spin effects in diluted magnetic semiconductors m. vladimirova, p. barate, s. cronenberger, f. teppe...
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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
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%
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
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
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)