Transcript Наноматериалы для спинтроники

Mechanisms of ferromagnetic
ordering and anomalous Hall effect
in 2D GaAs/InGaAs/GaAs structures
with Mn delta layer
Aronzon B.A.
Rylkov V.V.
Lagutin A.S.
Davydov A.B.
Pankov M.A.
Meilikhov E.Z.
Pashaev E.M.
Zvonkov B.N.
Danilov Yu. A.
Vikhrova O.V.
Laiho R.
Lashkul A.
RRC “Kurchatov Institute”, Moscow, Russia
NIFTI, N. Novgorod , Russia
Vihuri Lab., Turku, Finland
Kulbachinskii V.A. MSU, Moscow, Russia
1
Outline
1 Motivation
2 2D DMS structure
3 Transport properties, FM ordering
4 Mechanisms
5 Anomalous Hall effect
6 Magnetization, magnetic structure
7 Conclusion
2
Motivation
Application
Incorporation of magnetism into modern electronics - spintronics
Basic Research
Incorporation of magnetism into physics of semiconductors
Coulomb interaction, disorder, e-e interaction, electron – phonon interaction,
+
strong exchange interaction
Mechanism of the exchange interaction;
Effects of the disorder, Coulomb and
exchange interactions interplay;
Peculiarities of the 2D quantum effects
in the presence of the ferromagnetism;
AHE origin;
Magnetic structure.
3
Possible interaction mechanism
Exchange via free electrons
RKKY interaction
Indirect exchange via empty states above the Fermi energy in the heavy hole
band. Impurity spins are parallel.
F
Mn
Fermi-energy
Mn
Zener
Quasi 2D DMS ?
A.M. Nazmul, M. Tanaka et al.;
T. Wojtowicz, J.K. Furdyna et al.
Low mobility structures (< 10 cm2/(V s))
2D structures
Парфеньев и др. 2009
Зайцев, Кулаковский и др., 2009
Аронзон и др., 2006
cap-layer GaAs, 30-40 nm
-layer Mn
spacer GaAs, 3 nm
.0
40
50
55
QW InGaAs, 9-10 nm
GaAs, 15-18 nm
Table 1. Structure parameters
x
65
-layer С
z, nm
300К
dMn,
ML
structure
Buffer layer GaAs, 0.5 μm
Substrate
i-GaAs (100)
Quantum well with Mn delta layer
77К
μeff,
см2/В·с
ps·10-12,
см-2
Rs, Ω/□
μeff,
см2/В·с
ps·10-12,
см-2
Ω/□
Rs,
А; M
0,21
0.5
176
10
3200
1860
2
1660
В; I
0,16
1.2
158
14,3
2760
1350
1,8
2540
С; I
0,18
0
270
1,3
18400
1598
0.5
5
7800
Crystal structure
a/a, %
X- Ray
characterization
4
InхGa1-хAs
cap-layer GaAs, 30-40 nm
-layer Mn
spacer GaAs, 3 nm
.0
40
50
55
0.3
2
0.2
ASample
yMn
Depth (z) profiles of
the lattice
mismatch related to
GaAs evaluated
from fitting the
experimental X-ray
rocking curves.
4831
(GaAs)1-yMny
0.1
0
0
10
20
30
40
50
60
70
Mn content
4
InхGa1-хAs
0.4
QW InGaAs, 9-10 nm
60
2
sample
B
(GaAs)1-yMny
4834
-layer С
0.3
yMn
GaAs, 15-18 nm
0.2
Buffer layer GaAs, 0.5 μm
Substrate
i-GaAs (100)
0.0
80
z, nm
0
0.1
0.0
0
10
20
30
40
50
z, нм
60
70
80
2D
25000
T=5K
B _I_ xy
20000
40000
InGaAs/GaAs QW
N4417
Rxy, Ohm
Rxx, Ohm
30000
15000
10000
2
Rk = h/e
20000
10000
5000
0
-12
-8
-4
0
4
8
0
12
4
8
16
20
24
28
B, T
B, T
15200
12
GaAs(Mn)/In0.17Ga0.83As/GaAs QW
Mn 0.5ML
d=10nm, N4417
15000
T=5K
14800
B in plane
Rxx, Ohm
Rxx, Ohm
40000
14600
0
4
8
B, T
12
11
ns = 4.56*10 cm
-2
20000
0
5
10
15
B, T
20
25
7
Methods
Temperature dependence of resitance
R
spin-dependent scattering
GMR effect
<
Anomalous Hall Effect
Tc
T
The Hall resistance RHd= yx = R0B + RsM
AHE is proportional to magnetization and is due to S-O interaction .
skew–scattering: Rs R1xx ; side-jump: Rs R2xx
For both mechanisms AHE depends
on the strength of the S-O interaction
and spin polarization of carriers.
AHE current arises due to
scattering asymmetry
Berry phase v(k) = grad [ε(k)]/h + (e/h)E(k)
z(k) = 2Im[<u/ky|u/kx>]
 - does not depend on scattering
Renewed interest in AHE nature
T. Jungwirth et al.(2002), T. Dietl et al.(2003), A.A. Burkov et al. (2003)
2D case: S.Y. Liu et al. (2005), V.K. Dugaev et al. (2005)
8
Temperature dependence of the sample
resistance
Rxx, Ohm
16000
4831
15000
4834
100000
4847
13000
Rxx, Ohm
Rxx, Ohm
14000
12000
4843
11000
10000
10000
0
10
20
30
40
50
60
70
80
90
T, K
spin-dependent scattering
Main feature – Hump or Shoulder.
Mn doped samples only.
<
J. Phys. Cond. Matt. 2008
9
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)
  
Curie temperature dependence on the depth of quantum
well
0,6
max
z
Mn 0,25 MC
Mn 0,3 MC
40
0,4

30
0,2
20
0
15
10
5
u0=3
-4
-2
0
2
4
q 0z
10 110 meV
Mn
GaAs
GaAs
0
U=100 meV
80
40
GaAs
U=140 meV U=180 meV
100 120 140 160 180
E, meV
30
25
20
0.10
JAP 2010
57 set Mn 0.15 Ml
35
Tc, K
Tc, K
55 set
0.15
E, eV
0.20
6
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)
Mn
GaInAs
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.
GaAs
12
Curie temperature dependence on the spacer thickness
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
2
3
d, nm
4
13
5
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)
-2
12
1.6x10
GaInAs
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
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
Mn
Anomalous Hall Effect
The Hall resistance RHd= yx = R0B + RsM
AHE is proportional to magnetization and is due to S-O interaction .
skew–scattering: Rs R1xx ; side-jump: Rs R2xx
For both mechanisms AHE depends
on the strength of the S-O interaction
and spin polarization of carriers.
AHE current arises due to
scattering asymmetry
Berry phase
v(k) = grad [ε(k)]/h + (e/h)E(k)
z(k) = 2Im[<u/ky|u/kx>]
 - does not depend on scattering
Renewed interest in AHE nature
T. Jungwirth et al.(2002), T. Dietl et al.(2003), A.A. Burkov et al. (2003)
2D case: S.Y. Liu et al. (2005), V.K. Dugaev et al. (2005)
Condenst-matter physists today have some acquaitance with skew-scattering, but 16
have
a harder time recalling what the Luttinger anomalous velocity is
Anomalous Hall Effect
200
0.5 ML
20
Rxya, Ohm
Rxya, Ohm
300
17 K
40
0
1.2 ML
100
0
-100
-200
-20
55 K
-300
~
-40
-400
-500
-4
-2
0
2
4
-4
-2
  0.07e / h
2
2
4
B, T
B, T
a
xy
0
2D
calculated
2
0.1e / h
 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

 2
рe

n
 
 xy 
c 
2 2 
a
a
2
 xy   xy /  xx
m  1  c  
 xya /  xyn   xya /  xyn   2
17
JETP Letters 2007; JAP 2010
Эффекты туннелирования InGaAs/GaAs:Mn
Квантовая яма
InGaAs
GaAs

-C QW
-
-C
5T
0.1 eV
~0.08 eV
3-5 nm
(a) 4847
+

10 nm
Эксперимент:
поляризация
фотолюминесценции из
квантовой ямы
PL intensity (arb.units)
1.3 eV
GaAs
1.5 eV
 - слой Mn
0T
1.30
(b)
4831
1.32

1.34
1.36
-Mn QW
+

-C
-
5T
o
A (Mn)
0T
1.26 1.28
(c) 4845
1.36
+
, 
1.38
-
1.40
1.42
-Mn -C QW
С.В. Зайцев, М.В.Дорохин, А.С.Бричкин,
О.В.Вихрова,
Ю.А.Данилов, Б.Н.Звонков,
5T
В.Д.Кулаковский, Письма в ЖЭТФ 90,730 (2009)
0T
1.28
1.30
1.32
energy (eV)
1.34
300
300
250
250
Rxy, 
200
a
Rxyanom, Ohm
Anomalous Hall Effect
150
150
100
1.2 ML
100
200
0
1000
50
2000
2
2
Rxx , (K)
0
30
20
30
40
50
60
70
T, K
Amplitude is negative at low
temperatures and change sign at Tc
80
- RAHE, Ohm
10
20
4831
10
0.5 ML
0
-10
10
20
30
T, K
40
50
19
AHE temperature dependence
300
3T
1T
100
0
0.3T
-100
11
-2
-200
p=4*10 cm
2
p=650 cm /V*s
-300
at T=30 K;
0
20
40
60
80
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 ,
Magnetization
low Mn content
10K
0
8
7
M (emu)
M (emu)
8
-8
6
5
0
-8
-6
-4
-2
0
100
2
200
T (K)
4
300
6
8
B (T)
Aronzon, Kulbachinskii et al., JETP letters, 2007
21
Magnetization
Metallic sample
Intermediate 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
22
Known for two phase systems with ferro - and anti-ferro inclusions,
for example, phase separation in manganites JETP Letters, 2008
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
23
JETP Letters, 2008
Nature for AFM regions
Tugushev et al. PRB (2009)
Conclusion
Maximum in the temperature dependence of resistance
and anomalous Hall effect are the sign for magnetic ordering
in 2D structures with Mn layer separated from the quantum well
Anomalous Hall effect was observed in 2D structures with Mn layer
separated from the quantum well and with relatively high mobility of carriers.
The change of its sign with temperature as well as its value supports the intrinsic
mechanisms.
The unusual shifted hysteresis loop was observed
Disorder and interactions affect strongly both transport
and magnetic properties of the structures
Spin-polarization of carriers were observed
THANKS FOR
YOUR
ATTENTION
25