Coherently induced ferromagnetism inDiluted Magnetic Semiconductors

Southampton, OCES9-SCES2 September 7st 2005

Joaquín Fernández-RossierDept. Física Aplicada, Univ de Alicante,Spain

jfrossier@ua.es. Slides in www.ua.es/personal/jfrossier/

Collaboration with:C. Piermarocchi (Michigan State), P. Chen (Taiwan), A. H. MacDonald (University of Texas),L. J. Sham, (UC San Diego)

G. Chiappe, E. Louis, E. Anda (Alicante)

Coherently induced ferromagnetism inDiluted Magnetic Semiconductors

Southampton, OCES9-SCES2 September 7st 2005

Joaquín Fernández-RossierDept. Física Aplicada, Univ de Alicante,Spain

jfrossier@ua.es. Slides in www.ua.es/personal/jfrossier/

(Zn,Mn)S

Coherently induced ferromagnetism inDiluted Magnetic Semiconductors

Southampton, OCES9-SCES2 September 7st 2005

Joaquín Fernández-RossierDept. Física Aplicada, Univ de Alicante,Spain

jfrossier@ua.es. Slides in www.ua.es/personal/jfrossier/

Magnetic OrderInduced by subgapLaser radiation

(Zn,Mn)S

Magnetic ImpuritiesLocalized ElectronsNuclei

Elaser>E

G

REAL population of electrons and holesCarrier Mediated Exchange Interactions

,k ,k',' k

'11 SS '22 SS

Optically Induced Exchange Interactions

Magnetic ImpuritiesLocalized ElectronsNuclei

VIRTUAL electrons and holesCarrier Mediated Exchange Interactions

,k ,k',' k

'11 SS '22 SS

22 EPn

COHERENTLY Induced Exchange Interactions

Elaser<E

G

C. Piermarocchi, P. Chen, L.J. Sham and D. G. Steel, PRL89 , 167402 (2002)

SYSTEM 1BULK diluted magnetic semiconductors (DMS) PARAMAGNETIC to FERROMAGNETIC transition

SYSTEM 23D Optical Cavity + Quantum Dot + 2 Mn atoms Full Quantum mechanical analysis of Optical RKKY

JFR, cond-mat 0508235 (2005)G. Chiappe, JFR, et al., cond-mat 0407639 (2004)

JFR, C. Piermarocchi, P. Chen, A. H. MacDonald, L. J. Sham,Phys. Rev. Lett 93, 127201, (2004)

OUTLINE•DMS•ORKKY: macro and micro•Coherently Induced Ferromagnetism•CAVITY-Spin-doped Dot

B C

Al Si

N O

P S

Ga Ge

In Sn

As Se

Sb

II

Zn

Cd

Hg

IV VIII VI

TeII-VIZn-SeZn-S Cd-Te

EF

II-VI Semiconductors

B C

Al Si

N O

P S

Ga Ge

In Sn

As Se

Sb Te

Zn

Cd

Hg

Mn

EF

(II,Mn)-VI PARAMAGNETIC Semiconductors

(II,Mn)-VI(Zn,Mn)-Se(Zn,Mn)-S (Cd,Mn)-Te

Zn: Ar: 3d10 4s2

Mn: Ar: 3d5 4s2

B C

Al Si

N O

P S

Ga Ge

In Sn

As Se

Sb Te

Zn

Cd

Hg

Mn

EF

(II,Mn)-VI PARAMAGNETIC Semiconductors

(II,Mn)-VI(Zn,Mn)-Se(Zn,Mn)-S (Cd,Mn)-Te

Mn: neutral impurity, SPIN S=5/2 (3d5)

EXCHANGE INTERACTIONS

iihih

iieie

iiii

AF

rSMJ

rSMJ

MMiiJH

)(

)(

)',( '',

Superexchange (AF)

Conduction Band

Valence Band

EF

1

2

he JJ41

OPTICAL EXCHANGE INTERACTION.MACROSCOPIC THEORY

Macroscopic Explanation of optical ferromagnetism

EEU L'

Reactive optical energy, due to matter-laser interaction:

•U depends on M

•Ferromagnetism

(M>0) minimizes U (M)•But entropy favors M=0

Competition between reactive optical energy and entropy

Electric Field of the Laser

Real part of retarded Optical Response function

•U depends on bands

•Bands Depend on M

<M>=0

L

jecMn<M>

jhcMn<M>

B

100 meV

PH

OT

ON

EN

ER

GY

(eV

)

(II,Mn)-VI

Bands DEPEND on Mn magnetization

Confined Levels depend on Mn state

EXPERIMENTS:L. Besombes et al., PRL 93, 207403, (2004)Y. Léger et al. PRL. 95, 047403 (2005)

THEORY: J. Fernández-Rossier, cond-mat/0508235

CdTe nanocrystal +1Mn

SINGLE SPIN DETECTION !!!

2S+1=6

CdTe+ 1Mn Quantum Dot:Carrier interacts with 1 Mn

J. Fernández-Rossier, cond-mat/0508235

MSJH

I

Ik MkSkJ

MJcMnkk

Bulk (II,Mn)VI: carrier interacts with many Mn

.. BECAUSE OF EXCHANGE

LjecMn<M>

jhcMn<M>

OPTICAL EXCHANGE INTERACTION.microSCOPIC THEORY

Microscopic Theory: HAMILTONIAN

Mean Field, VC aprox, HF-Pairing

JFR, C. Piermarocchi, P. Chen, A. H. MacDonald, L. J. Sham,Phys. Rev. Lett 93, 127201, (2004)

KEY PARAMETERS

2

23

0

na

Ed

E

cv

LG

k

kkH

2

1

kU

kL

kE

EH

0

0

2

1

EU(k)

EL(k)

Rotating FrameRWA

00

01

2

2

vuv

uvu Coherent

Occupation

Microscopic Theory: Density Matrix

L

01

T

RESULTS for Zn0.988 Mn0.012 S

Hamiltonian + Density Matrix + approximations yield U(M) (reactive energy),S(M) (entropy)

MneMnh cJcJ ,,,

0 1 2M

-1.45

-1.44

-1.43

-1.42

-2

(b)

-0.4

-0.2

0-K

BT

S T=115 mKT=105 mK

(a)

-2 -1 0 1 2M

-1.2

-1

U

0 0.5 1T /TC

0

1

2

M

=26 meV, TC=780 mK

=41 meV, TC=114 mK

=71 meV, TC=22 mK

Results for (Zn0.988,Mn0.012) S

G

1.50

1.00

0.50

Transition Temperature for (Zn0.988,Mn0.012) S

Linear response fails there

3

2

cT

1.02

23

na

Transition Temperature for (Zn0.988,Mn0.012) S

Also from ORKKY+ Mean Field

ji

jiORKKY SSjiJH,

),(

ORKKY:C. Piermarocchi, P. Chen, L.J. Sham and D. G. SteelPRL89 , 167402 (2002)

Isothermal transitions for (Zn,Mn) S

T=0.5 K

Switching ferromagnetis

m on and off

!!!

JFR, C. Piermarocchi, P. Chen, A. H. MacDonald, L. J. Sham,Phys. Rev. Lett 93, 127201, (2004)

Experimental Issues

• Materials:– Moderate x (avoid superexchange)– Large exciton binding energy (osc.

Stre)

• Detection: Easy (polarized PL)• Smal detuning vs unwanted heating• Transition Time vs Laser Pulse

duration

Ferromagnetic Transition Time

0 1 2M

Gib

bs

Free E

nerg

y

0 1 2M

0 1 2M

Laser off Laser OnTL<T1

Laser OnTL>T1

Cavity-Dot ORKKY. Motivation

• Effect of exciton dimensionality (JFR, L. Brey, PRL 2004)

• Confine Photons (increase Rabi)(G. Chiappe, JFR et al., condmat 2004)

Optical RKKY in the Cavity-QD system:•Photons are treated quantum mechanically•Mn-exciton interaction is treated exactly•Photon-exciton interaction is treated exactly

Cavity Dot System. State of the Art

J. P. Reithmaier et al., Nature 432, 197 (2004)

III-V

g=0.1 meV g=16 meV

M. Obert, APL 84,1435 (2004)

Magnetic tuning in excitonic Bragg structures of (Cd,Mn)Te/(CdTe)J. Sadowski, H. Mariett, A. Wasiela, R. André, Y. Merle d’Aubigné, T. DietlPhys. Rev. B56, R1664 (1997)

II-VI

Cavity Dot System

1P,0X

0X,0P

1X,0P

Photon

LOWER ENERGY EXCITED STATE:Half and Half

Exciton

0

Cavity Dot System

Exciton

1P,0X

0X,0P

1X,0P Photon

1P+0X

1X,0P

LOWER ENERGY EXCITED STATEMOSTLY Photon

0

Cavity Dot System

Exciton 1P,0X

0X,0P

1X,0P

Photon

LOWER ENERGY EXCITED STATEMOSTLY Exciton

0

Single Spin conditional Cavity Tuning

1P,0X

0X,0P

1X(+1),0P(-)Mn(-5/2)

Photon

LOWER ENERGY EXCITED STATEMOSTLY Exciton

Single Spin conditional Cavity Tuning

1P,0X

0X,0P

Photon

LOWER ENERGY EXCITED STATEMOSTLY Exciton

1X(+1),0P(-)Mn(+5/2)

Cavity + QD exciton + 2 Mn

G. Chiappe, JFR, et al., condmat 2004

Cavity –QD exciton – 2 Mn

2,1'''' )()(

21

),,(

IIeh

ehhehe

dc

MccIJddIJ

bcddcb

ddEccEbbHF

G. Chiappe, JFR, et al., condmat 2004

Single Cavity mode, Single exciton

CAVITY DOT spin correlationT= 1 Kelvin

121 MM

REGION I

REGION III

REGION II

0

0

1.50

1.00

0.50

BULK Tc (ORKKY)

CAVITY DOT spin correlationT= 1 Kelvin

121 MM

OutlookIncoherent exciton coupling (magnetic polarons)

Experiments and theory

Virtual excitons (ORKKY)

Theory

Polariton exciton (QORKKY)

TheoryExperiment: Planar Cavities with Mn

Condensed exciton coupling (BEC-RKKY)

Theory (GIANT POLARON)PRB 1998, Kavokin

CONCLUSIONS

• New mechanism for ferromagnetism: coherently photoinduced

• Cavity + Spin Doped Dot: non-trivial spin-photon-exciton correlations

Email: jfrossier@ua.esSlides available in www.ua.es/personal/jfrossier/