L.BesombesY.Leger H. Boukari D.FerrandH.Mariette

J. Fernandez-Rossier

CEA-CNRS team « Nanophysique et Semi-conducteurs »

Institut Néel, CNRS Grenoble, FRANCE

Department of applied physics, University of Alicante, SPAIN

Optical control of an individual spin

Introduction

Ultimate semiconductor spintronic device: Single magnetic ion / individual carriers

-Control of the interaction between a single magnetic atom and an individual carrier.(spin injection, spin transfer)

-Manipulation of an individual spin (memory, quantum computing)

II-VI Semi-Magnetic semiconductor QDs

Localized carriers

Magnetic doping (Mn: S=5/2)

…Towards a single spin memory.

Theoretical proposals

Transport: A single QD containing a Mn atom could be use as a spin filter

Nano-magnetism : electrical control of the magnetism.

Hawrylak et al. Phys. Rev. Lett. 95, 217206 (2005)

Qu et al. Phys. Rev. B74, 25308 (2006)

Memories : writing and reading of the spin state of a single Mn atom.

A.O. Govorov et al., Phys. Rev. B 71, 035338 (2005)

1. Probing the spin state of a single Magnetic atom - II-VI magnetic self assembled QDs - Carriers-Mn exchange interaction - Importance of QD structural parameters on the spin detection (Shape anisotropy, valence band mixing)

2. Carrier controlled Mn spin splitting

- Anisotropy of the hole-Mn interaction - Charge tunable Mn-doped QDs

3. Carriers and Mn spin dynamics

Outline

UHV-AFM image of CdTe QDs on ZnTe.UHV-AFM image of CdTe QDs on ZnTe.

QDs density: 5.109 cm-2

Size: d=15nm, h=3nm(Lz<<Lx,Ly)

TEM image of CdTe QDs on ZnTe.TEM image of CdTe QDs on ZnTe.

Individual CdTe/ZnTe QDs

1950 2000 2050 2100

d 0,25 m

d 0,5 m

d 20 m

6,5 MLs

PL

Int

ensi

ty (

arb.

uni

ts)

Energy (meV)

meV50

eV50

100 m

Micro-spectroscopy.Micro-spectroscopy.

Jz=+1

Jz= -1

Jz= - 2

Jz= +2

G.S.

B=0 B=0

eh

eh

- +

meV10

e: spin 1/2h: anisotropic (Jz=3/2)

Jz= -3/2

Jz= -1/2

Jz= +3/2

Jz= +1/2

Sz= +1/2Sz= -1/2

+ -

e

hh

lh

Optical selection rules:

z

Optical transitions in an individual QD

Electrical control of the charge.

Transfer of holes from the surface states: p type doping of the QDs.

V

p-ZnTe

CdTe

Gated charged quantum dots

Te

Cd

Mn

•Mn remplace Cd: Mn2+

•Mn2+ S=5/2, 2S+1=6

Cd: 3d10 4s2

Mn: 3d5 4s2

Exchange interaction:

•Mn - electron

•Mn - hole

)x (SMJ IeI

Ie

I

IhIh )x(SMJ

Mn doped II-VI QDs

Electron: σ = 1/2

Hole: jZ = ±3/2

Mn atom: S = 5/2

nm

nm

h

The presence of a single magnetic atom completely control the emission structure.

Measurement of the exchange interaction energy of the electron, hole, Mn

Phys Rev Lett. 93, 207403 (2004)

Emission of Mn-doped individual QDs

2zJ

1zJ

X X+Mn2+

Sz = ±5/2, ±3/2, ±1/2

Mn2+

-5/2Jz = -1eh Jz = +1

eh

-3/2

-1/2

+1/2

+3/2

+5/2Jz = -1eh

+5/2

+3/2

+1/2

-1/2

-3/2

-5/2

Exchange constant: s-d, >0p-d, <0

Jz = +1eh

Heavy holeexciton

))S.jS.j(2/1S.j(I

))S.S.(2/1S.(I

zzMnh

zzMne

Mn2+

Heavy-hole exciton / Mn exchange coupling

2zJ

1zJ

X X+Mn2+

Heavy holeexciton

))S.jS.j(2/1S.j(I

))S.S.(2/1S.(I

zzMnh

zzMne

Mn2+

-

-5/2

+5/2

…

+

+5/2

-5/2

…

1 photon (energy, polar) = 1 Mn spin projection

Overall splitting controlled by Ie-Mn and Ih-Mn .

Heavy-hole exciton / Mn exchange coupling

Magnetic field dependent PL intensity distribution.

NMn=0 NMn=1

Mn-doped individual QDs under magnetic field

eh Mn2+

eh

Mn2+

eh Mn2+

Mn2+

B

eh Mn2+

+-

B

Jz = -1 Jz = +1

gMn=2

Mn spin conservation

Mn spin polarization

Boltzmann distribution of the Mn-Exciton system:

latticeeff TT

K5TLatt

Teff=12K

Polarization of the Mn spin distribution

Resonant excitation

Complex excited states fine structure

Selection of Mn spin distributionand

spin conservation during the lifetime of the exciton.

Statistic Mn spin distribution

B=0T

S.I Mne

j.I he

zzBhzzBe BjμgBσμg

2B

zzMnh .Sj I

zzBMn BSμg

-1 0 1 2

Energy (meV)

Th.Exp. Effective spin Hamiltonian:

Carriers-Mn exchange coupling

- X-Mn Overlap- QD shape- Strain distribution

Ie-Mn in a flat parabolic potential:

26nmd

3nmLz

Exchange integrals controlled by the overlap with the Mn atom.

Decrease ofX-Mn overlap

1.3 meV

Detection condition: Exciton-Mn overlap

Influence of the QD shape

Phys Rev Lett. 95, 047403 (2005)

Influence of the valenceband mixing

Jz=+ - 3/2

Jz=+ - 1/2

Sz= +- 1/2 e

hhlh

Phys Rev B. 72, 241309(R) (2005)

QD3QD1 QD2

Heavy-hole + Mn

Detection condition: Structural parameters

Inhomogeneous relaxation of strain in a strained induced QD (Bir & Pikus Hamiltonian):

0.. SjSjIMnh

|3/2> |1/2> |-1/2> |-3/2>

|3/2> = c1 |3/2>+ c2 |-1/2> c1>>c2

|-3/2> = c3 |-3/2>+ c4 |1/2> c3>>c4

~

~

<3/2| j - |-3/2> = 0~ ~ via cross components because

12

3,

2

3

13

10

3

2

2

1,

2

3

k

E

Valence band mixing in strained induced QDs

Allows simultaneous hole-Mn spin flip

Possibility to flipfrom jz= +3/2 to -/3/2 via light holes

Effective h-Mn interaction term in the Heavy hole Subspace

eh

eh

lh : Heavy-light hole

mixing efficiency

))..(.( SjSjSjIlhzzMnh

2zJ

1zJ

X X+Mn2+

~~

Influence of valence band mixing

Allows simultaneous hole-Mn spin flip

Effective h-Mn interaction term in the Heavy hole Subspace

eh

eh

lh : Heavy-light hole

mixing efficiency

))..(.( SjSjSjIlhzzMnh Exp.

Th.

Emission of “non-radiative” exciton states

Possibility to flipfrom jz= +3/2 to -/3/2 via light holes

~~

Phys Rev B. 72, 241309(R) (2005)

Influence of valence band mixing

X-Mn in transverse B field«0»

B//

Faraday

B┴

Voigt

Voigt: Complex fine structure…Suppression of the hole Mn exchange interaction

Faraday:Zero field structure is conserved

001

001

«+1 »«-1 »

Phys Rev B. 72, 241309(R) (2005)

1. Probing the spin state of a single Magnetic atom - II-VI magnetic self assembled QDs - Carriers-Mn exchange interaction - Importance of QD structural parameters on the spin detection (Shape anisotropy, valence band mixing)

2. Carrier controlled Mn spin splitting

- Anisotropy of the hole-Mn interaction - Charge tunable Mn-doped QDs

3. Carriers and Mn spin dynamics

Increase of the excitation density

Increase of the number of carriers in the QD.

Formation of the biexciton(binding energy 11meV)

Similar fine structure for the exciton and the biexciton

.

.

.

ehX

X2

eh

Biexciton in a Mn-doped QD

Optical control of the magnetization:

- One exciton splits the Mn spin levels- With two excitons, the exchange interaction vanishes…

X2 (J=0)

X, J=±1

G.S.

σ +

σ -

Phys Rev B. 71, 161307(R) (2005)

Carrier controlled Mn spin splitting

Charge tunable sungle Mn-doped QDs allow us to probe independantly the interactions between electron and Mn or hole and Mn

eh

eh

Phys Rev Lett. 97, 107401 (2006)

Gated charged Mn-doped quantum dots

Ie-Mn = 40 μeV

Ih-Mn(X+) = 95 μeVIh-Mn(X) = 150 μeVIh-Mn(X-) = 170 μeV

♦ The hole confinement is influenced by the Coulomb attraction

X+, Mn X, Mn X-, Mn

Mn

h

e

Increasing the hole-Mn overlap by injecting electrons in the QD

X+, Mn hardly resolved

eh

eh

Variation of hole-Mn exchange interaction

J=3

J=2

Final state:1 e + 1 Mn

•Isotropic e-Mn interaction•Anisotropic h-Mn interaction

Initial state:1 h + 1 Mn

eh

)S.j(I zzMnh

eh

2

5

2

5

2

5

2

5

Negatively charged exciton in a Mn doped QD

J=3

J=2

2

5

♦ Optical transitions between:

hzeeMnz jSi

eMnzSf

Proportional to the overlap:

,SJ,J zz

Eigenstates of He-Mn

Jz=-1

Optical recombination of the charged exciton

2

56

6

13,3

2

56

6

13,3

J=3

2

35

2

51

6

12,3

2

14

2

32

6

11,3

2

51

2

35

6

12,3

2

32

2

14

6

11,3

2

13

2

13

6

10,3

J=2

2

5

2

5

Energy

Prob

abil

ity

1

Optical recombination of the charged exciton

J=3

J=2

2

5

2

5

2

31

2

55

6

12,2

2

12

2

34

6

11,2

2

55

2

31

6

12,2

2

34

2

12

6

112,

2

13

2

13

6

10,2

Energy

Prob

abil

ity

1

2

5

2

5

Optical recombination of the charged exciton

J=3

J=2

2

5

2

5

Energy

Prob

abil

ity

1

e-Mn: isotropich-Mn: anisotropic

2

5

2

5

Optical recombination of the charged exciton

J=3

J=2

Final state:1 e + 1 Mn

Initial state:1 h + 1 Mn

eh

))..(.( SjSjSjIlhzzMnh

(+3/2,-1/2)(-3/2,+1/2)

Phys Rev Lett. 97, 107401 (2006)

Charged exciton in a single QD: Influence of VBM

J=3

J=2

Final state:1 e + 1 Mn

Initial state:1 h + 1 Mn

eh

))..(.( SjSjSjIlhzzMnh

(+3/2,-1/2)(-3/2,+1/2)

Charged exciton in a single QD: Influence of VBM

♦ X-, Mn ♦ X+, Mn

e, Mn

h, Mn

h, Mn

e, Mn

♦ Reversed initial and final states

J=3J=2

Negatively / Positively charged Mn-doped QDs

Heisenberg

ST

Q=-1 Q=0 Q=+1

Free

hh

Ising

Mz

Mn+1h= Nano-Magnet

En

ergy

Gated controlled magnetic anisotropy

1. Probing the spin state of a single Magnetic atom - II-VI magnetic self assembled QDs - Carriers-Mn exchange interaction - Importance of QD structural parameters on the spin detection (Shape anisotropy, valence band mixing)

2. Carrier controlled Mn spin splitting

- Anisotropy of the hole-Mn interaction - Charge tunable Mn-doped QDs

3. Carriers and Mn spin dynamics

Spin dynamics vs photon statistics

1 photon (σ, E) 1 Mn spin state

1 Mn atom Sz

If Sz(t=0) = -5/2

t0

1

~1/6

-5/2

?

P (Sz = -5/2)

-

-5/2

+5/2

…

+

+5/2

-5/2

…

Photon statistics ?

Correlation measurement on single QDs

Use of a SIL to increase the signal

Select a QD witha large splittingto spectrally isolate a Mn spin state

PL

int

(arb

. uni

ts)

20402039203820372036 Energy (meV)

Single emitter statistics :

Antibunching: The QDs cannot emit two photons with a given energy at the same time

Whole PL autocorrelation

Single Mn spin dynamicsP

L in

t (a

rb. u

nit

s)

20402039203820372036 Energy (meV)

Auto Correlation on one linein one polarization

One Mn spin projection

2zJ

1zJ

X X+Mn2+

E

τX-Mn

Photon bunching at short delay

8 ns

t

+, -5/2)

PL

int

(arb

. un

its)

20402039203820372036 Energy (meV)

Auto Correlation on one linein one polarization

σ +

One Mn spin projection

2zJ

1zJ

X X+Mn2+

E

τX-Mn

Single Mn spin dynamics

Mixing between Mn spin relaxation time and X-Mn spin relaxation time

2 x P0

P0

3 x P0

Power dependence

Single Mn spin dynamics

-

-5/2

+5/2

…

+

+5/2

-5/2

…

Direct evidence ofthe spin transfer

PL

int

(arb

. un

its)

20402039203820372036 Energy (meV)

Polarization Cross-Correlation

σ +

One Mn spin projection

σ -

Influence of magnetic field?...To be continued…

Optical probing of a single carrier/single magnetic atom interaction.

- The exchange coupling is controlled by the carrier / Mn overlap.

- BUT, real self assembled QDs: - Shape anisotropy- Valence band mixing

…. Store information on a single spin?

Hole-Mn complex is highly anisotropic but non-negligeable effects of heavy-light hole mixing

Charged single Mn-doped QDs: Change the magnetic properties of the Mn with a single carrier.

Summary

Photon statistics reveals a complex spin dynamics.