Spin effects in diluted magnetic semiconductors

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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

2
Diluted magnetic semiconductors
II
VIII
VII
VI
V
IV
III
II
I
He
H
Ne
F
O
N
C
B
Be
Li
Ar
Cl
S
P
Si
Al
Mg
Na
3d
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
Co
Fe
Mn
Cr
V
Ti
Sc
Ca
K
Xe
I
Te
Sb
Sn
In
Cd
Ag
Pd
Rh
Ru
Mo
Nb
Zr
Y
Sr
Rb
Rn
At
Po
Bi
Pb
Tl
Hg
Au
Pt
Ir
Os
Re
W
Ta
Hf
La
Ba
Cs
CdMnTe
5/2
Mn 4s2 3d5
3/2
1/2
-1/2
-3/2
-5/2
S5/2 Localized spins
N0 concentration of cations X Mn fraction
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Diluted magnetic semiconductors
CdMnTe Paramagnetic n-CdMnTe
Paramagnetic p-CdMnTe Ferromagnetic(Tc2K)
CdMnTe
CdTe
Carriers mediated interaction between magnetic
moments
ferromagnetism
Magnetic polaron
Localized electrons interacting with magnetic
ions
Super exchange
T. Dietl and J. Spalek, PRL 48, 355 (1982)
Antiferromagnetic clucters
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Exchange interaction
exchange integral
in the mean field approximation
Overhauser shift
Exchange coupling is ferrromagnetic for electrons
and antiferromagnetic for holes
Out-of-equilibrium electrons depolarize Mn
spins Out-of-equilibrium holes polarize Mn spins
Knight shift
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Giant Zeeman Splitting
Energy
s
s -
p
CdMnTeelectron
Magnetic field
Allowed optical transitions
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Nearest neighbors Mn-Mn pairs do not contribute
in the effective field
Large splitting only at low temperatures (Tlt10K)
x ? xeff T?TT0
x(1-x)12
x ? xeff T?TT0
Modified brillouin function
Gai, Planel, Fishman Solid State Commun 29, 435
(1979)
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Magnetization Mn density x Mn spin polarization
Temperature dependence
Mn content dependence
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Optically excited CdMnTe QWs
B
Band diagram
Magnetic field in Voigt configuration
CB
1/2
hn
se1/2
-1/2

• 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-gtspin precession
• Spin relaxation few 10 ps

VB
3/2
-3/2
sh3/2
hh
1/2
lh
-1/2
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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

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How does the polarised light affect the Mn ions
Magnetic polaron
Electrons (holes) localized by the potential
fluctuations or on donors
EF
Mean field approximation is not valid at low
fields
e or h
N Mn ion spins
Exchange energy gain
T. Dietl and J. Spalek, PRL 48, 355 (1982)
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How does the polarized light affect the Mn ions
Impulsive coherent rotation of Mn

• Electrons photocreated 2DEG -gt spin precession
• Hole spin locked in growth direction -gt impulsive
  coherent rotation of Mn
• Crooker et al PRL 77, 2814 (1996)
• Akimoto et al PRB 57, 7208 (1998)

electrons
holes
XZ is a QW plane
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How does the polarised light affect the Mn ions
Energy and polarization transfer via spin-flip
scattering
TS
2 levels system
In general
Electron or hole spins out of equilibrium
1
0
Nup/Ndown
e-Mn spin-flip time
Other spin relaxation mechanisms

1. With electrons
2. With holes

t , tSF ltlt tSL
Mn spins, TS
Spin-lattice relaxation
Lattice, T2K
Ryabchenko et a, Sov. Phys. JETP 55, 951
(1982) CdMnTe 5, exchange scattering with holes
? Mn spin cooling
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Magneto-optical Kerr (Faraday) effect
Rotation of the polarization plane in magnetic
media
w
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Pump-induced Kerr (Faraday) rotation
sample

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

Dt
probe
qK(t)
pump
Polarisation of the probe beam is rotated after
reflection (transmission) from the polarized
media
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CdMnTe QWs
Iodine doped
CdMg0.27Te (10 nm)
Iodine doped
QW - CdMn0.0052Te (8 nm)
Barrier CdMg0.27Te (150 ML)
CdTe/CdMgTe SL
CdMg0.27Te (0.7 µm)
1010
3.1010
7.1010
1011
Buffer CdTe (6.7 µm)
ZnTe (3 nm)
Substrat GaAs (100)

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

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Time-domain spin resonance
Xeff0.45
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• First example Spatial instability of Mn spin
  temperature in CdMnTe QWs

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Spontaneous magnetization patterning
xeff0.45, T2K, P15W/cm2
at high field and excitation density formation
of domains with distinct Mn spin temperatures
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High excitation density
Low excitation density

• Domain temperature does not depend on magnetic
  field
• Domain temperature does not vary much with
  excitation power density

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Summary of experimental results

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

High excitation density G
Mn spin temperature domains
High magnetic field B

• Equipartition of domain areas
• Thot increases slightly with excitation density

Resonant excitation Eexc
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Interpretation Positive feedback loop for Mn
heating
cold
hot
hot
cold
cold

• e generation
• e recombination
• e diffusion
• Mn diffusion
• e-Mn spin-flip
• Mn spin relaxation

e
x
Mn
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Rate equations accounting for diffusion
Electron diffusion and drift
Mn spin diffusion
Exchange potential
n
2V
Spin flip rates
n-
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Linear stability of the steady-state homogeneous
solution

• Time and space derivatives 0
• ? n0, N0
• n n0 Aexp(Wtiqx)
• N N0B exp(Wtiqx)
• Calculate W(q) in the adiabatic approximation
• Linearly stable if W(q) lt 0 for all q
• Unstable for q such that W(q) gt 0

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Domain sizes!
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Linear stability of the steady-state homogeneous
solution
two threshold values !
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Numerical solution Hysteresys loop
Tbath2K t 10-10 s g 104 s-1 w0 10-4 cm2
/s N0a 220 meV x 0.0045 g 1018 cm-2 s-1 g1
? 0.25 W/cm2 DMn/D10-9
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• Second example Collective spin-flip excitations
  of electron and Mn

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Spin-flip excitation energies
Here exchange splitting saturates
Zeeman splitting mainly, ge-1.5
Mn
e-
resonance

• Electrons Exchange and Zeeman splittings have
  different signs (agt0)
• Two coupled spin flip transitions

x0.002
Anticrossing?
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Spin-flip Raman scattering
CdMnTe QW 2d20meV

• Experiments
• EPR and Raman scattering
• Dynamics?
• Theory
• ferromagnetism possible in n-CdMnTe QWs, Tc0.4mK
• Finite spin relaxation times and interacting 2DEG
  susceptibility not taken into account

F. J. Teran et al, PRL 91, 077201 (2003) J.
König and A. H. MacDonald PRL 91, 077202 (2003)
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Samples
0.2 Mn
2DEG density
M1120 ne0.7x1011 cm 2
M1118 ne2.2x1011 cm-2
LSP, Grenoble, France
V. Huard et al, PRL 84, 167 (2000)
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M1118 (ne2.2x1011cm-3)
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M1120 (ne0.7x1011cm-3)
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Summary M1120 (ne0.7x1011cm-3)
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Mean field model
Coupled Bloch equations
Knight field
Overhauser 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
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Mean field model
coupled oscillators wMn, we, coupling energy

• K,D depend on B, T, ne, NMn
• gMn ltlt ge

Strong vs weak coupling
anticrossing
Relaxation rate changes
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Solution of Bloch equations
w , w-, eigen frequencies of the mixed modes
Initial conditions photocreated electrons and
holes impulsive coherent rotation of Mn
B
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Summary M1120 (ne0.7x1011cm-3)
te20 ps, tMn2ns
2d20meV
tMP40ps
We should suppose that electron spins are fully
polarized
K0.3meV
D1.2 meV
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Summary M1118 (ne2.2x1011cm-3)
te20 ps, tMn2ns
30meV
tMM40ps
2DEG spin polarization is 3 times stronger than
expected from Fermi distribution
K0.4 meV, D1.2 meV
Electron spins are almost fully polarized
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Thank you !
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Strong vs weak coupling
gMn ltlt ge

• The transition SC-gtWC is controlled by ge

SC
WC

• SC At resonance mixed modes have the same
  relaxation rate
• WC Strong modification of relaxation times

geSCltgeWC
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Dynamics of coupled spins
Rabi period
Strong coupling
Rabi period
Weak coupling
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Magnetic polaron
Electrons localized by the potential fluctuations
EF
Mean field approximation is not valid at low
fields
e-
N Mn ion spins
Exchange energy gain
T. Dietl and J. Spalek, PRL 48, 355 (1982)
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Magnetic polaron at spin-flip resonance
Resonance condition EeSFEMnSF
B0 EeSFEMnSF0
2d
N-1 degenerate states
N degenerate states
EeSFgtgtEMnSF
R. Fiederling et al, PRB 58, 4785 (1998)
ltSzgt 5/2-gt 2deMP
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Magnetic polaron /Mean field
Magnetic polaron
e-
N Mn ion spins
2DEG

• if ltszgt 1/2
• If if ltszgt lt 1/2

(NNMn/Ne)
d provides the information on the electron spin
polarization
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Time-resolved Kerr rotation
B
-
?K ? Sy

?t
pump
probe

• 100 fs pulses spectrally filtered -gt ps
  resolution
• Excitation power 250 mW, resonant with hh exciton
• Pump-probe ratio 21
• Sy may include electron, Mn, hole or mixed mode
  contribution

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TRKR at resonance
M1118 ne2.2x1011 cm-3
Questions

• Mn non interacting modes or electron-free
  spatial regions?
• Relative contribution of Mn and electron spin
  polarization in TRKR signal

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Conclusions

• Measuring the dynamics of collective electron
  Mn spin flip excitations Rabi oscillation
  between pure electron and Mn states
• Manipulating 2DEG hn -gthh -gt Mn -gt2DEG
• Coupled modes splitting can be used as a tool to
  measure the 2DEG susceptibility strong
  enhancement of 2DEG polarization is observed

Perspectives

• 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!

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n-CdMnTe QWs
In-plane localization potential
0.2 Mn
F. Teran and this work
EF
EF
this work
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Microcavities with DMS
Magnetic tuning of exciton mode
H. Ulmer-Tuffigo et al, Superlattices and
Microstructures 22, 383 (1997)
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Microcavities with DMS QW Enhanced Faraday
rotation
QW in a microcavity
N round trips of light in the cavity
qK 3 in (In,Ga)As/GaAs QW microcavity _at_ 11.25T
A. Kavokin et al, PRB 56, 1087 (1997)
qK 140 in CdMnTe QW microcavity _at_ 1T
M. Haddad et al, SSC 111, 61 (1999)