Download Mn 2 +

Optical control of an individual spin
L.Besombes
Y.Leger
H. Boukari
D.Ferrand
H.Mariette
J. FernandezRossier
CEA-CNRS team « Nanophysique et Semi-conducteurs »
Institut Néel, CNRS Grenoble, FRANCE
Department of applied physics, University of Alicante, SPAIN
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
Magnetic doping (Mn: S=5/2)
Localized carriers
…Towards a single spin memory.
Theoretical proposals
Transport: A single QD containing a Mn
atom could be use as a spin filter
Qu et al. Phys. Rev. B74, 25308 (2006)
Nano-magnetism : electrical control of the
magnetism.
Hawrylak et al. Phys. Rev. Lett. 95, 217206 (2005)
Memories : writing and reading of the spin state
of a single Mn atom.
A.O. Govorov et al., Phys. Rev. B 71, 035338 (2005)
Outline
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
Individual CdTe/ZnTe QDs
UHV-AFM image of CdTe QDs on ZnTe.
Micro-spectroscopy.
6,5 MLs
QDs density: 5.109 cm-2
TEM image of CdTe QDs on ZnTe.
PL Intensity (arb. units)
d  20 m
 50meV
100 m
d  0,5 m
 50eV
d  0,25 m
Size: d=15nm, h=3nm
(Lz<<Lx,Ly)
1950
2000
Energy (meV)
2050
2100
Optical transitions in an individual QD
B=0
B=0
Jz=+1
e: spin 1/2
h: anisotropic (Jz=3/2)
e
h
Jz= -1
 0  1meV
Jz= - 2
e
h
Jz= +2
G.S.
s-
s+
Optical selection rules:
Sz= -1/2
s+
Sz= +1/2
e
s-
z
Jz= +3/2
Jz= -3/2
Jz= +1/2
Jz= -1/2
hh
lh
Gated charged quantum dots
 Transfer of holes from the surface states: p type
doping of the QDs.
V
p-ZnTe
CdTe
Electrical control of the charge.
Mn doped II-VI QDs
Cd: 3d10 4s2
Mn: 3d5 4s2
hn
Cd
Te
2-3 nm
Mn
•Mn remplace Cd: Mn2+
•Mn2+ S=5/2, 2S+1=6
Electron: σ = 1/2
Exchange interaction:
•Mn - electron J e

I
•Mn - hole
Jh

I
10-15 nm
 

M I  Se ( x I )
 

M I  Sh ( x I )
Hole: jZ = ±3/2
Mn atom: S = 5/2
Emission of Mn-doped individual QDs
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)
Heavy-hole exciton / Mn exchange coupling
Ie- Mn (s z .Sz  1 / 2(s  .S-  s - .S ))
Exchange constant:
s-d, a>0
p-d, b<0
Ih - Mn ( jz .Sz  1 / 2( j .S-  j- .S ))
Mn2+
X
X+Mn2+
e
Jz = -1 h
Jz  1
Heavy hole
exciton
e
Jz = +1 h
-5/2
+5/2
-3/2
+3/2
-1/2
+1/2
+1/2
-1/2
-3/2
+3/2
e
Jz = -1 h
Jz   2
Mn2+
+5/2
Jz = +1
e
h
-5/2
Sz = ±5/2, ±3/2, ±1/2
Heavy-hole exciton / Mn exchange coupling
Ie- Mn (s z .Sz  1 / 2(s  .S-  s - .S ))
1 photon (energy, polar) = 1 Mn spin projection
Ih - Mn ( jz .Sz  1 / 2( j .S-  j- .S ))
X
X+Mn2+
-5/2 +5/2
…
Jz  1
…
+5/2 -5/2
Heavy hole
exciton
Jz   2
s-
Mn2+
s+
 Overall splitting controlled by Ie-Mn and Ih-Mn .
Mn-doped individual QDs under magnetic field
 Magnetic field dependent PL
intensity distribution.
NMn=0
NMn=1
Polarization of the Mn spin distribution
e
h
e
h
Mn2+
Mn spin polarization
Jz = +1
Jz = -1
e
h
Mn2+
e
h
Mn2+
s-
Mn2+
TLatt  5K
Teff=12K
s+
Mn spin
conservation
Boltzmann distribution of the
Mn-Exciton system:
gMn=2
B
Mn2+
B
Teff  Tlattice
Statistic Mn spin distribution
Resonant excitation
B=0T
Complex excited states fine structure
Selection of Mn spin distribution
and
spin conservation during the lifetime of the exciton.
Carriers-Mn exchange coupling
Exp.
Th.
Effective spin Hamiltonian:
Ih - Mn jz .Sz
 
I e- Mn s .S
 

Ie- hs. j

geμBσ z Bz  ghμB jz Bz

g Mn μBS z B z

B 2
- X-Mn Overlap
- QD shape
- Strain distribution
-1
0
1
Energy (meV)
2
Detection condition: Exciton-Mn overlap
1.3 meV
Ie-Mn in a flat parabolic potential:
Decrease of
X-Mn overlap
L z  3nm
d  26nm
Exchange integrals controlled by the overlap with the Mn atom.
Detection condition: Structural parameters
QD1
Heavy-hole + Mn
QD2
Influence of the QD shape
QD3
Influence of the valence
band mixing
Sz= +- 1/2
Jz=+ - 3/2
Jz=+ - 1/2
Phys Rev Lett. 95, 047403 (2005)
e
hh
lh
Phys Rev B. 72, 241309(R) (2005)
Valence band mixing in strained induced QDs
 Inhomogeneous relaxation of strain in a strained induced QD (Bir & Pikus Hamiltonian):
|3/2> |1/2> |-1/2> |-3/2>
E
1/2
-1/2
-3/2
3/2
1/2
-1/2
k
~
~
<3/2| j - |-3/2> = 0
via cross components because
I h-Mn  j .S -  j- .S    0
~
|3/2> = c1 |3/2>+ c2 |-1/2>
c1>>c2
~
|-3/2> = c3 |-3/2>+ c4 |1/2>
c3>>c4
3 1
2
1
,- 
0  
-1 
2 2
3
3
3 3
,-  - 1 
2 2
Influence of valence band mixing
I h-Mn ( jz .S z  e lh ( j .S -  j- .S  ))
elh : Heavy-light hole
mixing efficiency
X
Possibility to flip
~
from jz= +3/2
~
to
-/3/2
via light holes
Effective h-Mn interaction term
in the Heavy hole Subspace
e
h
e
h
Allows simultaneous hole-Mn spin flip
Jz  1
Jz   2
X+Mn2+
Influence of valence band mixing
I h-Mn ( jz .S z  e lh ( j .S -  j- .S  ))
Exp.
elh : Heavy-light hole
mixing efficiency
Possibility to flip
~
from jz= +3/2
~
to
-/3/2
via light holes
Effective h-Mn interaction term
in the Heavy hole Subspace
e
h
Th.
e
h
Allows simultaneous hole-Mn spin flip
Emission of “non-radiative” exciton states
Phys Rev B. 72, 241309(R) (2005)
X-Mn in transverse B field
«0»
001
B┴
«-1 »
«+1 »
Voigt
001
B//
Voigt:
Complex fine structure…
Suppression of the hole Mn
exchange interaction
Faraday
Faraday:
Zero field structure is conserved
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
Biexciton in a Mn-doped QD
X
X2
e
h
e
h
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
.
.
.
Carrier controlled Mn spin splitting
X2 (J=0)
σ+
X, J=±1
σG.S.
Optical control of the magnetization:
- One exciton splits the Mn spin levels
- With two excitons, the exchange interaction
vanishes…
Phys Rev B. 71, 161307(R) (2005)
Gated charged Mn-doped quantum dots
e
h
e
h
Charge tunable sungle Mn-doped QDs allow us to probe
independantly the interactions
between electron and Mn or hole and Mn
Phys Rev Lett. 97, 107401 (2006)
Variation of hole-Mn exchange interaction
e
h
e
h
Ie-Mn = 40 μeV
Ih-Mn(X+) = 95 μeV
Ih-Mn(X) = 150 μeV
Ih-Mn(X-) = 170 μeV
♦ The hole confinement is influenced by the Coulomb attraction
X+, Mn
X, Mn
e
Mn
h
X-, Mn
Increasing the hole-Mn overlap
by injecting electrons in the QD
X+, Mn hardly resolved
Negatively charged exciton in a Mn doped QD
•Isotropic e-Mn interaction
•Anisotropic h-Mn interaction
e
h

-
5
  
2

5
  
2
Ih- Mn ( jz .S z )
Initial state:
1 h + 1 Mn
e
h

5
  
2
-
5
  
2
J=2
Final state:
1 e + 1 Mn
J=3
Optical recombination of the charged exciton
-
♦ Optical transitions between:
i  Sz
Mn
f  Sz
Mn


e

Jz=-1
j
e z h
e
Proportional to the overlap:
J, J z S z , 
Eigenstates of He-Mn
5
  
2
s-
J=2
J=3
Optical recombination of the charged exciton

1 
5
6




2
6

3,2 

1 
3
5
  1
 
 5
2
2
6

3,1 

1 
1
3
  2
 
 4
2
2
6

3,0

1 
3
1
2


4



2
2
6

3,-2 

1 
5
3
  5 
 12
2
6

3,-3 

5
  
2
1

1 
1
1
  3
 
 32
2
6

3,-1 
5
  
2
Probability
3,3 
-
s

1 
5
 
 62
6

J=2
J=3
s-
Energy
Optical recombination of the charged exciton

1 
3
5
 - 5
 
 1
2
2
6

2, 1 

1 
1
3
2


4




2
2
6

2,0 

1 
1
1
3

3




2
2
6

2,-1 

1 
3
1
4

2



2
2
6


1 
5
3
2,-2 
5

1



2
2
6

5
  
2

5
  
2
1
s
s-

J=2
J=3

5
  
2
-
5
  
2
Probability
2,2 
-
Energy
Optical recombination of the charged exciton
-
5
  
2

5
  
2
s
s-

e-Mn: isotropic
h-Mn: anisotropic
J=2
J=3

5
  
2
-
5
  
2
Probability
1
Energy
Charged exciton in a single QD: Influence of VBM
I h-Mn ( jz .S z  e lh ( j .S -  j- .S  ))
e
h

Initial state:
1 h + 1 Mn
(+3/2,-1/2)
(-3/2,+1/2)
J=2
Final state:
1 e + 1 Mn
J=3
Phys Rev Lett. 97, 107401 (2006)
Charged exciton in a single QD: Influence of VBM
I h-Mn ( jz .S z  e lh ( j .S -  j- .S  ))
e
h

Initial state:
1 h + 1 Mn
(+3/2,-1/2)
(-3/2,+1/2)
J=2
Final state:
1 e + 1 Mn
J=3
Negatively / Positively charged Mn-doped QDs
♦ X-, Mn
♦ X+, Mn
♦ Reversed initial
and final states
e, Mn
h, Mn
e, Mn
J=2
J=3
h, Mn
Energy
Gated controlled magnetic anisotropy
ST
Heisenberg
Mz
Free
Ising
hh
Q=-1
Q=0
Q=+1
Mn+1h= Nano-Magnet
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 Mn atom Sz
If Sz(t=0) = -5/2
P (Sz = -5/2)
1
-5/2
-5/2
+5/2
…
…
+5/2
-5/2
s-
s+
?
~1/6
0
t
Photon statistics ?
1 photon (σ, E)
1 Mn spin state
Correlation measurement on single QDs
Whole PL autocorrelation
PL int (arb. units)
Single emitter statistics :
Select a QD with
a large splitting
to spectrally isolate
a Mn spin state
2036
2037 2038 2039
Energy (meV)
2040
Use of a SIL
to increase the signal
Antibunching: The QDs cannot emit
two photons with a given energy
at the same time
Single Mn spin dynamics
Auto Correlation
on one line
in one polarization
s+, -5/2)
E
X
X+Mn2+
8 ns
PL int (arb. units)
Jz  1
τX-Mn
Jz   2
2036
2037 2038 2039
Energy (meV)
2040
One Mn spin
projection
t
Photon bunching at short delay
Single Mn spin dynamics
Power dependence
Auto Correlation
on one line
in one polarization
σ+
P0
E
X
X+Mn2+
2 x P0
PL int (arb. units)
Jz  1
τX-Mn
Jz   2
3 x P0
2036
2037 2038 2039
Energy (meV)
2040
One Mn spin
projection
Mixing between
Mn spin relaxation time
and
X-Mn spin relaxation time
Single Mn spin dynamics
Polarization Cross-Correlation
σ+
σ-
PL int (arb. units)
Direct evidence of
the spin transfer
-5/2
+5/2
…
…
+5/2
-5/2
s-
2036
2037 2038 2039
Energy (meV)
s+
2040
One Mn spin
projection
Influence of magnetic field?...To be continued…
Summary
 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
 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.
 Photon statistics reveals a complex spin dynamics.
…. Store information on a single spin?