Coherently photo-induced ferromagnetism

in diluted magnetic semiconductors

J. Fernandez-Rossier (University of Alicante, UT), C. Piermarocchi (MS), P. Chen (UCB), L. J. Sham (UCSD), A.H. MacDonald (UT)

Paramagnetic semiconductor (II,Mn)VI can become ferromagnetic when illuminated by coherent unpolarized light of frequency below the semiconductor band-gap.

EGEF

Properties of the Diluted paramagnetic (II(1-x),Mnx)-VI

(II(1-x),Mnx)-VI(Zn(1-x),Mnx)-Se(Zn(1-x),Mnx)-S (Cd(1-x),Mnx)-Te

Mn-Mn interaction: only first neighbors. For x=0.012 • 0.002 coupled to nn (2%)•0.01 is free (80%) -PARAMAGNET

If doped with holes, FERROMAGNET at Tc<2 Kelvin

Laser features:

• Frequency below gap: =EG-L>0• No Photocarriers, no doping

• Intensity (=dcvE0>0.1 meV)

• Polarization state: not relevant

Coherently photo-induced ferromagnetism

This prediction is a logical consequence of:•Experimentally established facts•Theoretical concepts in agreement with experiments

<M>=0

Exchange Interaction. Giant Spin Splitting Selection Rules

L

jsdcMn<M>

jpdcMn<M>

B

Macroscopic Explanation of optical ferromagnetism

EEU L'

Reactive optical energy, due to matter-laser interaction:

MMU

22

•U depends on <M>: U(M)•Ferromagnetism (<M>0) minimizes U (M)•But entropy favours <M>=0

Competition between reactive optical energy and entropy

Electric Field of the Laser

Real part of retarded Optical Response function

MTSkMUTMG B

,

Entropic PenaltyParamagnetic Gain

(Optical Energy)

Functional of Carrier Density Matrix

What is the density matrix of the laser driven (II,Mn)-VI semiconductor?

Density matrix: effect of the laser

L

k

kkH

2

1

Rotating FrameRWA

kU

kL

kE

EH

0

0

2

1

EU(k)

EL(k)

> >(T1)-

1

BBeeH titi LL int

BBeH ti L 2int 1

00

01

2

2

vuv

uvu Coherent

Occupation

0'' L

No absorption= No real carriers

eff= -|J|>0

2

McJJMJ Mneh

Interaction “Bosonic Model”

Laser Matter Linear response (*)

h-Mn, e-Mn MF VCA

Electron-Hole All orders

e-e and h-h Irrelevant (linear response)

Microscopic Theory: Relevant Interactions

•(*) Linear Response: Good if >•OK, since >|J|> and |J|>20 meV

BBgBBMJH

02 1s

Vg

2

McJJMJ Mneh

MJMJMU

V s 11

)0(2

,,1 2

1

2

Microscopic Theory: Bosonic Model

0 1 2M

-1.45

-1.44

-1.43

-1.42

G (

10-2

meV

nm

-3)

(b)

-0.4

-0.2

0S

(10

-2 m

eV n

m-3)

T=115 mKT=105 mK

(a)

-2 -1 0 1 2M

-1.2

-1

U (

10-2

meV

nm-3

)

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

1.50

1.00

0.50

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

•Tc2

•Tc -3

Linear response fails there

Isothermal transitions for (Zn,Mn) S

T=0.5 K

Switching ferromagnetism

on and off!!!

Materials and Lasers

Important material properties:•Robust Excitons•Not much Mn (x=1%)•(Zn,Mn)S, (Zn,Mn)Se•(Zn,Mn)O ??

Laser properties:•Tunable, around material band-gap•Intense lasers•Tc <50 mK with cw laser•Pulse duration longer thanSwitching time•Switching time: interesting question !!!!

ORKKY vs coherently photo-induced FM

jpd jpd

jpd

jsd

jsd jsd

2121 )( SSRRJH

2

13

22 )0(

3

1sMnpdsdc cJJ

SST

The SAME than Bosonic Model

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

Conclusions

•New way of making semiconductors ferromagnetic•Ferromagnetism mediated by virtual carriers•Originated by optical coherence•Possible at T>1 Kelvin (with the right laser)

Phase DiagramAlways

absorbing T

(/J)

Absorbing FM

Coherent PM

Always coherent

PM

PM

FMFM

T=1.5 KT=2.0

K

Interaction ‘BCS’ “Bosonic Model”

Laser Matter All orders Linear response (*)

h-Mn, e-Mn MF VCA MF VCA

Electron-Hole Pairing All orders

Mn-Mn AF s-exc x replaced by xeff x replaced by xeff

e-e and h-h Hartree-Fock Irrelevant (linear response)

Microscopic Theory: Relevant Interactions

* Linear Response: Good if >

No absorption= No real carriers= Optical Coherence:

eff= -|J|>0, where 2

McJJMJ Mneh

Carrier mediated ferromagnetism

MTSkMETMG Bcarrier

,

Entropic Penalty

Paramagneticgain

MSJMEMEcarrier

0

Functional of carrier density matrix

What is the density matrix of the laser driven (II,Mn)-VI semiconductor?

B C

Al Si

N O

P S

Ga Ge

In Sn

As Se

Sb

II

Zn

Cd

Hg

IV VIII VI

Te

EGEF

II-VIZn-SeZn-S Cd-Te

II

B C

Al Si

N O

P S

Ga Ge

In Sn

As Se

Sb

IV VIII VI

Te

Zn

Cd

Hg

Mn

EGEF

Diluted paramagnetic semiconductor

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

Laser features:

• Frequency below gap: =EG-L>0• No Photocarriers

• Intense (=dcvE0>0.1 meV)

• Non circularly polarized

Coherently photo-induced ferromagnetism

II

B C

Al Si

N O

P S

Ga Ge

In Sn

As Se

Sb

IV VIII VI

Te

Zn

Cd

Hg

Mn