UCSD

Tailoring spin interactions in artificial structures

Joaquín Fernández-Rossier

Work supported by and Spanish Ministry of Education

Part 1: theory ferromagnetic semicondutor heterostructures

2D structures of ferromagnetic semiconductor

(Ga,Mn) As

with L.J. Sham (UCSD)

GaAsMn GaAs

Experiment R. K. Kawakami et al.,

J. Appl. Phys., 87, 379 2000).

Part 2: Theory of the quantum mirage

Phys. Rev. B. 63, 155406 (2001)

With Diego Porras (UAM)

Experiment: H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000)

Cu(111)

Cobalt

Quantum Mirage

Kondo effect in a quantum corral in a metallic surface

•Localized magnetic moments + itinerant carriers : Kondo effect, ferromagnetism

•Artificial structures shape wave function of itinerant carriers: new physics, new devices .

Main Ideas

Motivation

• Information technology trend: making smaller devices

• New strategies: spintronics

• Fun: exciting new physics

Outline of the first part

• Introduction– Main facts– Motivation– Origin of ferromagnetism

• Heterostructures– Experiments– Our theory: model and results

• Conclusions

Material: Ga(1-x) AsMnx

• Ferromagnetic below 110 kelvin• Homogeneous alloy for x<0.08

• Transport: p-doped semiconductor (p<cMn)

FERRO

PARA

Doping GaAs with Mn:

1) Mn is an acceptor

2) Mn has a magnetic moment ( 5/2 ?)

Ga

Mn

AcceptorMagnetic Moment

Motivation3 things you can do with GaAsMn (better than with Fe)

1. Ferromagnetic-Semiconductor heterostructures

2. Electrical Control of Curie Temperature

3. Spin injection in a semiconductor

Digital Multilayer

R. K. Kawakami et al.,

J. Appl. Phys., 87, 379 2000).

Low energy

2 Mn, 1 hole1 donor

The origin of ferromagnetism

1 Mn, 1 hole

High energy

RKKYLow density ofholes

• Itinerant holes, effective mass approximation

• Localized d electrons

• Local hole-Mn exchange interaction

• Virtual Crystal approximation

• Mean Field approximation

The ‘standard’ model

• k.p Luttinger holes (SPIN-ORBIT)

• Spin wave fluctuations (beyond mean field theory)

Our model for heterostructures

1. Calculation of the electronic structure of the heterostructure (self- consistent Poisson-Schrödinger multi sub-band approach). Calculation of the non-local spin susceptibility

2. TC: Solution of an integral equation

Modeling for Delta Doping

1 cMn=2 1014 cm-2

3 Gaussian distributionOf impurities:

p=2 1013 cm-2

Mn=Comp+ Holes2

-60 -40 -20 0 20 40 600 Holes

Impurities (Mn+comp)

Gaussian:

(cMn, p, )

Self consistent Electronic Structure

-60 -40 -20 0 20 40 600

Holes

Impurities (Mn+comp)

200

0 0.05 0.1k|| (A

-1)

0

50

100

150

-100 -50 0 50z(A)

0

50

100

150

200

Ene

rgy

(meV

)

hh

hh

lh

•Envelope function•Kohn-Luttinger Hamiltonian•Spin-Orbit Interaction

=5 A. p=2.5 1013 cm-2

cMn=2 1014 cm-2

Mean Field Critical Temperature

S=5/2x= Mn ConcentrationJ= Exchange constant= Spin Susceptibility

of bare GaAs

•Tc does not depend on the sign of J

•Tc is linearly proportional to cMn

•Tc depends A LOT on |J|

•Tc is hole density dependent

PLANAR HETEROSTRUCTURE

')'()'()',(3

)1()(

2

dzzMzczzTk

JSSzM

cB

2

3

)1(Jc

SSTk MncB

BULK

J=150 mev nm3

cMn=2 1014 cm-2

Single layer results

0 1e+14 2e+140

50

100

150

200

=5A

=10A

=15A

=20A

Cri

tica

l Tem

pera

ture

(K

) =0

Density of Holes (cm-2)

0 1e+14 2e+140

5

10

15

20

Cri

tica

l Tem

pera

ture

(K

)

-60-40-20 0 20 40 60-60-40-200 20 40 60

(A

)

Density of Holes(cm-2)

Tc=35 Kelvin

Impurities

Holes Holes

0 5 10 15 20

(A)

0

50

100

15075%50%40%20%10%

TC (

K)

-150 -50 50 150

10 ML

20ML

40ML

-150 -50 50 1500

2e-05

4e-05

6e-05

8e-05

0.0001 0

2e-05

4e-05

6e-05

8e-05

0.0001 0

2e-05

4e-05

6e-05

8e-05

0.0001

=5 A. p=2.5 1013 cm-2

0 10 20 30 40 5030

40

50

60TheoryEXPERIMENT

Interlayer Distance (ML)10 20 30 40 50

30

40

50

60 =15 A, p=8 1013 cm-2

TC (

K)

Interlayer Distance (ML)

10 ML

20 ML

40 ML

Engineering Tc: Digital layer in a QW

-50 0 50z (A)

-300

-200

-100

0

100V

(m

eV)

V}

Ga1-xAlxAs

-50 0 500

5e+11

1e+12

Den

sity

(cm

-3)

0

5e+11

1e+12

Den

sity

(cm

-3)

-50 0 50

Position (Amstrongs)

-50 0 50

0 100 200 300 400 500V (meV)

30

40

50

60

70

80

Tc

(kelvin)

Density profiles for differentbarrier heights (V)

Tc vs barrier height

DOUBLING Tc !!!

Conclusions (Part I)

• GaAsMn is a ferromagnetic semiconductor.

Exchange and itinerant carriers produce Ferromagnetism

• Planar heterostructures of GaAsMn:– Tailoring Mn-hole interaction and TC

– Promising for new physics and devices

Part 2: Theory of the quantum mirage

Phys. Rev. B. 63, 155406 (2001)

With Diego Porras (UAM)

Experiment: H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000)

Cu(111)

Cobalt

Quantum Mirage

Kondo effect in a quantum corral in a metallic surface

STM BASICS

1) READ: measure I(V,x,y,z)

),(),( rVELDOSrVdV

dIF

2) WRITE

The Kondo effect

Cobalt

Conduction electrons screen the magnetic moment of

the impurity

Collective many body state: Enhancement of DOS

at EF

Single magnetic atom in a surface

H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000)

V. Madhavan et. al., SCIENCE 280, 567(1998)

Elliptical Quantum Corral

H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000)

QUANTUM MIRAGE

Kondo dip Phantom dip

Phantom dip

10Å

80Å

The questions

• What is the explanation?– Black box Green function theory– Hand-waving explanation

• Is the ellipse necessary?

t

R

,,),,( 2 RRGtRRG c

Black Box Theory

..)( *

,

** chdcRVnUnddccH ii

Iidddi

iii

Surface electrons Impurity electrons Coupling

),,(Im1

),( eVERRGReVELDOS FF

,,)(,, RRtVGGRRtVG IcdIc

IR

The Ellipse LDOS

250 350 450 550 650energy (meV)

0

2

4

6

8

fre

e L

DO

S a

t th

e f

ocu

s (a

.u.)

i

ii RRLDOS 2

)(,LDOS(EF) LDOS in the

foci

22)()(Im)(),( IEdE RGRRG

FF

,,)(,,),( RRtVGGRRtVGRG IcdIc

k k

RRki

Ic i

e

ARRG

I

)(1,,

Decays for (|R-RI|) >>kF-1 10 Å

-20 -10 0 10 20eV (meV)

0

2

4

6G

(V)

(arb

. u

nits

)

-20 -10 0 10 20eV (meV)

0

2

4

6

0.60.40.2

0

Empty focusImpurity focus

EXPERIMENTS

H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000)

Our theory

D. Porras, J.Fernandez-Rossier andC. TejedorPhys. Rev. B. 63, 155406 (2001)

Summary part II

• Mirage: projection of the local Kondo resonance to a ‘remote’ location

• Explanation: Single ‘confined’ state at the Fermi level carries information. No destructive interference.

• Ellipse: convenient, not necessary. ‘Semiclassical geometrical interpretation’: not needed.

Exchange Interaction

• Coulomb Exchange: ferromagnetic (Reduction of Coulomb repulsion )

• Kinetic Exchange: Antiferromagnetic d5

d6

As Mnd5

d6

As Mn

MSJH hEXCH

Cobalt

Copper