GaAs/InGaAs/GaAs quantum well with remote Mn delta

Disorder effects in 2D ferromagnetic semiconductor
structures:
GaAs/InGaAs/GaAs quantum well with remote Mn
delta-layer
B. Aronzon, A. Davydov, K. Kugel, V. Tripathi, K. Dhochak, A.
Lashkul and E. Lahderanta
1. Introduction.
Structure description. Proofs of 2D and ferromagnetic ordering.
2. Disorder effects. Resistivity.
3. Disorder effects. Noise.
4. The nature of ferromagnetic ordering. Models.
5. Conclusion.
Semiconductor spintronics. 2 problems.
Tc and 2D
2Dcap-layer GaAs, 30-40 nm
-layer Mn
spacer GaAs, 3 nm
QW InGaAs, 9-10 nm
GaAs, 15-18 nm
-layer С
Buffer layer GaAs, 0.5 μm
Substrate
i-GaAs (100)
Quantum well with Mn
delta layer
Awshalom et al., 2004
Zaicev, et al., 2009
Aronzon et al., 2006,
2009, 2010, 2011, 2012
Wegscheider et al.,
2007, 2010
Dietl et al. 2010
Sapega et al. 2012
B.N. Zvonkov et al.
N. Novgorod
cap-layer GaAs, 60-80
нм
δ-layer Mn
spacer GaAs, 1-5 нм
QW InGaAs, 9-10 нм
GaAs, 5 нм
δ-Be
Buffer GaAs, 25 нм
Substrate
GaAs, (100)
Y. Furdyna et al.
Buffalo
Parametes of the samples
2
25000
T=5K
B _I_ xy
40
Rxy, KOhm
20000
Rxx, Ohm
Quantum Hall Effect
2D
15000
10000
InGaAs/GaAs QW
30
2
Rk = h/e
20
10
5000
0
-12
-8
-4
0
4
8
12
0
10
B, T
15000
T=5K
14800
B in plane
14600
0
4
8
B, T
12
20
30
GaAs(Mn)/In0.17Ga0.83As/GaAs
Mn 0.5ML
Rxx, KOhm
Rxx, Ohm
15200
B, T
40
d=10nm,
11
-2
ns = 4.56*10 cm
20
0
J. Appl. Phys. 107, 023905 (2010)
10
20
B, T
3
Transport proofs for ferromagnetism
Resistivity
? Metal - insulator
transition under rise of
Mn content ?



Anomalous Hall effect
Hall resistance dependes on spin-orbit
interaction and carrier polarization
RHd= yx = R0B + RsM
Pure carbon doping (Sample 5) shows no resistance anomaly.
Samples 1 and 4 show hysteresis in magnetisation curve.
[ JETP Lett. (2008)]
Anomalous Hall effect observed in all samples doped with Mn.
Fluctuation potential
After Gergel’ and Suris paper and Shklovskii and Efros
Formation of charge carrier puddles in the quantum well (QW) from
competition of doping disorder and nonlinear screening.
z0
Location of holes in the
transverse direction
Hole wavefunction in transverse
direction
Typical potential fluctuation Vfluc
Partially ionized Mn dopants
Schematic of the quantum well potential (shown
inverted). Dashed (blue) line represents the quantum well
potential in the absence of fluctuations and the solid (red)
line shows the potential well with an attractive fluctuation
potential. The dotted line indicates the Mn dopants at a
distance from the left face of the quantum well.
Model of nanoscale inhomogeneities
RMS potential fluctuation:
V fluc z  = e
z0
 2 z 
  Rc  2 
n' a e 2

log 1+ 
 
2 2
16  0
   + z  
[Kennett, Tripathi, PRB (2006)]
Screening length
n’a - Density of ionized Mn
corresponds
atoms
to carrier density p:
Rc =
PRB, 2011
n' a / 
p
Electrical resistance:
Role of ferromagnetic correlations
EA + J(1-cos θi j )
Vb a
θi j
rrier
Di j
i

j

Extra energy cost
due to spin
orientation
 
T  = ρ0exp E A / T + J 1  cosθij / T
ρ
PRB, 2011

cosθ
ij = exp  Dij / ξ
M
Cosine term changes appreciably when
magnetic correlation length becomes of
the order of droplet separation.

Resistivity anomaly
corresponds to rapid
change of magnetic
contribution.
Resistivity
PRB, 2011
Two phase system
Tc
Tс – local transition in
magnetic islands
Observed temperature dependence of resistance for (a) Sample 4, in units of the
resistance at 70 K, and (b) Sample 1, in units of the resistance at 90 K (points), and
theoretical fits (solid lines). Sample 4 is near the percolation threshold and Sample 1 is
well-insulating. The fits were made using Eq. (13). Parameters such as the activation
energy EA and the droplet separation D1 were chosen close to the values obtained from
the droplet model. The magnetic parameters J and TC were then varied to obtain the
above fits. In both cases, the best fit value of TC was significantly larger than the
temperature, at which the resistance anomaly (hump or shoulder) was observed.
Power Spectal density x frequency
-1
Power Spectral Density (Hz )
Power spectral density of electrical noise
1E-13
1E-14
at 10Hz
1E-15
at 150Hz
1E-16
10
100
T (K)
1E-12
1E-13
1E-14
0,1
10
100
1000
frequency, Hz
23K
4
2,0x10
1
0
1
2
3
4
5
1
2
3
4
5
Rxx, Ohm
22.6K
21.4K
Percolation transition
in magnetic subsystem?
4417
10
20
30
40
50
T, K
60
70
80
90
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
20.9K
4
0
0
0.15
21.5K
1,5x10
There are no transitions
in transport properties.
0
20.6K
20.3K
20.1K
18.94K
PRB, 2012
18.94K
9
Noise fit: Frequency dependence
The long-time dependence of the resistivity
autocorrelation functionSρ(t) extracted from
the noise data at T = 4.0 K together with
fits. The red curve is a fit to Sρ(t)=A/t1.05 +
Bln(t/t0), blue curve is a fit to Sρ(t) = A/t2/5 +
Bln(t/t0). In 2D, Sρ(t ) ∼ t−1 behavior is
expected for a disordered RKKY
ferromagnet and Sρ (t ) ∼ t−2/5 for doubleexchange ferromagnets. The logarithmic
time dependence indicates 1/f noise
contributions. The fit to the RKKY model is
better than to the double exchange.
Frequency dependence of noise at T = 4 K (solid curve)
together with fits to the low- and high-frequency regimes. At
the low-frequency end, the dashed curve and the dotted curve
are fits to Sρ ∼ A − Bf2 and Sρ ∼ A − B lnf − Cf,
respectively. At the high-frequency end, the fit is to Sρ ∼Af−1.53.
PRB, 2012
Sρ f  ~ f 1.53
10
Noise fit: Temperature dependence
Sample 4
f = 150Hz
S  f  ~
Fit to TC= 52K
PRB, 2012
2 Tc
 e
/T
Curie temperature dependence on the depth of quantum
well
0,6
max
z
40
Mn 0,25 MC
Mn 0,3 MC
55 and 57 set
5763
5569
0,4

0,2
30
5765
0
20
-4
-2
0
40
10 110 meV
5764
Mn
GaAs
GaAs
0
U=100 meV
80
2
4
6
q 0z
5572
GaAs
U=140 meV
U=180 meV
100 120 140 160 180
E, meV
J. Phys. Conf. Ser. 2013
48 set Mn 0.5 Ml
4843
35
4832 -4846
Tc, K
Tc, K
5570
15
10
5
u0=3
30
4831
4836
25
4834
20
0.10
0.15
E, eV
0.20
Curie temperature dependence on the spacer thickness
Mech
cap-layer GaAs, 30-40 nm
cap-layer GaAs, 60-80 нм
-layer Mn
spacer GaAs, 3 nm
δ-layer Mn
spacer GaAs, 1-5 нм
QW InGaAs, 9-10 nm
QW InGaAs, 9-10 нм
GaAs, 5 нм
δ-Be
Buffer GaAs, 25 нм
Substrate
GaAs, (100)
GaAs, 15-18 nm
-layer С
Buffer layer GaAs, 0.5 μm
32
Substrate
i-GaAs (100)
30
26
24
22
MBE
Tc, K
Tc, K
30
CVD
28
5574
Mn 0,3
In 0,3
1
5570
Mn 0,3
In 0,3
2
3
d, nm
5575
Mn 0,3
In 0,3
4
5
25
1
J. Phys. Conf. Ser. 2013
2
3
d, nm
4
13
5
Models
Mn
Itinerant FM ordering in GaMnAs layer.
(S.Caprara et al. PRB (2011)).
M=0
Averkiev et al. – resonance tunneling.
PRB (2012).
GaMnAs
GaAs
GaInAs
Meilikhov et al. – overlapping of the wave function
tails with GaMnAs layer.
JETP Letters (2008)
Two phase system
Tс – local transition in magnetic islands
EF
Tc
L
Mn layer – GaMnAs
GaMnAs
GaAs
GaInAs
Conclusion
Disorder and magnetic interactions affect
strongly both transport and magnetic
properties of the structures and could
explain the temperature dependence of
resistance and noise quantitatively.
THANKS FOR
YOUR
ATTENTION!
15
Model of nanoscale inhomogeneities
z0
Assume Gaussian white noise
distribution for ionized dopants:
nr nr'   n 2 = n' a  r  r' 
Fluctuation charge in circle of
radius R:
nR 2 =
Disorder screened by holes in QW:
PRB, 2011
p=
n' a
R 2
nR 2 = n' a /  / Rc
Ferromagnetic correlations: models
I. Isotropic 2D Heisenberg ferromagnet
H =  J  Si  S j
No long-range magnetic order
at finite temperature.
ij

 a / 1  Tc / T , T ≫Tc 

ξ
=


M

aexp Tc / 2T , T  Tc 

II. Uniaxial 2D Heisenberg ferromagnet
H =  J  Si  S j  K  S jz 
2
ij
T0 ~
i
Tc
ln  2 J / K


M. Bander, D. Mills, PRB (1988)


a / Tc  T , T ≫Tc


ξ
T0  T  Tc 
M = aexp Tc / 2T ,


γ


a
/
1

T
/
T
,
T
~
T
0
0


 = 1.25 for Ising
Voltage noise: magnetic fluctuations
Resistivity noise from magnetic fluctuations
2
S ρω / ρ
 J / T 
2
 Dij / ξ


M




C
0,
ω
+
e
C
D
,
ω

,

αα
αα ij

α 
Cαβr,  =  αβ
2T

 d q e
2
iqr
Im  αβq, 
Autocorrelation function
of magnetisation
Autocorrelation function contains information on dynamics, and can shed
light on the mechanism of ferromagnetism.
Magnetic correlations: dynamics
 αβ  0 T 
Resistivity noise is sensitive to  αβ q,  =
2
1+ q M   i / q, 
the dynamics of the ferromagnet:
Interested in two broad universality classes depending on
whether the dynamics has a hydrodynamic description:
Model A: No conserved order parameter
e.g. anisotropic Heisenberg
q, 
Model B: Conserved order parameter
e.g. Isotropic Heisenberg
q, 
Hohenberg, Halperin, RMP (1977)
2
=
const.
/

M
q,ω0
2
=
Dq
q,ω0
2D
X-ray diagnostics of the samples
a/a, %
4
InхGa1-хAs
0.3
2
4831
(GaAs)1-yMny
0.1
0
J. Appl. Phys. 107, 023905 (2010)
-layer Mn
spacer GaAs, 3 nm
.040
10
20
30
40
50
60
70
Mn content
4
50
55
QW InGaAs, 9-10 nm
GaAs, 15-18 nm
0
0.0
80
InхGa1-хAs
0.4
2
60
sample
B
(GaAs)1-yMny
4834
-layer С
0.3
yMn
cap-layer GaAs, 30-40 nm
0.2
ASample
yMn
Profile of the deviation
of the lattice constant
from its value for GaAs
along the sample
depth (z)
0.2
Buffer layer GaAs, 0.5 μm
Substrate
i-GaAs (100)
z, nm
0
0.1
0.0
0
10
20
30
40
50
z, nм
60
70
80
Noise fit: Frequency dependence
Sample 4
T=4K
Sρ f  ~ A  Bln f  Cf
(Model B)
Sρ f  ~ A  Bf
2
(Model A)
Sρ f  ~ f 1.53
Model A: Random Telegraph
Model B: Diffusive spin dynamics
−2
Model A: ~ f
−1
Model B: ~ f
M
Carrier-mediated
FM via
carriers in the
2D conductivity
channel
quantum well.

GaAs(Mn)
GaInAs
GaAs
GaInAs
U(z)
GaAs
GaAs
E0
Mn
(z)
(z)
0
L
z

E.Z. Meilkhov and R.M. Farzetdinova,
JETP Letters (2008)
  
M
FM ordering inside Mn layer
Mn
FM ordering occurs in
GaMnAs layer due to
itinerant mechanism.
Carriers in the quantum
well do not invoolved.
V.V. Tugushev et al.
PRB (2009)
(z)
From Lucev et al. PRB 2009
Mn
GaInAs
GaAs
There is 2D spin – polarized collective state in the
GaMnAs aria. The corresponding wave function is
expanded inside quantum well and acts on carriers
causing their spin-polarization.
23
Модель
Mn
M=0
GaMnAs
GaAs
GaInAs
ФМ упорядочение в GaMnAs слое обусловлено
обменом спинов Mn через носители в этом же
слое. Носители из квантовой ямы в обмене
почти не участвуют (S.Caprara et al.PRB (2011)).
Вблизи дельта слоя возникает 2D спин –
поляризованное состояние. Волновая функция
проникает из дельта слоя в квантовую яму,
вызывая спиновую поляризацию дырок.
Аверкиев и др. – резонансное туннелирование,
Мейлихов и др. – перекрытие хвостов
волновой функции из КЯ в слой GaMnAs
Двухфазная среда
Tс – локальный ФМ в островках
EF
Tc
L
Mn – содержащий слой GaMnAs
GaMnAs
GaAs
GaInAs
Voltage noise: frequency dependence
Sample 4
Characteristic frequency
f S f ~ f − 0.53
f Sf~ f ?
Freq. dependence of the voltage noise for temperatures below
resistivity anomaly.
Freq. dependence is not 1/f. Random telegraph? Griffiths?
Conclusions



At low carrier density, competition of disorder and nonlin
screening causes formation of charge puddles in 2DHG.
Resistance anomaly arises when magnetic correlation le
becomes comparable with a relevant length scale. Anom
not evidence for a phase transition.
In 2D (unlike 3D) resistance anomaly may occur far belo
Curie temperature.
Noise is non-1/f over a large window of frequencies.
Data in reasonable agreement with both Model A
(Random Telegraph) and Model B (Diffusive spin dynami

Magn
намагниченность
Диэлектрический образец
Ferromagnet
-5
4.0x10
-5
Загадка 3
M (emu)
3.0x10
-5
2.0x10
ZFC
FC
Mn in QW sample
B=1T
-5
0.0
0
20
40
60
80
100
T (K)
-4
1.0x10
Mn in QW sample
T=3K
-5
5.0x10
M (emu)
В чем
причина
необычного
вида
гистерезиса?
1.0x10
0.0
-5
-5.0x10
-4
-1.0x10
-2
-1
0
1
2
B (T)
Exchange bias of hysteresis loop
27
Известен для двухвазных систем с ферро- и антиферромагнитными включениями,
JETP Letters, 2008
например, в манганитах.
Намагниченность
Малое содержание Mn
Magn
10K
M (emu)
8
0
-8
-8
-6
-4
-2
0
2
4
6
8
B (T)
28
JETP Letters, 2007
Magn
Model
Mn rich lake
Jf-af
Mn delta layer
M
spacer
Ferromagnetic region
2DEG
Jf
Antiferromagnetic region
QW, high carrier
concentration
Magnetic moment of the lake is pinned by Jf-af
The percolation transition in magnetic system affect scattering and results in
decrease of resistance – reason of the noise.
Due to shape anisotropy
magnetic moment of Mn layer aligns along
Due to quantization
spin of heavy holes aligns
perpendicularly
Is the exchange possible?
Yes, due to high Fermi energy and disorder.
dqw=10 nm, rloc= 20-30 nm, K in plane is about Kz
JETP Letters, 2008
PSS, 2008
29
Magn
Nature for AFM regions
Fig from Lutcev et al. PRB (2009)
Tugushev et al. PRB (2009)
Mag
Magnetization
Metallic sample
Low Mn content
Insulator sample
High Mn content
Ferromagnet
-5
4.0x10
-5
M (emu)
3.0x10
-5
2.0x10
ZFC
FC
Mn in qw4834
B=1T
-5
1.0x10
What is the
reason for
unusual
hysteresis
loop?
-5
8.0x10
-5
Mn in qw4831
T=3K
0.0
-4.0x10
-5
-8.0x10
-5
-2
0
20
40
60
80
100
T (K)
-4
1.0x10
Mn in qw4834
T=3K
-5
5.0x10
M (emu)
M (emu)
4.0x10
0.0
0.0
-5
-5.0x10
-4
-1
0
1
2
-1.0x10
-2
-1
B (T)
0
1
2
B (T)
Exchange bias of hysteresis loop
31
Known for two phase systems with ferro - and anti-ferro inclusions,
for example, phase separation in manganites JETP Letters, 2008
Model of nanoscale inhomogeneities 1
Formation of charge carrier puddles in the quantum well (QW) from
competition of doping disorder and nonlinear screening.
(Gergel' & Suris, JETP (1978))
Typical potential fluctuation
Partially ionized Mn dopants
Estimate of the droplet sizes
Virial theorem:
2
 2 kmax,
1
n
= V fluc z0n , R pn 
2m
2
Droplet charge distributed over subbands:


2
2
2
Emax,1  Emax,2 =
k max,

k
1
max,2  E2  E1
2m
n' a R p1

k
=
max,1 R p1 
2
2

k
+
max,2 R p 2 
2
2
Solve these nonlinear
equations to get droplet
size
Results of the calculations
T= 77 K
T= 5 K
Флуктуационный потенциал и температурная
зависимость сопротивления
Вслед за работой Гергель, Сурис, ЖЭТФ (1978)
Загадка 1
Расчетная температура не совпадает с максимумом R(T).
Две температуры?
PRB 2011
AHE
AHE temperature dependence
300
100
1T
100
0
11
-200
-300
at T=30 K;
20
40
60
80
10
-2
p=4*10 cm
2
p=650 cm /V*s
0
0
-100
0.3T
-100
20
5569
Bsatur, T
RAHE, Ohm
3T
-200
0
20
40
60
80
100
T, K
11
T=4.6 K; p=3.1*10
-2
cm ,
2
100
200
=350 cm /Vs
12
T=77K; p=1*10
T, K
AHE change sign with T
2
11
-2
p=3.3*10 cm ,
0
2
=850 cm /Vs
12
-100
T=100 K; p=1.4*10
11
T=50 K; p=5*10
2
=1000 cm /Vs
-2
cm ,
2
Two contributions
intrinsic and side-jump
-2
cm ,
=1200 cm /Vs
100 T=33 K;
RAHE, Ohm
RAHE, Ohm
200
-200
=1100 cm /Vs
-2
0
B, T
2
-2
cm ,
Аномальный эффект Холла
AHE
Холловское сопротивление RHd= yx = R0B + RsM
Аномальный вклад пропорционален намагниченности и
зависит от S-O взаимодействия и спиновой поляризации носителей.
17 K
40
20
Rxya, Ohm
Rxya, Ohm
200
0.5 ML
0
-20
1.2 ML
0
-200
55 K
-400
-40
-4
-2
0
2
B, T
  0.07e / h
a
xy
2
-4
4
2D
расчет
  0.1e 2 / h
a
xy
-2
0
2
4
B, T
 xya  0.17e 2 / h
S.Y. Liu, X.L. Lei, Phys. Rev. B 72, 195329 (2005).
V.K. Dugaev, P. Bruno, M. Taillefumier, B. Canals, C. Lacroix, Phys. Rev. 71, 224423 (2005).
2
2
 xyn   xyn /  xx2


рe

n
2







xy
c
 xya   xya /  xx2
m  1  c2 2 
 xya /  xyn   xya /  xyn   2
37
J. Phys. Cond. Matt. 2008, JAP2010
Fluctuation potential
After Gergel’ and Suris paper and Shklovskii and Efros
Schematic of the quantum well potential (shown inverted). Dashed (blue) line represents
the quantum well potential in the absence of fluctuations and the solid (red) line shows
the potential well with an attractive fluctuation potential. The dotted line indicates the Mn
dopants at a distance from the left face of the quantum well.
Geometry of the
droplets
Voltage noise: charge fluctuations
Fluctuations in inter-droplet tunnelling
A. L. Rakhmanov et al., PRB (2001) [phase-separated manganites]
ω2
2
 1  e

 EC
 2 Dij 
/T 

 1+  2 Dij 2
Random-telegraph type
(consistent with experiment)
 D / +E /T J / T 1  cos ij 
1
 0 e ij loc C
 2 Dij 
Different from characteristic
time associated with resistivity.
Temperature dependence not in agreement with data.
Need to look at magnetic contribution to noise.
Mech
FM transition in the Mn layer affects the
conductivity in QW
U(z)
GaInAs
GaAs
GaAs
Mn
V-band
L

z
FM transition in the Mn layer affects the
conductivity in QW
p, cm
12
2.0x10
U(z)
12
1.6x10
GaInAs
-2
5569
Tcl
12
1.2x10
FM transition
occurs
11
8.0x10
Tc
11
4.0x10
0
GaAs
20
40
GaAs
60
80
100
T, K
p, cm^-2
Mn
mob, cm^2/V*s
12
1.2x10
-2
p, cm
V-band
3000
QW 4831
2500
11
9.0x10
L

z
2000
0
20
40
T, K
60
, cm2/V*s
Mech
Two-dimensionality
Sample 3 (metallic)



Negative magnetoresistance consistent with 2D weak
localisation corrections.
Observation of Shubnikov-de Haas oscillations for fields
perpendicular to plane of hole gas.
Quantum Hall effect in all samples, including Sample 1.
[B. A. Aronzon et al., J. Appl. Phys. (2010)]
Photolumiscence InGaAs/GaAs:Mn
EL intensity
1.0
0.5
dS= 3 nm (a)
dS = 3 nm


B=5T
EL
PL


1,34
h (eV)
PC
1,33
reference LED
0.0
Psat
0
4
B (T)
8
(b)
0.4
0.2
Pc(B) dependences for EL and PL
of sample 2 and of the reference
sample 5 without δ-Mn layer.
Inset shows polarized EL spectra;
(b) Pc(9 T) values vs. ds in LEDs
with x = 0.1.
Psat (9 T) values vs. ds
reference LED
0.0
0
5
dS (nm)
10
Zaitsev, Kulakovskii et al. Jetp letters
90,730 (2009)
Outline
1. Introduction.
Structure description. Proofs of 2D and ferromagnetic ordering.
2. Disorder effects. Resistivity.
3. Disorder effects. Noise.
4. The nature of ferromagnetic ordering. Models.
5. Conclusion.
Semiconductor spintronics. 2 problems.
Tc and 2D
45