Outline

• 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