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• Basics of an IR probe of electronic processes in solids• Electrostatic doping of new materials: challenges, opportunities
and first accomplishments• Intrinsic electronic transport in organic molecular crystals
October 18
October 25
November 1
November 8
• High Tc superconductivity: new materials or new state of matter?• The search for a pairing glue in high-Tc superconductors
• High Tc superconductivity by kinetic energy saving? • Infrared spectroscopy of correlated electron matter at the nano-scale
• Magnetic phenomena in semiconductors• Ga1-xMnxAs: first correlated electron semiconductor?
Infrared and optical properties of novel correlated matterD.N. Basov
University of California, San Diego http://infrared.ucsd.edu
Electron:particle with negative electric charge q = - eand spin 1/2 (magnetic moment m = µB )
Why bother with spintronics?
•new fundamental physical questions•new phenomena•new devices and applications
Potential advantages:
•non-volatility of memory•increased data processing speed•increased integration densities•decreased electric power consumption
-2000 -1500 -1000 -500 0 500 1000 1500 2000
Peter Grunberg Albert Fert
Magnetism timeline. 1988: Spin Electronics (Spintronics)
All-metals spintronics: giant magneto-resistance /GMR/F1NF2
low ρdc
F configuration
F1NF2
high ρdc
AF configuration
FAF
FAF
RRRRMR
+−
=
F1INSF2
low ρdc high ρdc
F1INSF2
All-metals spintronics: spin tunneling device
2
-2
-4
Majority Minority
Ene
rgy
(ev)
0
Fe*
Band structure Schematics Half-metallic FM
CrO2GaMnAs?
F1INSF2
low ρdc high ρdc
F1INSF2
All-metals spintronics: spin tunneling device
S.Datta&B.Das APL 56, 665 (1990)
Spin field effect transistor
gate
Silicon
S DSiO2
Spin field effect transistor
Requirements: effective spin injection, slow spin relaxation, reliable spin detection.
Ferromagnetic semiconductors!
F1INSF2
low ρdc high ρdc
F1INSF2
Polarizer
Electro-opticalmodulator
Charge FETs and spin FETs
Requirements: effective spin injection, (relatively) slow spin relaxation, reliable spin detection.
Ferromagnetic semiconductors!
gate
Silicon
S DSiO2
Control of barrier for charge transport Control of the spin state
Min barrier height requirement: 25 meV No switching barriers!
Magnetism timeline. 1996: Ferromagnetic III-V semiconductors
A.M. Nazmul et al. PRL95, 17201 (2005)TC up to 250 K
Basics of III-V semiconductors
Undoped (intrinsic):
gapconduction band
valence band
InAs GaAs GaN GaPEg, eV 0.2 1.42 3.5 2.2
Doping: Introduce charged impurities
Example: replace Ga by Si in GaAs
Si has one valence electron more→ introduces extra electron: donor
Si4+ weakly binds the electron:hydrogenic (shallow) donor state
Example: replace Ga by Zn in GaAs
Zn has one valence electron less→ introduces extra hole: acceptor
Zn2+ weakly binds the hole:hydrogenic (shallow) acceptor state
EF
CB
VBEF
CB
VB
E0de
nsity
of s
tate
s
VB CB
EFFor heavy doping the impurity band overlaps with the VB or CB
Basics of III-V semiconductors
Ga
As
Mn
Ferromagnetic: x=2-10%
Ga1-xMnxAsMBE Lab @ UCSB
LT - MBE
Ga1-xMnxAs/GaAs
Ga
As
Mn
Ga1-xMnxAs Mn doping:
•magnetic moments
•holes•localization
As anti-sites•defects
Mn interstitials
Mn
0 0.02 0.04 0.06 0.08x
0
40
80
120
T C ,
(K)
Ferromagnetic Ga1-xMnxAs
H.Ohno JMMM 200, 110 (1999)
Penn State, UCSB, Nottingham
Jungwirth et al. PRB72, 165204 (05)
“insulating”
“metallic”
Tunable ferromagnetism in III-V seriesH.Ohno et al Nature 408, 944 (2000)
metal gateinsulator
InAs
(In,Mn)As
Vg = 0metal gateinsulator
InAs
(In,Mn)As
Vg < 0
TC TC
metal gateinsulator
InAs
(In,Mn)As
TC
Vg > 0
k
Ener
gy
Spin polarization and optics
Ener
gy
k
σ+ σ+σ+σ+σ+σ+σ+
Y.Ohno et al.Nature 402, 790 (1999)
Super-exchange: AF (typically)
Exchange interaction: Coulomb repulsion + Pauli exclusion Heisenberg model:
nmmn SSJHrr
∑−=int21int SSJHrr
•−=Spin Hamiltonian: ts EEJ −=
Exchange interaction in magnetic semiconductors
Direct exchange: wave function overlap FM
Double exchange: FM
La1-xSrxMnO3: La3+, Sr2+ O26- Mn – mixed valence
TTx C∝σ
Super-exchange: AF (typically)
Exchange interaction: Coulomb repulsion + Pauli exclusion Heisenberg model:
nmmn SSJHrr
∑−=int21int SSJHrr
•−=Spin Hamiltonian: ts EEJ −=
Direct exchange: wave function overlap FM
Exchange interaction in magnetic semiconductors
Double exchange: FMSuper-exchange: AF (typically)
Exchange interaction: Coulomb repulsion + Pauli exclusion Heisenberg model:
nmmn SSJHrr
∑−=int21int SSJHrr
•−=Spin Hamiltonian: ts EEJ −=
Direct exchange: wave function overlap FM
Exchange interaction in magnetic semiconductors
Kinetic exchange: FM; spin polarized Fermi sea
hole position impurity position
hole spin 1/2 impurity spin 5/2
( )lilipd RrSsJHrrrr
−⋅−= ∑ δ
Ferromagnetism in III-Mn-V semiconductorsDouble-exchange? Kinetic exchange?
GaAs
-4
0
4
-6
-2
2
6
Ener
gy (e
V)
L Λ Γ ∆ X
GaAs: Mn
0.113 eV
-4
0
4
-6
-2
2
6
Ener
gy (e
V)L Λ Γ ∆ X
EF
MetalTC<180 K
FM mediated by:delocalized holes in the valence band
Ga1-xMnxAs x=5-10%
Dietl et al. 2001Jungwirth, Yang, Sinova,
Timm, Masek, Kucera, MacDonald 2001-06
Priour, Hwang and Das Sarma 04
EF
-4
0
4
-6
-2
2
6
Ener
gy (e
V)
L Λ Γ ∆ X
Mn
doped semiconductorTC < 70 K
FM mediated by:localized holes
in the impurity band
Ga1-xMnxAs x=1-5%
Akai 1998; Alvarez et al. 2002Savinto et al. 01; Berciu and Bhatt 01
Kaminski and Das Sarma 02Durst 2002; Fiete 2003
Litvinov 2003; Zunger 04; Tang and Flatte 2004
Mn Mn
From dilute Mn impurities to ferromagnetic Ga1-xMnxAs
Sub-THz Far-IR mid-IR - visible UV
1 10 100 1000 10000 cm-1
100 1000 10000 100000 1000000GHz
1 10 100 1000meV
interband transitions2DES: plasmonsintersubband transitions2D Electron gas: EF
intraband absorptionphonons
(magnetic) polarons
CR: holesCR: electrons
CR in quantum dots Zeeman splitting
spin-orbit splitting
III-V II-VI
-4
0
4
-6
-2
2
6
L Λ Γ ∆ X
EF
Mnσ1(ω) + iσ2(ω) σ1(ω) + iσ2(ω)
Infrared and optical spectroscopy of magnetic semiconductors
Ga1-xMnxAs x=5-10%
Detector: T(ω)
substratethin film
interferometer
Er
Detector: R(ω)
momentum
-2
-1
0
1
E (e
V)100 1000 10000cm -1
0
50
100
150
200
Re
cond
uctiv
ity, (
Ωcm
)-1
10 100 1000meV
EG
Ga
As
EG
GaAs: optical conductivity
momentum
-2
-1
0
1
E (e
V)100 1000 10000cm -1
0
50
100
150
200
Re
cond
uctiv
ity, (
Ωcm
)-1
10 100 1000meV
Ga1-xMnxAs: optical conductivity
Ga
As
Mn
x=1.7%
LT-GaAs
dVdIR.M.Feenstra et al.PRL 71, 1176 (93)
Singley et al. PRL 89, 97203 (02)
100 1000 10000 cm -1
0
100
200
300
Re
cond
uctiv
ity, (
Ωcm
)-1
x=0.052
x=0.017
Ga1-xMnxAs: optical conductivity
Wavenumber cm-1 Ga
As
Mn
increase of intragap σ1(ω)resonance at 2000 cm-1metallic transport
Mn doping:gap edge smearing
Singley et al. PRL 89, 97203 (02)
100 1000 10000 cm -1
0
100
200
300
Re
cond
uctiv
ity, (
Ωcm
)-1
x=0.028
x=0.04
x=0.052
x=0.017
Ga1-xMnxAs: sum rule analysis of σ1(ω)
Wavenumber cm-1 Ga
As
0 2 4 6 80
20
40
60
80
Tc
x (% Mn)
( )∫Ω
ωωσ=0
1* dmn
x=0.066
x=0.079
Singley et al. PRL 89, 97203 (02)
0 2000 4000
0
100
200
300
σ1(ω), (Ωcm)-1
Understanding the optical conductivity of Ga1-xMnxAs
x=0.052
0
-0.4
-0.2
0.0
0.2
k
E (eV)
1017 Mn/cm-3
x50
Wavenumber cm-1
0 2000 4000
0
100
200
300
σ1(ω), (Ωcm)-1
Understanding the optical conductivity of Ga1-xMnxAs
x=0.052
0
-0.4
-0.2
0.0
0.2
k
E (eV)
1017 Mn/cm-30
-0.4
-0.2
0.0
0.2
EF
k
E (eV)
J.Sinova et al.
x50
Wavenumber cm-1
100 1000 100000
100
200
300
400
500
100 1000 100000
100
200
300
400
500
100 1000 100000
100
200
300
400
500
cm-1 cm-1 cm-1
σ(ω), Ω-1cm-1 σ(ω), Ω-1cm-1 σ(ω), Ω-1cm-1
E.J.Singley et al. PRL 89, 97203 (02)
Ga1-xMnxAs 5.2%TC=70 Kc.2001
Ga1-xMnxAs 5.2%TC=80 Kc.2005
Ga1-xMnxAs 5.2%TC=120 Kannealed
Intra-gap conductivity
Burch et al. PRL 97, 87208 (2006)
L Λ Γ ∆ X-1.5
-1
-0.5
0
0.5
-1.25
-0.75
-0.25
0.25
100 1000 100000
100
200
300
400
500
cm-1
σ(ω), Ω-1cm-1
Ga1-xMnxAs 5.2%TC=120 Kannealed
EF
E.J.Singley et al. PRL 89, 97203 (02)
Understanding intra-gap conductivity: doping dependence
E, eV
Burch et al. PRL 97, 87208 (2006)
100 1000 100000
100
200
300
400
500
cm-1
σ(ω), Ω-1cm-1
Ga1-xMnxAs 5.2%TC=120 Kannealed
cm-1
σ(ω), Ω-1cm-1
-1.5
-1
-0.5
0
0.5
-1.25
-0.75
-0.25
0.25
L Λ Γ ∆ XJ.Sinova et al. PRB66, 41202 (02)
E, eV
EF
Understanding intra-gap conductivity: doping dependence
0 1000 2000 30000
400
800
1200
Burch et al. PRL 97, 87208 (2006)
cm-1
σ(ω), Ω-1cm-1
4x1020 8x10201200
1600
2000
p (cm-3)Neff cm-3/me
100 10000
200
400
600cm-1cm-1
Impurity band and intra-gap conductivity of Ga1-xMnxAs
-1.5
-1
-0.5
0
0.5
-1.25
-0.75
-0.25
0.25
L Λ Γ ∆ X
E, eVR.Braunstein (1959)W.Songprakob et alJAP 91, 171 (2002)
5x1020 1x10211200
1600
2000
Burch et al. PRL 97, 87208 (2006)
5x1020 1x10211200
1600
2000
cm-1
σ(ω), Ω-1cm-1
4x1020 8x10201200
1600
2000
p (cm-3)Neff cm-3/me
100 10000
200
400
600cm-1cm-1
0 0.5 1.0 1.5ω/t
0.20
0.15
0.10
0.05
0.00
σ(ω)
Hwang, Milis and Das Sarma PRB65, 233206 (02)
Impurity band and intra-gap conductivity of Ga1-xMnxAs
Burch et al. PRL 97, 87208 (2006)
100 1000 100000
100
200
300
400
500
cm-1
σ(ω), Ω-1cm-1
Ga1-xMnxAs 5.2%TC=120 Kannealed
Intra-gap conductivity: Drude response revisited
1/τ
*mp
=
100 1000 100000
100
200
300
400
500
cm-1
σ(ω), Ω-1cm-1
Ga1-xMnxAs 5.2%TC=80 Kc.2005
1/τ
100 1000 100000
100
200
300
400
500
cm-1
σ(ω), Ω-1cm-1
E.J.Singley et al. PRL 89, 97203 (02)
Ga1-xMnxAs 5.2%TC=70 Kc.2001
IBIntra-band
Burch et al. PRL 97, 87208 (2006)
100 1000 100000
100
200
300
400
500
cm-1
σ(ω), Ω-1cm-1
Ga1-xMnxAs 5.2%TC=120 Kannealed
Intra-gap conductivity: Drude response revisited
1/τ
*mp
=15-30 me35-70 mem*
140 K120 KTC
7.3%annealed
5.2 %annealed
Ga1-xMnxAs Transport:Ku et al. APL 82, 2302 (03)Wang et al. PRB72, 115207 (05)
-321 cm 10≈p
Vs/cm 51 2−≈µpolymers, a-Si
Vs/cm 12080 2−≈µp-GaAs
*meτµ =
Burch et al. PRL 97, 87208 (2006)
Spectroscopic evidence for the impurity band in Ga1-xMnxAsInfrared
Singley et al. PRL 89, 97203 (02)Hirakawa et al.PRB65,193312 (02)
100 1000 cm-10
100
200
300σ(ω)Ω-1cm-1
Ga1-xMnxAs5% Mn
MCDB.Beschoten et al. PRL83,3073(99)Tang&Flatte PRL92, 47201 (04)
STM Yakunin et al. PRL 95, 256402 (05)
Hot electron PLSapega et al. PRL 94, 137401 (05)
eV
Transport
emm
Vscmme
5015*
/51*
2
−=
−==τµ
ARPESFujimori prb64, 125304 (2001)
E,eV
Digital ferromagnetic heterostructures
0.5 MLMnAs
10-200 MLGaAs
R.K.Kawakami et al. APL 77, 2379 (2000)
0 50 100 150 200 250GaAs thickness (ML)
0
20
40
60
T C (K
)
Sub-monolayer MnAs?Continuous film? Clusters? Overdoped Ga1-xMnxAs?
100 1000 10000Wavenumber, cm-1
0
100
200
300
σ1(ω), (Ωcm)-1
100 1000 10000Wavenumber, cm-1
0
100
200
300
σ1(ω), (Ωcm)-1
300 K 300 K
MnAs(0.5)/GaAs(10)Ga1-xMnxAsx=5.2%
Energy
DO
S
VBCBAsGa
Energy
DO
S
VBCBAsGa
100 1000 10000Wavenumber, cm-1
0
200
400
σ1(ω), (Ωcm)-1
Digitally doped Ga1-xMnxAs
Spacing:10 ML15 ML25 ML
T = 7 K
EF
Metallic FM
EFInsulating FM
K.S. Burch et al. Phys. Rev. B 71, 125340 (2005).
100 1000 100000
100
200
300
400
500
Scanning near field optical microscopy of Ga1-xMnxAs?
Burch et al. PRL 97, 87208 (2006)
σ(ω), Ω-1cm-1
Ga1-xMnxAs 5.2%TC=120 Kannealed
cm-1100 1000 100000
100
200
300
400
500
1.7%
5.0%4.2%2.8%
7.2%
5.2%
far-IR – mid IR
( )∫= ωωσ1*d
mn
Homogeneous Ga1-xMnxAs?
•Hole-rich regions in hole-depleted host?
Hamaya et al, PRL94, 147203 (2005)
• Mn clusters?
• MnAs clusters?
• Sphere resonance?S.Seo et al. JAP95, 8172 (04)
• More?
Optics of inhomogeneousmedium
insulator ε1=const
Drude metal
Problematic absolute values
New features / artifacts
Kramers-Kronig breakdown
σ(ω)
f=1
f=0.1
0 2000 4000 cm-110
100
1000 f=0.50.40.30.2
Scanning near field infrared microscopy of Ga1-xMnxAs
100 1000 100000
100
200
300
400
500
Burch et al. PRL 97, 87208 (2006)
σ(ω), Ω-1cm-1
cm-1
1.7%
5.0%4.2%2.8%
7.2%
5.2%
far-IR – mid IR 0 nm
4.5 nm500nm
Near Field Profile
1.0
.5
Near Field Profile1.0
.5
Topography
x=0.06annealed
ω=960 cm-1
S 2(x
),ru
S 2(x
),ru
Scanning near field IR microscopy of Ga1-xMnxAs: implications
0 nm
12 nm
Near Field Profile
1.0
.5Near Field Profile
1.0
.5
500nm
ω=960 cm-1x=0.077annealed
homogeneous
• x=3-7%: homogeneous• x>7%: oxide clusters on the surface• σ(ω) analysis is valid!• heavy effective masses
surfaceoxide
cluster S 2(x
), ru
Ga1-xMnxAsEF
-4
0
4
-6
-2
2
6
L Λ Γ ∆ X
Mn
eV1. Impurity band
• Infrared• STM• ARPES• PL• MCD• Transport
• High TC
samples
2. Unconventional metal-Insulator transition
Homogeneous?
3. Ferromagnetism mediated by mobile and localizedholes
4. Disorder