スピントロニクスデザインコース
講義10

Organic Spintronics

Graduate School of Engineering Science
Tatsuhiko Ohto

Tada Laboratory
1000 nm

100 nm

10 nm

1 nm

Organic Electronics

Molecular Electronics

This film devices

Single molecular measurement

Organic wires

Nano-gap electrodes

Molecular thermoelectric device
ColdHotsS
ZT =T
k2

σ：Electrical conductance
S ：Seebeck coefficient
κ：Thermal conductancePhonon scattering
Chemical modfication

Themopower (Seebeck Coefficient)
S=-p 2 kB2T æ ¶ln t (E) öçè
3e¶E

÷ø
E=EF

Gradient of the contantanceElectron or hole?

Calculation of T(E) fromconductance and thermopower
Reddy et al, Science 315(2007) 1568

Thermopower measurement

BDT()

V = S junction - SCu DT

C60

Substrate → Au and Ni
Lee, Ohto, et al. Nano Lett. 14(2014)5276

Thermopower measurement
BDT

C60

Lee, Ohto, et al. Nano Lett. 14(2014)5276

Ni(111)-BDT-Ni(111)SMEAGOL module (NEGF-DFT), LDA functionalp 2 kB2T æ ¶ln t (E) öS=ç÷3e è ¶E ø E=E

LUMO
Spin upHOMO

1Spin down
HOMO

0.1
TotalUp
Down

0.01-2-101
2E-EF (eV)34

SNi-BDT-Ni=-14.2 (calc), -12.1±1.3 (exp) μV/K
Splitting of HOMO due to the spin polarization
Lee, Ohto, et al. Nano Lett. 14(2014)5276

F

First report oflateral organic spin valve

T. Kamiya et al. Phys. Rev. B 95 (2017) 085307

Organic Spin Valve2004 Vardeny
Organic Spin Valve

Xiong et al. Nature 427 (2004) 821

Weak spin-orbit interaction
Molecular design, light weightProblems of vertical devices?

D. Sun et al., Chem. Commun., 50, 1781 (2014).

Can we inject spin into organic materials?

Lateral Device

Spin valve

Hanle effect

X. Lou et al. Nature Physics 3 (2007) 197

Lateral Organic Spin Valve

Pressured α-(BEDT-TTF)2I3 Crystal

T. Kamiya et al. Phys. Rev. B 95 (2017) 085307

Outline
1. Molecular Spin Valve
2. Introduction of Non-equilibrium Green’sFunction (NEGF) method
3. NEGF-DFT and its applications
4. Organic Magetoresistance, OMAR

1. Molecular Spin Valve

Spintronics
Spin

Magnetics

Spintronics

・Hard disk
・Magnet・Sensor
etc…

・TMR head・ReRAM
・Spin Seebeck
・Spin Transistor
etc…

-eelectron

Electronics

Electron・Transistor
・Laser・LSI
etc…

http://www.s-graphics.co.jp/nanoelectronics/index.html

Tunneling Magnetoresistance (TMR)
・Tunneling electron through an insulator
・Spin polarization of electrodes determines
the MR ratio

MgO crystal blocks d electron ofmajority spin

W. H. Butler et al. Phys. Rev. B 63 (2001) 054416

Single Molecular TMR Devices

Rocha et al. Nat. Mater. 4 (2005) 335

S. Sanvito Nat. Phys. 6 (2010) 562

Tunneling Anisotropic Magnetoresistance (TAMR)

J.-J. Li et al. J. Am. Chem. Soc. 137 (2015) 5923

Experimental Methods
Histogram

STM tipCurrent

Conductance

2e2/h→1 G0
Atomic contact
MolecularConductanceTip displacement
Break Junction (BJ) Method

Occurrence

Theoretical Design of Molecular Spin Valve・Origin of magnetoresistance・TMR・TAMR・Molecular structure
・Spin filter effect2. Non-Equilibrium Green’s
Function (NEGF) method

Programs
Atomic Orbial(SIESTA)
molecule
10~100 atoms

electrodes
8x8x6x2=768 atoms(!)

TranSIESTA（Spain, Denmark）
with SIESTAATK (Quantum Wise)
Commercial TranSIESTASMEAGOL（Ireland, UK）
Spin Transport
HiRUNE（Japan, AIST）
Electron-phonon
OpenMX（Japan）

Plane Wave

Quantum Espresso

Gaussian BasisTurbomoleNEGF
H0 H0 H0 H0

H0 H0 H0 H0Scattering Region

μL = EF + 1/2 eV

μR = EF - 1/2 eV

NEGF
ΣR

ΣLScattering Region

μL = EF + 1/2 eV

μR = EF - 1/2 eVNEGF
Hermitian problem for an open infinite system

Non-Hermitian problem for a finite system

 ES LL  H LL  Σ L ( E ) ES Lc  H Lc
G CC ( E )  ES † Lc  H † Lc
EScc  H cc
††
0ES
HRcRc

EScR  H cR
ES RR  H RR  Σ R ( E ) 0H eff  H  Σ L ( E )  Σ R ( E )0Σ𝐿 𝐸 = (𝐸S𝐿𝐶 − H𝐿𝐶 )† G𝐿𝐿(𝐸)(𝐸S𝐿𝐶 − H𝐿𝐶 )Surface Green’s function

1Surface Green’s Function
Tight Binding Layer (TBL) Method




H 




H0H10H 1
0H0H 1

H1
H00 0 H 1

S. Sanvito et al. Phys. Rev. B 59(1999)11936

0H10

H0

H1 0










M…degrees of freedom
1/ 2 ik zkkZ  n e H  H e
01ik  H 1e ik   SE  k  0  H11  H 0  SE   H11 H 1 0
Sign of the group velocity→ Bloch, Evanescent States

LeadZ-1

ZZ+1JH1
H0H1H0H0

Surface Green’s Function
Tight Binding Layer (TBL) Method

S. Sanvito et al. Phys. Rev. B 59(1999)11936

Mikl ( z  z ') † 1
ekl , z  z ' kl
 l 1gz,z '   M
  eikl ( z  z ') † 1 z  z 'klkl l 1

Lead

Z-1

ZZ+1JM   H 1 k eik ( z  z ')k†  k eik ( z  z ')k† llll 1ll

H1l

H0Green’s function of infinite leadsMM

†




k k k l 1l†kl

l 1llk†k  k†k   lhlhl

l

H1
H0H0

Solution of H, φ…
~→ Dual basis φM z  z ', z0    z  z ', z0    kh eikh ( z  z0 )k†h kl eikl ( z0  z ')k†l 1l , h 1g L     kh eikh k†h kl eikl k†l  1
 l ,h 1
M

Boundary condition Z = Z0→ Semi-infinite (Surface Green’s function)

NEGF
G = G0 + G0 Σ G

Dyson Equation=＋GG0Γ L ( E )  i  Σ L ( E )  Σ†L ( E ) 𝑇 = Tr[GΓL G † ΓR ]

Σ=ΣL +ΣR

We can add any interactions through ΣΣL/R ・・・left/right electrodes Σe−ph ・・・electron-phonon interaction<< †G = GΣ G

Keldysh-Kadanoff-Baym (KKB) Equation↑ lesser self energyNEGF-SCF“Lesser” Green’s functionG CC( E )  G CC ( E ) ΣG †CC ( E ) Keldysh-Kadanoff-Baym (KKB) Equation

DCC 1dEG(E)CC
2 i
Integral Contour
M. Brandbyge et al. Phys. Rev. B 65(2002)165401

 ES LL  H LL  Σ L ( E ) ES Lc  H Lc
G CC ( E )  ES † Lc  H † Lc
EScc  H cc††0ESHRc
Rc
Convergence of density matrix

EScR  H cR
ES RR  H RR  Σ R ( E ) 01

Transmission Function T(E)
LUMO

HOMO

Molecular orbital (MO)in the gas phase

ProjectedDensity ofstates (PDOS)
T(E)

1 G0~ 7.75 × 10-5 S

ELorentz function withCenter EMO + DWidthg

EF

𝑇 = Tr[GΓL G † ΓR ]

3. NEGF-DFT and its
application

What we can obtain…
・Transmission Function V V  †T ( E,Vb )  Tr  ΣL ( E )G CC( E )  ΣL ( E )G CC( E )  =Tr Γ L  E  b  G CC ( E)Γ R  E  b  G CC( E) 22 ・TMR ratio
The ratio of the transmission function with parallel/antiparallel magnetization

・Current voltage characteristics

I (Vb ) 1dET ( E ,Vb )  f  E   L   f  E   R  ・Spin Transfer Torque・TAMR

with SMEAGOL

Ni-BDT-Ni
LUMO
Spin-upHOMO

1Spin-down
HOMO

0.1
Parallel
Antiparallel

0.01-2-1012
E-EF (eV)TMR~20%34

IETS
Melamine/Cu(001) switch
1.99 eV
1.70 eV

TS1TS20.95 eV
0.72 eV

C2C10.00 eVGSQ・Switching rate from first-principles
・Activation energy under bias
(NeqNEB)
T. Ohto et al. Phys. Rev. B 87 (2013)205439

Breaking of atomic wires
Al wire breaking

4. Organic Magnetoresistance(i)Marine Fayolle, Mariko Yamaguchi, Song Toan Pham, Tatsuhiko Ohto,and Hirokazu Tada;“Determination of the mechanism behind the organic magnetoresistanceby using impedance spectroscopy”
International Journal of Nanotechnology 12, 238-247 (2015)(ii)Marine Fayolle, Mariko Yamaguchi, Tatsuhiko Ohto, and Hirokazu Tada;“Impedance spectroscopy of organic magnetoresistance devices – Effect ofinterface disorder”
Journal of Applied Physics, 117, 075501-075501-8 (2015)

Organic magnetoresistance(OMAR)
Usual MROMARNONMAGNETICMAGNETIC

Room temperature.
Low magnetic field (mT)

GMR, TMR
Spinvalve.

Up to several 1000%
Y. Wang et al. Phys. Rev. X 6, 011011 (2016)

MC (%) 

Sanvito, Nat. Mater. 10 (2011) 484.

MR: magnetoresistanceI ( B)  I (0)I (0)Nguyen et al. J. Mater. Chem. 17 (2007) 1995

Theory: Single vs. Double carriers
The magnetic field modifies
the ratio between SINGLET and TRIPLETP. Bobbert et al., Phys.
Rev. Lett. 99, 216801(2007).

Single carriers

Double carriers

Only ONE type of carrier

BOTH hole and electron are requirehhoreeheheTheory: Single vs. Double carriers
The magnetic field modifies
the ratio between SINGLET and TRIPLET

Single carriershh

BIPOLARONee

SPIN BLOCKING

Double carriers
heheSinglet: Recombination/Dissociation
Triplet: Reaction with charge

Singlet bipolaron allowed

Triplet bipolaron forbidden

Modified singlet to triplet ratio

Theory: Single vs. Double carriers
Single carriers

Double carriers

BipolaronsExcitons and e/h pairs

hhoreeB decreases the number of bipolarons

Bipolaron lifetime:shorthehe

B changes the singlet/triplet ratio

Singlet:recombination

Triplet:Reaction with charge

longEnhancedwith long
lifetime-MC+MCor –MC+MC or -MC +MCwith HFEImpedance spectroscopy
Vtotal  VDC  V0 sin( t )V0ei (t )VZ I I 0ei (t  )Measurement

Equivalent circuit

Capacitance vs frequency

1 G  i CZ

Nyquistdiagram,Phase.

Give information on electronicprocesses

Capacitance

Fitting of the dataSingle

DoubleSign : type ofinjection
Value: traps
characterizationOMAR results
I-V characteristics:
Int. J. Nanotechnol.,12, 238-247, 2015

MC (%) I ( B)  I (0)I (0)OMAR results:
Region 1Alα-6T
ITO

Region 3Region 2
HFE-MC

α-6T

Region1 Region2 Region3HFE–MC with HFE

HFE

HFE+MC with HFE

How to explain the various OMAR shapes?

SingleCapacitance results
Region 1Region 2Region 3

C > 0:
Singleinjection

C < 0:
Doubleinjection

C < 0:
Doubleinjection

Bipolaron OMAR

Transition: double+ single carriers
OMAR mix

Negative OMAR

DoubleDouble carriers OMAR
Positive OMAR

Pentacene doping
α-6T

HFE

Direction of increasing
Pen concentration

The current decreases with Pen.
At low Pen concentration only, HFEappears.

HFE

HFE

HFE

At 1.5 V (Region 1, bipolaron OMAR)

I-V chracteristics
α-6T only

α-6T + low Pen concentration

α-6T + high Pen concentration
3.1

1 to 3.28
4.28

ITO

α-6TPentaceneAl

4.8

4.92
5.3

Pen onlyOMAR results
α-6T only

HFE

HFE

Δg mechanism

HFEHFEΔg mechanism

α-6T + low Pen concentration

Different environment
α-6T + high Pen concentration

Δg ≠ 0Spin precession out of phase. Cause aneffect opposite to the effect at low field.
Bobbert et al., PRB 84 (075204) 2011

Pen onlySummary
Single carriers

Double carriers

Disorder
α-6TBipolarons
hhExcitons and e/h pairs

heheΔg mechanism-MC+MC with HFE

The mechanism is identified.

Magnitude and shape ofOMAR is tuned.
47

Summary• Theoretical design of molecular spin valve• NEGF-DFT and its application tospintronics and thermoelectronics• OMAR and its mechanisms