Transcript スライド 1 - kitpc

KITPC2010
Semiconductor and Graphene Spintronics
Spintronics applications : spin FET
role of interface
on spin-polarized current
in FM/SC, FM/graphene junctions
Jun-ichiro Inoue
Nagoya University, Japan
Collaborators
Syuta Honda
PD, Kansai University
A.Yamamura
T. Hiraiwa
R. Sato
MC students, Nagoya University, Japan
Hiroyoshi Itoh
Asc. Prof., Kansai University, Japan
(computer codes)
Outline
 Introduction
- role of junction interface on GMR, TMR
- spin MOSFET and issues for SC, graphene
 Spin injection and MR in spin MOSFET
- some experiments
- role of Schottky barrier on spin polarized current
 Two-terminal lateral graphene junctions
- a simple model for MR
- band mixing at interface; effects on DPs
- more realistic models
Spintronics
 Usage of both charge and spin of electrons
e  |e|
Sz  
2
Sz  
2
 Phenomana and applications
- GMR, TMR, CIMS  sensors, MRAM
- GMR: spin dependent scattering at interfaces
- TMR: matching/mismatching of band symmetry between
two electrodes (D1 symmetry)
 Semiconductor spintronics
- spin FET, spin MOSFET with semiconductors
- or graphene
Spin MOSFET
 Conventional MOSFET
- Unipolar transistor
 Spin transistor
- Monsma et al.: hot electron spin transistor
- Datta-Das: gate control of SOI
 Sugawara-Tanaka
FM
gate
2DEG with SOI
- Spin MOSFET with half-metals
- logic + memory device
 Many proposals
- Flatté-Vignale: Unipolar spin diodes &transistors
- psuedospintronics, valleytronics in graphene
Issues and materials
Electrons
gate
FM
 Spin injection, transport and detection
 Materials
- Si: promising candidate, compatible with Si CMOS technology,
weak spin-orbit interaction (SOI)
- GaAs: high mobility, gate controllable SOI
many experiments on spin injection
- Graphene: high mobility, weak SOI
long spin diffusion length,
 Role of interface on spin-dep. Transport
in GaAs and graphene junctions
Some Experiments
 Spin injection into GaAs:
- Schottky barrier or tunnel barrier
- spin polarization 40 ~ 50 %
- optical detection
- GaMnAs as spin injector
 high ratio only at low T
e.g. O. M. van’t Erve et al., APL 84, 4334 (2004)
X. Jiang et al., PRL94, 56601 (2005)
Van Dorpe et al. PRB (2005)
 Spin injection into Si:
- spin polarization 10~20%
B. T. Jonker et al., Nature (2007)
Imaging of spin injection
 Positive spin accumulation in GaAs
- Lateral Fe/GaAs/Fe, Kerr effect
 Negative spin polarization in current
from GaAs to Fe
 Negative spin polarization
- Fe/GaAs/Fe junctions, negative TMR
Moser et al., APL 89, 162106 (2006)
- Current induced by photo-excited electrons
Kurebayashi et al., APL 91, 102114 (2007)
P>0
P<0
e-
S. A. Crooker et al.,
Science 309, 2192 (2005)
 see also:
Kotissek et al., Nat. phys. 3, 872 (2007)
Lou et al., Nat. phys. 3 193 (2007)
Electronic states at interface of GaAs
 Band structure of GaAs
at interface
Ene rgy [e V ]

Conduction band
D1

EC


L
IRS
(Schokley state)
G aA s


X U,K
Fe GaAs
 IRSs mix with Fe bands
- ↑spin bands; strong mixing
- ↓spin bands; weak mixing
due to band symmetry
↑spin
spin
EC
Valence band
Interfacial resonant states (IRSs) : local DOS
2
DOS [eV1]
1
spin
As contact
Ga contact
GaAs bulk
DS
0.7eV
EC
spin
spin
D S  0.1
200 ML
0
Fe n-GaAs
Spin dependent IRSs appear in SB.
↓spin IRSs in Fe-As contact are sharp.

spin
2
EF
0
As contact
2
Ga contact
EEC [eV]
Ls = 200ML, Ds = 0.5 eV
Exp. barrier height ~ 0.49 – 0.44 eV
Fe
As
Fe
Ga
Bias dependence of spin polarization
P

0.7
0.5
Spin polarization of current
becomes negative for small
Schokley barrier height.
0.4
0.1
DS=0.3eV

P

0
0.2
0.4
0.6
I  I
I  I
0.8
1
Bias [V]
Zero bias:
large I↑ due to D1 band symmetry
Negative bias:
Contribution from ↓spin IRSs
V
Fe
Shift of IRSs
GaAs
Momentum resolved conductance

DOS
 spin
 spin
 spin
 point
0.0
D(k||)
4.0
[eV1]
 spin
8
Log (k||)
0
[e2/h]
(DS=0.3eV, Bias=0.3V)
IRSs spread over whole Brillouin zone,
but those near the  point contribute to the conductance
due to small Fermi surface of GaAs assumed.
 Large P
Fe/GaAs/Fe tunnel junctions
Fe –As contact
Potential profile
DS
Fe
Fe
GaAs

[105]
IP
IAP
2
MR
I [e2/h]
3
0
MR 
1
0
0
0.2
0.4
0.6
0.8
1

0
0.4
0.6
Bias [V]
Bias [V]
Bias~0.0V
Bias~0.6V
P↑
D1
0.2
P↓
AP
D1
0.8
I P  I AP
I P  I AP
1
DS [eV]
0.75(without Schottky barrier)
0.80
1.0
Summary of first part
 Fe/GaAs with Schottky barrier and Fe/GaAs/Fe
- Interfacial resonant states are spin dependent and give
large positive and negative spin polarization.
 Control of Schottky barreir is crucial.
 several issues,
- Conductivity mismatch vs spin relaxation by SOI
Semiclassical model by Fert-Jaffres (2001) for FM/I/SC/I/FM
- roughness
- stacking direction SC layer
- half-metallic electrodes
- spin injection into Si
Conductivity
mismatch
(barrier resistivity)
SOI
Graphene
Structure

2-D Honeycomb lattice of C
zig-zag
edge
y
Electronic states
x
armchair edge
s, px, py orbitals  s bands
 pz orbital  p bands (zero-gap semiconductor)
 Linear dispersion : Dirac points
 Zero effective mass

2
p

E
E
2
kx
ky
4
K
Γ
M
Characteristics of Graphene
Massless fermions
  High mobility, low resistivity

New material for electronics
  2  10

10
8
6
5
m
s  4e / h
2
Carbon atoms : light element
  Weak spin-orbit interaction


2
4  10 cm /V s
Long spin diffusion length
application to spintronics
2-dimensionality
  Gate control
Possible applications
Graphene transistor, spin-FET, terra-hertz wave, …
FM/G/FM spin FET
Graphene sheet
Top gate
Spin injection / MR effect
FM
Back gate
 Current: on/off by gate
– energy gap
Exp. MR ratios a few %
nano-ribbon
bilayer graphene
Hydrogenation - graphane
 Magnetization control
 Fabrication method
Non-local measurement
Shiraishi’s group (2007)
A simple model of MR
 Matching of the conduction pass with DP
10
DE [eV]
E [eV]
10
DE
0
0
Dirac point of Graphene
10
0
1
k||
2
3 0
1
k||
2
3
10
0
2 4 6 0
 [e2/h]
MR
1
E(k// ) for nano-ribbon with zigzag edge
k//: momentum along the edge
MR appears when momentum matching is spin-dependent, and
when the band width of conduction band is narrow.
However, usual transition metal FM
Wide conduction band
 no MR
MR in lateral FM/graphene/FM junctions
 A single orbital tight-binding model + Kubo formula
 DP shifts due to contact with leads
 tunneling via states near DP
K'
L
W=∞
 [e2/h]
Zigzag edge contact
with electrodes (square lattice)
Effective DP
1.0
a
0.8
0.01
0.05
0.1
0.3
0.5
1.0
0.6
0.4
0.2
0.0
2.09
2.10
2.11
k||
tI
L=12[ML]
tI=sps  a
EF
Tunnel
barrier
DP
k//

1
L
Energy states of finite size junction
20ML
Graphene
s-□
50ML
50ML
k//
probability density of graphene
0.0
k//
Large band mixing
E(k)
Small band mixing
s-□
1.0
More details
 Shift of DP with
- Graphene length
- Band mixing at the contact
 spin dependent G for FM electrodes
Realistic contacts
 Electrodes with fcc (111) lattice or triangular lattice
wide overlap region between graphene and electrodes
sp3
sp3d5
sp3d5
y

a
Zigzag edge
L
a
z
4ML


x
Some preliminary results
 [e2/h/atm]
 Shift of DP with
- overlap of graphene and electrodes (triangular lattice)
- band mixing
100
100
10-1
10-1
10-2
10-2
LL=LR=1
LL=1 LR=400
LL=LR=400
-3
10
10-3
10-4
10-4
10-5
2.07
1.0
0.5
0.1
0.05
0.01
2.08
2.09
2.1
10-5
2.11 2.07
2.08
2.09
k//
2.1
k//
1000 [ML]
S+P
k//
5 [ML]
LL [ML]
LR [ML]
2.11
MR in bccFe/graphene/bccFe
 Spin dependent band mixing at interface  MR
100
Bcc lattice on leads
P
P
AP
W=∞
 [e2/h]
102
L
104
L=1000
106
K’
108
2.06
2.08
2.1
2.12
k||
sp3
sp3d5
1
P
tg
P
103
tI
AP
0.8
0.6
MR
102
0.4
0.2
101
0
0
1000
L [ML]
2000
MR
 [e2/h]
sp3d5
MR in graphene junctions with Fe alloys
 Materials dependence of MR – shifting the up spin band
Ferromagnetic alloys for lead
Fe0.7Co0.3
Fe0.9Cr0.1
1.0
Fe
MR
0.8
0.6
0.4
0.2
0.0
2.0
1.0
0.0
DE [eV]
1.0
2.0
Change in the electronic state
of Fe alloys at the contact
matching of conduction channel
becomes worse in up spin state
Summary of the second part
 MR in FM/graphene/FM junctions
- Spin dependent shift of Dirac points appears
in zigzag edge contact.  moderate MR effect
- MR can be large for some FM alloy electrodes.
 Importance of electronic structure near the interface
on spin injection and MR
Other effects unconsidered should be examined to
confirm the present results.
Zigzag edge vs Armchair edge
  of n-type graphene/graphene/n-graphene junctions
Interfacial hopping = tg J
arm-chair edges
zigzag edges
k//
Log  [e2/h / (atom spin)]
L (101 ML)


J = 1.0

L (100 ML)
J = 1.0
2
3
4

6
0
0.5
J = 0.5
J = 0.1
0.01 0.02 0.03 0.04 0.05 1.9
k//
0.1
2
K
2.1
k//
2.2
2.3
2.4