KITPC2010
Spintronics applications : spin FET role of interface on spin-polarized current in FM/SC, FM/graphene junctions
Jun-ichiro Inoue
Nagoya University, Japan

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)


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


Usage of both charge and spin of electrons e
 
S z
 
2
S z
 
2

Phenomana and applications
- GMR, TMR, CIMS
 sensors, MRAM
- GMR: spin dependent scattering at interfaces
- TMR: matching/mismatching of band symmetry between two electrodes (
D
1 symmetry)

Semiconductor spintronics
- spin FET, spin MOSFET with semiconductors
- or graphene


Conventional MOSFET
Unipolar transistor

Spin transistor
- Monsma et al.: hot electron spin transistor
- Datta-Das: gate control of SOI gate

Sugawara-Tanaka
- Spin MOSFET with half-metals
- logic + memory device
FM
2DEG with SOI

Many proposals
- Flatté-Vignale: Unipolar spin diodes &transistors
- psuedospintronics, valleytronics in graphene

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


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)


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) e -
P >0
P <0
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)


Band structure of GaAs at interface




GaAs
D
1
Conduction band
E
C
IRS
(Schokley state)
 
L X U,K
Valence band
Fe GaAs

IRSs mix with Fe bands
- ↑spin bands; strong mixing
- ↓spin bands; weak mixing due to band symmetry
↑ spin
 spin
E
C

2
1
As contact
Ga contact
GaAs bulk
 spin
D
S

 spin spin
E
C
0.1 0.7eV
0

 spin E
F
2
0
E

E
C
[eV]
L s = 200ML,
D s = 0.5 eV
2
Exp. barrier height ~ 0.49 – 0.44
eV
200 ML
Fe n-GaAs
Spin dependent IRSs appear in SB.
↓spin IRSs in Fe-As contact are sharp.
As contact
Fe As
Ga contact
Fe Ga


0.7
0.5
Spin polarization of current becomes negative for small
Schokley barrier height.


0 0.2
0.4
0.1
D
S
=0.3eV
P

I


I

I


I

0.4
0.6
Bias [V]
0.8
1
Zero bias: large I
↑ due to
D
1 band symmetry
Negative bias:
Contribution from ↓spin IRSs
V
Shift of IRSs
Fe
GaAs

DOS
 spin

 spin
 spin
 spin
 point
0.0
D ( k
||
) [eV
4.0
1

8
] Log
( k
||
0
)
[e 2 /h]
(
D
S
=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 –As contact Potential profile
Fe
D
S
Fe
GaAs
[

10

5 ]
3
I
P
I
A
P

2
1
0
0 0.2
0.4
0.6
0.8
Bias [V]
1
Bias~0.0V
0
MR

I
P

I
I
P

I
AP
AP

0 0.2
0.4
0.6
0.8
Bias [V]
1
D
S
[eV]
0.75(without Schottky barrier)
0.80
1.0
Bias~0.6V
P↑
D
1
P↓ AP
D
1


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 SOI
(barrier resistivity)

Structure
 2-D Honeycomb lattice of C y
Electronic states

 s, p x
, p y p z orbitals
 s bands x armchair edge orbital
 p bands (zero-gap semiconductor)
 Linear dispersion : Dirac points

Zero effective mass
2 p

E
2
4
K k x k y
Γ
M zig-zag edge

Massless fermions
  High mobility, low resistivity
 New material for electronics
   6 

10

8  m s 
4 e
2
/ h
Carbon atoms : light element

 Weak spin-orbit interaction
 Long spin diffusion length
 application to spintronics
2-dimensionality

 Gate control
Possible applications
Graphene transistor, spin-FET, terra-hertz wave, …


Spin injection / MR effect
Graphene sheet
Top gate
Back gate
Exp. MR ratios a few %

Current: on/off by gate
– energy gap nano-ribbon bilayer graphene
Hydrogenation - graphane

Magnetization control

Fabrication method
FM
Non-local measurement
Shiraishi’s group (2007)


Matching of the conduction pass with DP
10 10
D
E
0 0
Dirac point of Graphene

10
0 1 2 3 k
||
0 1 k
||
2 3
E ( k
//
) for nano-ribbon with zigzag edge k
//
: momentum along the edge

10
0 2 4

[e 2 /h]
6 0
MR
1
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


A single orbital tight-binding model + Kubo formula

DP shifts due to contact with leads
 tunneling via states near DP
K '
Zigzag edge contact
Effective DP with electrodes (square lattice) 1.0
a
L
W = ∞
0.8
0.6
0.4
0.01
0.05
0.1
0.3
0.5
1.0
0.2
0.0
2.09
2.10
k
||
2.11
L= 12[ML] t
I t
I
=sp s  a
E
F
Tunnel barrier
DP k
//
 
1
L

20ML
Graphene s□
50ML s□ k
//
50ML
Large band mixing
Small band mixing k
// probability density of graphene
0.0
1.0

 Shift of DP with
- Graphene length
- Band mixing at the contact
 spin dependent G for FM electrodes


Electrodes with fcc (111) lattice or triangular lattice wide overlap region between graphene and electrodes sp
3 d
5 sp
3 sp
3 d
5 y
 a L a
Zigzag edge
4ML z x
 


Shift of DP with
- overlap of graphene and electrodes (triangular lattice)
10
0
- band mixing
10
0
10
-1
10
-1
10
-2
10
-3
10
-4
10
-5
2.07
2.08
2.09
k
//
10
-2
LL=LR=1
LL=1 LR=400
LL=LR=400
10
-3
10
-4
2.1
2.11
-5
10
2.07
1000 [ML]
2.08
2.09
k
//
S+P
2.1
1.0
0.5
0.1
0.05
0.01
2.11
5 [ML] k
//
L
L
[ML] L
R
[ML]


Spin dependent band mixing at interface

MR
10 0
Bcc lattice on leads
L
10

2
10

4

P


P


AP
W = ∞
L =1000
10

6
K
’
10

8
2.06
2.08
k
||
2.1
2.12
sp 3 d 5 sp 3 sp 3 d 5 t g t
I
10 3
10 2
1

P


P


AP
MR
0.8
0.6
0.4
0.2
10 1
0 1000
L [ML]
2000
0


Materials dependence of MR – shifting the up spin band

Ferromagnetic alloys for lead
Fe
0.7
Co
0.3
Fe
0.9
Cr
0.1
1.0
0.8
0.6
0.4
0.2
0.0

2.0

1.0
D
E

0.0
[eV]
1.0
Fe
2.0
Change in the electronic state of Fe alloys at the contact
 matching of conduction channel becomes worse in up spin state


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.

  of n-type graphene/graphene/n-graphene junctions
Interfacial hopping = t g

J arm-chair edges zigzag edges k
//
L (101 ML)


J = 1.0
2
3
J = 0.5
4
 J = 0.1
6
0 0.01 0.02 0.03 0.04
k
//
0.05
J = 1.0
0.5
L (100 ML)
0.1
K
1.9
2 2.1
2.2
2.3
2.4
k
//
