Spin effects in diluted magnetic semiconductors

M. Vladimirova, P. Barate, S. Cronenberger, F. Teppe and D. Scalbert, 

Groupe d'Etude des Semi-conducteurs, CNRS-Université Montpellier 2 France 

C. Misbah 

Laboratoire de Spectrométrie Physique, CNRS- Université Joseph-Fourier Grenoble, France 

T. Wojtowicz, J. Kossut 

Institute of Physics, Polish Academy of Sciences, Warszawa, Poland

•What is DMS : electrons, holes, magnetic ions and polarized light

•Manipulation of magnetic ions spins by light

•Pump-induced Kerr rotation technique

•Examples of spin effects in CdMnTe QWs : inhomogeneous Mn spin heating and mixed e-Mn spin excitations

Diluted magnetic semiconductors

RnAtPoBiPbTlHgAuPtIrOsReWTaHfLaBaCs

XeITeSbSnInCdAgPdRhRuMoNbZrYSrRb

KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK

ArClSPSiAlMgNa

NeFONCBBeLi

HeH

VIIIVIIVIVIVIIIIII

3d

II

Mn 4s2 3d5

S=5/2 Localized spins -5/2-3/2

-1/21/23/25/2

Mn 3d5

BC

BV

Eg (x)~2 eV

3 eV

CdMnTe

N0 concentration of cationsX Mn fraction

Diluted magnetic semiconductors

CdTe CdMnTe

CdMnTe Paramagnetic

n-CdMnTe Paramagnetic

p-CdMnTe Ferromagnetic(Tc=2K)

Super exchange

Localized electrons interacting with magnetic ions

Carriers mediated interaction between magnetic moments

ferromagnetism

Antiferromagnetic clucters

Magnetic polaron

T. Dietl and J. Spalek,PRL 48, 355 (1982)

Exchange interaction

ii

iexch SsRH 2)(

ze SxN 0

“Overhauser shift”

in the mean field approximation

exchange integral

BMn

eeMn g

B

zh SxN 0

BMn

hhMn g

B

0

0

K

~meV ~eV

Exchange coupling is ferrromagnetic for electrons and antiferromagnetic for holes

Out-of-equilibrium electrons depolarize Mn spins

Out-of-equilibrium holes polarize Mn spinsezee snK

“Knight shift”Bee g

KB

Bh

hh g

KB

h

zhh snK

Mn

e- h+

B

Mn

B

Giant Zeeman Splitting

-3/2

-1/2

+1/2

+3/2

-1/2

+1/2

Energy

- +

BgSxN Beze 0

BgSxN Bhzh 0

eVN 22.00

eVN 10

0 2 4 60,0

0,1

0,2

0,3

xeff

=0.2%T=2K

Spi

n sp

littin

g (m

eV)

Magnetic field (T)

CdMnTeelectron

Magnetic field

Allowed optical transitions

Large splitting only at low temperatures (T<10K)

0 2 4 60,0

0,1

0,2

0,3

T=15K

T=10KT=5K

xeff

=0.2%

T=2K

Spi

n sp

littin

g (m

eV)

Magnetic field (T) 0,0 0,2 0,4 0,60,00

0,02

0,04

0,06

x eff

Mn content x

Nearest neighbors Mn-Mn pairs do not contribute in the effective field x → xeff; ;T→T+T0

~x(1-x)12

Gai, Planel, Fishman Solid State Commun 29, 435 (1979)

Modified brillouin function x → xeff; ;T→T+T0

)2

1coth(

2

1)

2

12coth(

2

12)(

SS

SSBS

0TTk

SBg

B

BMn

2

5S

effB

Beffexch Tk

BgBxSNE

Mn2/50 2

5

exch

BMnzeffBMn gSNxgM

0

Magnetization = Mn density x Mn spin polarization

0 2 4 6 8 10

2K

Magnetiz

atio

n

Magnetic field (T)

5K

0 2 4 6 8 10

1%2K

Magnetiz

atio

n

Magnetic field (T)

0.2%

Temperature dependence Mn content dependence

Optically excited CdMnTe QWs

CB

VB+3/2-3/2

+1/2

-1/2

-1/2

+1/2

se=1/2

sh=3/2 hh

lh

Band diagram Magnetic field in Voigt configuration

Hole•Strong hh-lh splitting•spin locked in the growth direction ↔ g-factor ~0•Fast spin relaxation ~few ps

Electron • Zeeman splitting + Exchange•excitation with circularly polarized light pulse->spin precession•Spin relaxation ~ few 10 ps

B

h

How does the polarized light affect Mn ions

1. Mn spin heating via mutual spin flips with optically created electrons

2. Mn spin cooling via mutual spin flips with optically created holes (bulk)

3. Impulsive coherent rotation of Mn by hole spin locked in the growth direction (QWs)

4. Magnetic polaron

How does the polarised light affect the Mn ions

Magnetic polaron

EF

NxSNMP /2

10

T. Dietl and J. Spalek,PRL 48, 355 (1982)

Exchange energy gain :

Mean field approximation is not valid at low fields

N Mn ion spins

e or h

Electrons (holes) localized by the potential fluctuations or on donors

z

x

y

B

electronsholes

MnM•Electrons : photocreated +2DEG -> spin precession

•Hole spin locked in growth direction -> impulsive coherent rotation of Mn

Crooker et al PRL 77, 2814 (1996)

Akimoto et al PRB 57, 7208 (1998)

Impulsive coherent rotation of Mn

How does the polarized light affect the Mn ions

XZ is a QW plane

How does the polarised light affect the Mn ions

Energy and polarization transfer via spin-flip scattering

Ryabchenko et a, Sov. Phys. JETP 55, 951 (1982)CdMnTe 5%, exchange scattering with holes → Mn spin cooling

1) With electrons

2) With holes

,SF<< SL

Electron or hole spins out of equilibrium

Mn spins, TS

Lattice, T=2K

e-Mn spin-flip time

Spin-lattice relaxation

Other spin relaxation mechanisms

s

smSB

B

s

smSB

B

Tk

gBm

Tk

gBmm

S

exp

expTS

10Nup/Ndown

Mn

e- h+

B

Mn

B

2 levels system

In general

F()

n-

n+

-

+

= +

F

M

Rotation of the polarization plane in magnetic media

Magneto-optical Kerr (Faraday) effect

Spin polarisation

• created by circularly polarized light

• probed by linearly polarized light as a function of time delay between pump and probe pulses

Polarisation of the probe beam is rotated after

reflection (transmission) from the polarized media

t

probe

K()

sample

pump

Pump-induced Kerr (Faraday) rotation

lock-in n°2

Chopper

probepumpff

prob

e

pum

p

Elasto-optical modulator

Del

ay li

ne

PC

Optical bridge

lock-in n°1

2

T > 1.8 K

0-6 T

Al 2O

3:T

iM

ille

nia

100 fs-1 ps

CdMnTe QWs

BarrierCdMg0.27Te (150 ML)

QW - CdMn0.0052Te (8 nm)

Buffer CdTe (6.7 µm)

SubstratGaAs (100)

CdMg0.27Te (10 nm)

CdMg0.27Te (15 nm)

CdMg0.27Te (0.7 µm)

CdTe/CdMgTe SL

ZnTe (3 nm)

Iodine doped

1.9 nm 4.9 nm

10 nm

QW

barrier

barrier

QW1 QW2 QW3 QW4

1010 3.1010 7.1010 1011

Iodine doped

Samples •Warsaw (GaAs substrate)•Grenoble (CdZnTe substrate)

Time-domain spin resonance

0 1 2 3 4 50,00

0,05

0,10

(T

Hz)

B(T)

g=1.5

g=2

h

Bg BMnMn

0 1 2 3 4 5 60.0

0.2

0.4

0.6

T=2K

(T

Hz)

B (T)

0,00 0,05 0,5 1,00

40

80

120

0 20 40 200 400Delay (ps)

K (a

rb.u

nits

)

T = 1.9 KB = 2 T

FFT

electrong=2

g=1.5

(THz)

BgTk

BgBxNh Be

effB

Beff

Mn

2/50 2

5

2

5

Xeff=0.45%

First example: Spatial instability of Mn spin temperature in CdMnTe QWs

Spontaneous magnetization patterning

0,00 0,10 0,50 1,000

electrong=2

g=1.5

B = 5 T

(THz)0,00 0,10 0,50 1,00

B = 2 T

electron

g=2

g=1.5

(THz)

xeff=0.45%, T=2K, P=15W/cm2

at high field and excitation density formation of domains with distinct Mn spin temperatures

0 1 2 3 4 5 60.0

0.2

0.4

0.6

Tbath

= 1.8 K

Iexc

= 15 W/cm2

(T

Hz) 8.8 K

2 K

B (T)0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

Tbath

= 1.8 K

Iexc

= 3 W/cm2

(T

Hz) 2 K

B (T)

High excitation densityLow excitation density

5 10 150

2

4

6

8

10B=4.5T

Hot ColdT

(K

)

Excitation density (W/cm2)

•Domain temperature does not depend on magnetic field

•Domain temperature does not vary much with excitation power density

Summary of experimental results

High excitation density G

High magnetic field B

Resonant excitation Eexc

Mn spin temperature domains

•Equipartition of domain areas

•Thot increases slightly with excitation density

•Two electron spin resonances in CdMnTe QW under femtosecond pulse excitation

Mn

e

Interpretation : Positive feedback loop for Mn heating

•e generation

•e recombination

•e diffusion

•Mn diffusion

•e-Mn spin-flip

•Mn spin relaxation

cold hothot cold cold

x

Rate equations accounting for diffusion

Electron diffusion and

drift

Mn spin diffusion

NNV 4

5

TkEV BZ /)2(exp

Exchange potential

Ne

Mn

N

+-

EZ

n+

n-

2V

dt

dN

dt

dNdx

NdDNNNnNn

dt

dN

dx

dV

en

dx

dnD

dx

dNnNn

nG

dt

dn

dx

dV

en

dx

dnD

dx

dNnNn

nG

dt

dn

Mneq

2

2

2

2

2

0

Spin flip rates

Linear stability of the steady-state homogeneous solution

Time and space derivatives = 0

n+0, N+

0…

n+ = n+0 + A+exp(t+iqx);

N+= N+0+B exp(t+iqx)

Calculate (q) in the adiabatic approximation

Linearly stable if (q) < 0 for all q

Unstable for q such that (q) > 0

bath

Mn

zzkTEE / /

0gg

bathsskTEE / DDd

Mn/1

Relevant dimensionless parameters :

Field Generation rate Temp-reMn and el-n relative

diffusion

0 50.0

0.5

1.0

0 5 10-2

-1

0

q

N+

g

Domain sizes!

mlq

lsd

122

2 0 5

0.0

0.5

1.0

0 5 10-2

-1

0

q

N+

g

q0)( q:q

MnD

q

Mn diffusion

defines the critical instability

wavelength

destroys the instability

14

02.0

3

7.0

s

z

E

d

E

g

Linear stability of the steady-state homogeneous solution

0 1 2 3

2

4

6

8

10

12

TMn

(K)

g

unst

able

stab

le

stab

le

1

2

3

4

5

0.4 0.8 1.2

d=0.05

d=0.005

Ez

d=0

g0

g=1 25W/cm2two threshold

values !

bath

Mn

zzkTEE / /

0gg

bathsskTEE / DDd

Mn/1

Relevant dimentionless parameters :

Field Generation rate Temp-reMn and el-n relative

diffusion

KT

TB

Ez

2

3

2

Numerical solution : Hysteresys loop

bath

Mn

zzkTEE / /

0gg bathss

kTEE / DDdMn

/1

Tbath=2K

= 10-10 s

= 104 s-1

0 = 10-4 cm2 /s

N0 = 220 meV

x = 0.0045

g = 1018 cm-2 s-1

g=1 0.25 W/cm2

DMn/D=10-90 1 2

0 25 50

2

4

6

8

2 4

3 6

2

4

6

8

g=0.7

EZ

Ez=3

T(K)

Magnetic field (T)

g

Excitation density (W/cm2)

Es=14

d=0.005

Second example: Collective spin-flip excitations of electron and Mn

0 2 4 60,0

0,1

0,22K

Spi

n sp

littin

g (m

eV)

Magnetic field (T)

electron

Mn

Spin-flip excitation energies

Anticrossing?

resonance

x=0.002

•Electrons: Exchange and Zeeman splittings have different signs (>0)

•Two coupled spin flip transitions

Here exchange splitting saturates Zeeman splitting mainly, ge=-1.5

BgTk

BgxBNE Be

B

BSFe

Mn

2/50 2

5

2

5

BgE BMnSFMn

Mn e-

Spin-flip Raman scattering

F. J. Teran et al, PRL 91, 077201 (2003)

J. König and A. H. MacDonald PRL 91, 077202 (2003)

Experiments :

•EPR and Raman scattering

•Dynamics?

Theory :

•ferromagnetism possible in n-CdMnTe QWs, Tc~0.4mK

•Finite spin relaxation times and interacting 2DEG susceptibility not taken into account

CdMnTe QW : ~20eV

Samples

CdZnTe

15% ZnCB

VBI2+

2DEG

CdMnTe QW

Al2+

CdZnTe

15% Zn

10nm

2DEG density

M1120 ne=0.7x1011 cm 2

M1118 ne=2.2x1011 cm-2

LSP, Grenoble, FranceV. Huard et al, PRL 84, 167 (2000)

~0.2% Mn

0

5.5T

5.6T

5.7T

5.8T

5.9T

6.0T

6.05T

Pump-probe delay (ps)

Ke

rr r

ota

tion

(a

rb. u

nits

)

6.1T

400 0,10 0,15 0,20

5.5T

5.6T

5.7T

5.8T

5.9T

6.0T

6.05T

Frequency (THz)

FF

T (

arb

. u

nits

)

6.1T

M1118 (ne=2.2x1011cm-3)

Pump-probe delay (ps) 4000

5.7T

Ker

r ro

tatio

n (a

rb. u

nits

)

5.8T

5.9T

5.95T

6T

6.05T

6.1T

0,10 0,15 0,20

5.7T

5.8T

5.9T

5.95T

6T

6.05T

6.1T

Frequency (THz)

FF

T (

arb.

uni

ts)

M1120 (ne=0.7x1011cm-3)

0 2 4 60,00

0,05

0,10

0,15

0,20

5,8 6,00,16

0,17

Fre

qu

en

cy (

TH

z)

Magnetic field (T)

x=0.002T=3.8K

)cos()exp(

)cos()exp(

)cos()exp()exp(

MnMnMn

Mn

hhK

tt

A

tt

B

tt

Bt

A

Summary M1120 (ne=0.7x1011cm-3)

Mean field model

0

0

eeeMneee

MnMnMneMnMnMn

MMBBMdt

Md

MMBBMdt

Md

Coupled Bloch equations

Overhauser field

Knight field

Relaxation terms

We consider small deviations of the magnetization from z-axis and look for the dynamics of the transverse component of the magnetization

B

MnM

eM

z

x

y

MM

eB

MnB

Mean field model

B

MnM

eM

z

x

y

MM

eB

MnB

coupled oscillators : Mn, ecoupling energy K2

2/)(2 MneK

Strong vs weak coupling

2/2 MneK

)Im()Im(

)Re()Re(

)Im()Im(

)Re()Re(

K, depend on B, T, ne, NMn

Mn << e

anticrossing Relaxation rate changes

2

2

42

KMneMne

2/ KeMn

eee

MnMnMn

i

Ki

zSxN 0

ze snK

+ Initial conditions : photocreated electrons and holes +impulsive coherent rotation of Mn

titiy

e

titiyMn

eBeBtM

eAeAtM

Solution of Bloch equations

B

+ , -, eigen frequencies of the mixed modes

B

MnM

eM

z

x

y

MM

eB

MnB

Summary M1120 (ne=0.7x1011cm-3)

5,5 6,0 6,50,150

0,155

0,160

0,165

0,170

0,175

0,180

Fre

quen

cy (

TH

z)

Magnetic field (T)

5,5 6,0 6,510

100

1000

Tim

e (p

s)Magnetic field (T)

2=20eV

K=0.3eV

2

2222

MneK

We should suppose that electron spins are fully polarized

tMP=40ps

te=20 ps, tMn=2ns

zSxN 0

ze snK =1.2 meV

Summary M1118 (ne=2.2x1011cm-3)

5,0 5,5 6,0 6,50,150

0,155

0,160

0,165

0,170

0,175

0,180

Fre

quen

cy (

TH

z)

Magnetic field (T)5,0 5,5 6,0 6,5

10

100

1000

Tim

e (p

s)Magnetic field (T)

30eV

2

2222

MneK

Electron spins are almost fully polarized

2DEG : spin polarization is 3 times stronger than expected from Fermi distribution

te=20 ps, tMn=2ns

K=0.4 eV, =1.2 meV

tMM=40ps

Thank you !

Strong vs weak coupling

0 1 2 3 4 5 6 710

100

1000

Tim

e (

ps)

Magnetic field (T)

0 1 2 3 4 5 6 70,00

0,05

0,10

0,15

0,20

Fre

qu

en

cy (

TH

z)

Magnetic field (T)

0 1 2 3 4 5 6 710

100

1000

T

ime

(p

s)

Magnetic field (T)

0 1 2 3 4 5 6 70,00

0,05

0,10

0,15

0,20

Fre

que

ncy

(T

Hz)

Magnetic field (T)

SC WC

•SC : At resonance mixed modes have the same relaxation rate

•WC : Strong modification of relaxation times

eSC<e

WC

Mn << e

•The transition SC->WC is controlled by e

Dynamics of coupled spins

0 100 200

Me

Time (ps)0 100 200

MMn

Time (ps)

0 100 200

MMn

Time (ps)0 100 200

Me

Time (ps)

Strong coupling

Weak coupling

Rabi period

Rabi period

Magnetic polaron

EF

NxSNMP /2

10

T. Dietl and J. Spalek,PRL 48, 355 (1982)

Exchange energy gain :

Mean field approximation is not valid at low fields

N Mn ion spins

e-

Electrons localized by the potential fluctuations

Magnetic polaron at spin-flip resonance

EeSF>>EMn

SF

B=0 Ee

SF=EMnSF=0

R. Fiederling et al, PRB 58, 4785 (1998)

i

iMneU

N 1

2

1

2

Resonance condition EeSF=EMn

SF

NSxNN

Hi

iMnexche /2

12 0

NxSNMP /2

10

N degenerate states

N-1 degenerate states

<Sz> ~5/2-> 2~MP

...e ..i

iMn

i

iMneL

N 1

2

1

Magnetic polaron /Mean field

zez snSxNK 0222

Magnetic polaron

2DEG

• if <sz> = 1/2

•If if <sz> < 1/2

NSxN /22 0

N Mn ion spins

e-

(N=NMn/Ne)

provides the information on the electron spin polarization

NSxNN

Hi

iMnexche /2

12 0

Time-resolved Kerr rotation

B

tpump

probe

K Sy+

- z

x

y

•100 fs pulses spectrally filtered -> ~ ps resolution

•Excitation power 250 W, resonant with hh exciton

•Pump-probe ratio 2:1

•Sy may include electron, Mn, hole or mixed mode contribution

)cos()exp(

)cos()exp(

)cos()exp()exp(

MnMnMn

Mn

hhK

tt

A

tt

B

tt

Bt

A

TRKR at resonance

0,00

0,01

0,02

250150

Ker

r ro

tatio

n (a

rb.u

nits

)

Pump-probe delay (ps)50

B=5.9TT

eff=3.6K Hole spin relaxarion ~few ps

Free Mn precession ~ few ns

M1118

ne=2.2x1011 cm-3

•Mn : non interacting modes or electron-free spatial regions?

•Relative contribution of Mn and electron spin polarization in TRKR signal

Questions

titi

Mn

titie

eAeAtS

eBeBtS

?

few 10 ps

Conclusions

• Measuring the dynamics of collective electron – Mn spin flip excitations : Rabi oscillation between pure electron and Mn states

• Manipulating 2DEG : h ->hh -> Mn ->2DEG• Coupled modes splitting can be used as a tool to

measure the 2DEG susceptibility : strong enhancement of 2DEG polarization is observed

• Relative contribution of e- and Mn2+ spins in the TRKR signal

• How one can increase the coupling and obtain longer spin relaxation times? Reduce inhomogeneous broadening!

Perspectives

n-CdMnTe QWs

CdZnTe

15% ZnCB

VBI2+

2DEG

CdMnTe QW

Al 2+

CdZnTe

15% Zn

10nm

In-plane localization potential

EF

EF

0.2% Mn

this work

F. Teran and this work

Microcavities with DMS

Magnetic tuning of exciton mode

microcavity with 2 DMS QWs Reflectivity spectra for + polarization

+8 T

-8 T

0 T

H. Ulmer-Tuffigo et al, Superlattices and Microstructures 22, 383 (1997)

QW in a microcavity: QWN 2 N round trips of light in the cavity

A. Kavokin et al, PRB 56, 1087 (1997)

~ 3° in (In,Ga)As/GaAs QW microcavity @ 11.25T

~ 140° in CdMnTe QW microcavity @ 1T

M. Haddad et al, SSC 111, 61 (1999)

Microcavities with DMS QW : Enhanced Faraday rotation