Spin injection into semiconductors:
theory and experiments
Claas-Henrik Möller, Andreas Wittmann,
Christian Heyn, and Dirk Grundler
Institut für Angewandte Physik
und
Zentrum für Mikrostrukturforschung,
Universität Hamburg
Bad Honnef, 317. WEH-Seminar, 13 January 2004
Motivation
Outline
Theoretical issues of spin injection
in ferromagnet/semiconductor hybrid structures
Novel hybrid device for spin transport
• preparation of ferromagnet/semiconductor hybrid structures
on the cleaved edge of an InAs heterostructure
• spin-transport experiments
(011) orientation
• field-effect transistor on the cleaved edge
with ferromagnetic contacts
Summary
Fe (Co)
ion
t
ta
n
rie
o
1)
0
(0
III-V semiconductor
Spin injection via spin filtering across epitaxial interfaces
η
η
η
η
•Similar results for
Fe/InAs(001): M. Zwierzycki et al.,
Phys. Rev. B 67, 092401 (2003).
Spin effects in ballistic FM / 2DES / FM hybrid structures
with narrow-gap semiconductors
R
Lateral spin valve
FM spin injector
2DES
FM spin detector
∆R
-Bc2 -Bc1 Bc1 Bc2
L
B
Positive spin valve effect
Ez
Spin precession due to Rashba field BR
Rashba coefficient α represents strength
of BR
BR
Spin
R
kx
-Bc2 -Bc1 Bc1 Bc2
−∆R
B
Ez
here:
∆Θ = 180°
generally: ∆Θ ~ αL
S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
Positive and negative
spin-valve effect possible,
depends on α and L
Diffusive transport theory: fundamental obstacle
Conductivity mismatch
prohibits spin injection
into bulk semiconductor
(“bad metal“):
η ≈0
∆R/R ~ 10-7
A diffusive
conductor
A ballistic
conductor
The Landauer formula
w, L << λe
w, L > λe
• few scatterers
• many scatterers
• no scatterer
w
σw
G =
L
2 L 1− T
≈
π λe
T
2-terminal conductance
obeys Ohm‘s law.
µ1
2e 2
G=
⋅ M ⋅T
h
2e 2
G=
⋅M
h
T: average transmission
probablity of an electron.
µ1
here: contact and channel
from same material.
µ1
µ
µ2
µ2
µ2
Exp.: R. de Picciotto et al.,
Nature 411, 51 (2001).
Band-structure mismatch
in epitaxial Fe|GaAs(001) interfaces
!
! ik!↑r!
Ψ↑ (r ) = uk ,↑ ( r ) e
majority spins
spin
and
!
! ik!↓r!
Ψ↓ (r ) = uk ,↓ ( r ) e
minority spins
Local density approximation
with screened KKR method:
=> different symmetry of the
majority and minority spin
bands at the Fermi level
(d-band electrons).
O. Wunnicke, P. Mavropoulos, R.Zeller,
P.H. Dederichs, and D. G., Phys. Rev. B 65, R241306 (2002).
spin
Spin filtering:
Symmetry-enforced spin polarization
Landauer-Büttiker formalism
including overlap of
Bloch wave functions
at the interface.
majority spins
Transmitted current is
spin polarized with η ~ 99 %.
minority spins
• Similar results for
Fe/InAs(001): M. Zwierzycki et al.,
Phys. Rev. B 67, 092401 (2003).
• Spin polarized current
for (110) direction:
L. Sacharow et al.,preprint;
O. Wunnicke et al.,
cond-mat/0308138.
Free-electron model
gives:
η ~ a few %
ΔR
= 2η 2e− L / Λs (M. Johnson, 1998)
R
ΔR
⇒
≈ 1 % for L << ΛS
R
With
C.-M. Hu and T. Matsuyama,
Phys. Rev. Lett. 87, 066803 (2001);
D. G., Phys. Rev. B 63, R161307 (2001).
!
!
! ik↑(↓ ) r!
Ψ↑(↓ ) (r ) = uk ,↑(↓ ) (r ) e
Prerequisites for magnetoresistance effects:
... planar interfaces
... in situ processing of interfaces
... low interface resistance, i.e., „ohmic“ contact,
Schottky barrier is not useful
!
(perspective)
!
... sub-micrometer length of the semiconductor channel !
... ferromagnetic contacts with different coercive fields Bc !
=>
Ferromagnet/semiconductor hybrid structures
on the cleaved edge
of an InAs heterostructure
Molecular beam epitaxy of strained InAs quantum wells
4 nm-wide InAs quantum well
(modulation doped)
- no Schottky barrier to metals
- carrier density nS ~ 1011..1012/cm²
(tunable)
Surface
- mobility:
up to 350.000 cm²/Vs (4 K)
=> λe = 0.5 ... 1.5 µm
z direction (001)
Ch. Heyn,
W. Hansen
- Rashba coefficient:
! ~ 2 x 10-11 eVm
∆Θ = 180° after L ~ 0.15 µm
Cleaved-edge overgrowth (CEO)
z direction
1) InAs Quantum well
Heterostructure
2) Cleaved Sample
[100]
[011]
4) Experiment:
Ferromagnet/Semiconductor
Hybridstructure for
Spin-polarized Transport
[011]
on
i
t
ec
r
i
zd
3) Metal Deposition
(Ferromagnet)
2DES
(InAs)
CEO of Au/InAs(2DES): C.H. Möller, O. Kronenwerth, D. G.,
W. Hansen, Ch. Heyn, and D. Heitmann, Appl. Phys. Lett. 80, 3988 (2002).
Magnetic
Field
Prestructuring the 2DES for
cleaved-edge overgrowth
Predetermined
breaking point
Conventional
RIE technique
2DES in InAs
Cleavage
Upright position
Cleaved edge
Step junction (ex situ processing)
Cleaved edge
Metal deposition
Ion beam etching
Photoresist mask
Upright position
Second metal deposition
Photoresist removal
• self-aligning process
• angle defines separation
• free choice of 2nd FM
Final lithography and etching on cleaved edge
Co contacts
etched step
1
200 µm
2
3 4
2DES
View on shadow gap (SEM picture)
r t
e
p ac
p
u nt
co
h ~ 50 nm,
l
p
a
g
200nm low
t
c
ta
n
o
c
er
l = 0 ... 200 nm,
dCo(Fe) = 5 ... 20 nm,
λe > 0.5 µm
Device configuration:
Overview
(011) orientation
• planar surfaces
• chemicals avoided
at the interface
(001)
• submicron
gap between source
(FM1) and drain (FM2)
• perspective of in situ
processing of interfaces
and epitaxial growth
W = 10 ... 200 µm
Transport in
Co / InAs(2DES) / Co hybrid structures
l ~ 140 nm,
B⊥
B II 2DES:
Spin precession for kx component
h ~ 60 nm,
λe ~ 0.5 µm.
BR
ky
B ⊥ 2DES:
Spin precession for kx and ky component
BR
kx
B ⊥ 2DES
B II 2DES
R (Ω)
169.7
4.2 K
4.2 K
169.6
−∆R
169.5
-0.2 -0.1 0.0 0.1 0.2
-0.2 -0.1 0.0 0.1 0.2
B (T)
B (T)
negative spin valve effect
positive spin valve effect
Fe / InAs(2DES) / Fe hybrid structures
BII
B⊥
B II 2DES:
Spin precession for kx component
B ⊥ 2DES:
Spin precession for kx and ky component
B ⊥ 2DES
B II 2DES
0.02 K
415.8
415.6
416.6
416.4
R (Ω)
R (Ω)
416.0
416.2
415.4
-0.2 -0.1 0.0 0.1 0.2
B (T)
0.02 K
416.0
-0.2 -0.1 0.0 0.1 0.2
B (T)
negative spin valve effect
positive spin valve effect
Spin injection efficiency η in
step-junction Co/InAs(2DES)/Co hybrid structures
B II 2DES
-∆R/R (%)
• carrier density nS varied by illumination
0.06
0.04
0.02
ΔR
= 2η 2e− L / Λ s
R
∆R/R (%)
0.00
B ⊥ 2DES
T = 4.2 K
(M. Johnson, 1998)
0.06
0.04
ηexp ≈ 2 % for L << Λ S
0.02
Free − electron model :
ηtheo ≈ a few %
0.00
0 1 2 3 4 5 6 7 8
11
-2
nS (10 cm )
Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET)
on a cleaved InAs heterostructure
Top view
Au gate
electrode
SEM of cross section
200µm
z
x
SiO2
y
Front view
2DES
Cobalt
2DES
2µm
(001) direction
Gate-controlled magnetotransport experiment
ill., VDC = +10 V
= 25 Vrms
Rdyn (a.u.)
B II 2DES
1.284 T = 4.2 K
1.282
1.280
Rdyn (a.u.)
unill., VDC = 0 V
1.306
1.304
1.302
ill.
unill., VDC = -10 V
no
Rdyn (a.u.)
VDC
1.950
1.947
1.944
-0.10 -0.05 0.00 0.05 0.10
B (T)
Summary
• Step-junction FM/InAs(2DES)/FM hybrid structures
show negative and positive spin-valve
behavior. This depends on the magnetization
B⊥
of the ferromagnetic contacts.
BII
• Behavior is tuned by illumination
and by a gate voltage.
The recalculated spin polarization is 2 %,
obtained without Schottky barrier.
• Further experiments will involve
in situ preparation on the cleaved edge
and thus further improvement of the interface quality.
We thank P. Dederichs, D. Heitmann and O. Wunnicke.
We gratefully acknowledge financial support by BMBF and DFG.