields ~
volts/angstrom:
NOT SMALL
to resolve divergence: put capacitor
(sheets of charge) around LaAlO3 layer to
cancel average field: =>charge density 1/2
electron per in-plane cell
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Summary:
structure of oxide interface systems
Control modalities (doping, quantum well,
modulation doping <=> polar interface) similar to
those of conventional semiconductors.
Extra variable: strain
Length scales very short
=>atomic scale control needed
=>charge densities can be very high
Transition metal oxides
key role of oxygen defects
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Sample fabrication and characterization
(very sketchy)
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Sample growth
Basic idea: slowly rain the atoms you want down on
surface. If you do it right, you build up a desired
structure layer by layer
http://homepages.warwick.ac.uk/~phsbm/mbe.htm
mxp.physics.umn.edu
Deposition of non-oxygen atoms is done in
oxygen atmosphere and/or with oxygen
post-annealing. How this is done is crucial
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LAO/STO: dependence of properties on
growth pressure/annealling
Ariando et al Nat Comm 2, 188 (2011)
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Sample characterization: scattering
--Electrons (TEM/TEM-EELS)--small size of
electron means beam ~0.1nm wide=>local
information
--Photons (X-Rays) periodic structures or
‘forbidden’ (in bulk) scattering at interfaces
--Neutrons (as with X-rays)
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Transmission Electron Microscopy (TEM)
Fitting-Kourkoutis et al, Phil Mag 90 4731 (2010)
=>Average over column
0.1nm wide beam in--see wide (typically ~103 unit cells)
angle elastic scattering as
function of beam posn. requires
Electrons in
thin sample
Out
Side view
Top view
Scattering amplitude depends strongly
on atomic number (Z)=>see where
heavy elements are
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TEM-EELS
alternative: inelastic
scattering (small
angle).
http://www.imaging-git.com/science/electron-and-ionmicroscopy/electron-energy-loss-spectroscopy
Energies where scattering
occurs: element (and valence)
specific
Correlate with wide angle scattering,
see which elements are where
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Measure charge distribution
Ohtomo, Muller, Grazul and Hwang, Nature 419 378 (2002)
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Application
Ti/V interdiffusion even though La is sharp
Kourkotis et al Phil Mag 90 4731 (2010)
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Application
Two terminations=>opposite doping
0.5 elec
0.5 hole
Problem: electron interface conducts
hole interface does not
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TEM EELS: to model, must include
oxygen deficient SrTiO3 as reference
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Concentrations deduced by fitting
TEM/EELS
At p-type
interface: oxygen
vacancies not
holes compensate
the polar
discontinuity
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Inelastic X-Ray scattering
Same basic idea: probe transitions from core to
unoccupied states. Dependence of scattering cross
section on polarization of incident, outgoing
light=>information on symmetry of final states
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Recent example: ((LaNiO3)4/(LaAlO3)4)8
8 repeats
Benckiser et al Nature
Materials 10 189 2011
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=>small difference in
orbital occupations
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Neutron reflectometry
LaMnO3/SrMnO3 superlattice
q
J Hoppler et al PRB82 174439 (2010)
dependence on q=(kf-ki).z
=>info on structure
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Summary
remarkably detailed examination of
behavior (at single unit cell scales) is
now possible.
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Systems of Current Interest
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Polar discontinuity doping
LaAlO3/SrTiO3
d
LaAlO3 :Wide bandgap, polar
SrTiO3: narrow gap, non polar
Reyren et al, Science 317 1196 (2007)
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However: 2DEG at LAO/STO Interface
new claim: doped gas is magnetic
Li, et al Nat. Phys. 7 762 (2011)
Bert et al, Nat. Phys. 7 767 (2011)
Moment: ~0.3 mu_B/
interface unit cell
Magnetism not seen in
host materials in
bulk=>?new interface
phase?
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Other systems
GdTiO3/SrTiO3
Son et al APL 99 192107 (2011)
See also Santander-Syro
Nature 469 139 (2011): Free
STO surface
GdTiO3 :Ferromagnetic
Mott insulator
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Quantum Wells
Thickness driven metalinsulator transition
Schematic:
2 layers of SrVO3
on many layers
of SrTiO3
Yoshimatsu et al PRL 104 147601 (2010)
Yoshimatsu et al Science 333 319 (2011)
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Other Quantum Wells
(SrRO3)n(SrTiO3)
(LaNiO3)n(LaAlO3)m
Xia et al PRB 79 140407 (2009)
Thickness driven metal-insulator
Liu et al arXiv:1101.5581
transition also observed. ? Generic?
(For mechanism, see M. Gibert talk
April 11)
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Quantum wells, magnetic properties
Claim: ferromagnet
(LaMnO3) couples
antiferromagnetically across
interface
Nature Physics 2 244 (2006)
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Superlattices
In CaMnO3/CaRuO3 superlattice, (AF/PM)
Ferromagnetism at
interface
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Artificial Multilayer: Potential for
‘materials by design’
Luders et al : Room temperature magnetism in
LaVO3/SrVO3 superlattices
PHYSICAL REVIEW B 80, 241102 (2009)
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More exotic behavior proposed
Proposal: use (111) superlattice to make material with
intersting ‘topological insulator’ properties:
LaAlO3/AlAuO3/YAlO3
Xiao...Okamoto arXiv:1106:4296
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Next time: April 4
Interface systems: LAO/STO and variants
Magnetism and superconductivity
Seminar M. Gabay
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