スピントロニクスデザインコース
講義9

有機スピントロニクス
Organic Spintronics
大阪大学院基礎工学研究科
Graduate School of Engineering Science
大戸達彦
Tatsuhiko Ohtohttp://molectronics.jp
Molecular Architectonics Research Group http://molarch.jp

Rnon-local ()Thin Film

17.76

17.72
2.5 K
17.68 L = 1,300 nm-400

Single Molecule

0B(G)

200

400

Thermoelectronics

Spintronics

Electronics
Au

-200

Au

Ni

Ni

Au

Au

ΔT=0K
ΔT=2K
ΔT=4K
ΔT=10K

ΔT=15K
1000/T

Magnetic Field (Oe)Voltage /μV

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

Why organic?
・Weak spin-orbit interaction

Rnon-local ()17.76

・Molecular design

17.72

・Abundant

2.5 K
17.68 L = 1,300 nm
-400

-200

0B(G)

200

400

・Frexible, light weight
Possibility of highly efficient spin valve device

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

Outline
1. Organic Thin Film Spin Valve

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

1. Organic Thin FilmSpin Valve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

Spin-pumping

The spin diffusion length is more than 1 μm
S.-J. Wang et al. Nat. Electron. 2 (2019) 98

2. Single MolecularSpin ValveSingle Molecular Electronics

Threshold
Rectification*Coulomb blockade(Diode)

ML Perrin et al., Nature
Nanotech. 8, 282 (2013).

I. Diez-Perez et al., Nature
Chem. 1, 635 (2009).
B. Capozzi et al., Nature
Nanotech. 10, 522 (2015).
(Asymmetric electrode)

Hysteresis
Negative differential(Memory/Switch) resistance (NDR)

Spin-cross over; T. Miyamachi et al.,ML Perrin et al., Nature
Nature Comm. 3, 938 (2012)
Nanotech. 9, 830 (2014).
Mg-Porphine; S. Saha et al., Apl.
(Double barrier resonant
Mater&Inter., 7, 10085 (2015).
tunneling)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

Experimental Methods
Histogram

STM tipCurrent

Conductance

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

OccurrenceExperimental Methods

MCBJ with magnetic electrodes
Yamada et al. APL 98 (2011) 053110

Experimental Methods

Electrical break junction method,
C60/Ni

Scanning tunneling microscopy(STM), C60/Cr(001)

K. Yoshida et al. Nano Lett. 13 (2013) 481

S. L. Kawahara et al. Nano Lett. 12 (2012) 4558

Theoretical Design of Molecular Spin Valve・Origin of magnetoresistance・TMR・TAMR・Molecular structure
・Spin filter effectTunneling Anisotropic MR (TAMR)

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

3. 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 Basis

TurbomoleNEGF
H 0 H0 H 0 H 0

H0 H0 H 0 H0Hs
Scattering Region

μL = EF + 1/2 eV

μR = EF - 1/2 eVNEGF
ΣR

ΣLHs
Scattering Region

μL = EF + 1/2 eV

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

H=Hs+H0+H0+H0+…
Non-Hermitian problem for a finite system

H=Hs+ΣL+ΣR
 ES LL − H LL − Σ L ( E ) ES Lc − H Lc
G CC ( E ) = ES † Lc − H † Lc
EScc − H cc††
0ES−HRc
Rc

EScR − H cR
ES RR − H RR − Σ R ( E ) 0H eff = H + Σ L ( E ) + Σ R ( E )0
Σ𝐿 𝐸 = (𝐸S𝐿𝐶 − H𝐿𝐶 )† G𝐿𝐿(𝐸)(𝐸S𝐿𝐶 − H𝐿𝐶 )Surface Green’s function−1

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−HRcRc
Convergence of density matrixEScR − H cR
ES RR − H RR − Σ R ( E ) 0−1

NEGF
G = G0 + G0 Σ GDyson 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

4. NEGF-DFT and itsapplication

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・TAMRwith SMEAGOLGold wire

H. Nakamura et al. Phys. Rev. B 78 (2008) 235420Au-BDT-Au

H. Nakamura et al. Phys. Rev. B 78 (2008) 235420

Ni-BDT-Ni
LUMO
Spin-upHOMO

1Spin-down
HOMO

0.1
Parallel
Antiparallel

0.01-2-101
2
E-EF (eV)3

TMR~20%4

Possibility of higher TMR

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

Thermoelectric devicesS
ZT =Tk2

σ：conductivity
S ：thermopower
κ：thermal conductivity
BioLite Inc.

https://www.aist.go.jp/pr20050531

Molecular thermoelectric device
ColdHotsSZT =Tk2

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

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

Ni(111)-BDT-Ni(111)SMEAGOL module (NEGF-DFT), LDA functional

per spin

p 2 kB2T æ ¶ln t (E) öS=ç÷3e è ¶E ø E=ESplitting of HOMO
⇒Sign change of the Seebeck coefficientF9Total
UpDown8765432Total
UpDown765432
1

10-4-3-2-1

0E-EF (eV)123Hexa-faced structure(most stable)•8

Transmission Coefficient

Transmission Coefficient

per spin

per spinNi(111)-C60-Ni(111)40-4-3-2-1

0E-EF (eV)12

Penta-faced structure

Transport through LUMO … negative Seebeck coefficient34How to improve S?

without Owith O

G. C. Solomon et al.
J. Chem. Phys. 129 (2008) 054701

Quantum Interference

Papadopoulos et al. PRB 74(2006)193306

Fano ResonanceSinge Molecular QR

S = 970 μV/K
M. H. Garner et al. Nature 558 (2018) 415

Long range transport wireBis(terpyridine)M
M=Co； β=0.001 Å-1
M=Fe； β=0.028 Å-1

σ~exp(-βL)

Tuccitto et al, Nat. Mat. 8(2009) 41

Resonant tunneling?

Reddy et al, Science 315(2007) 1568

MO level is close to the Fermi level

High S is expectedTransport calculations
HiRUNE module (NEGF-DFT), PBE functional

Bridged Bis-terPy(M) M=Cu, Fe, Ru, Vac etc.

γR, γL

Nakamura, Ohto, et al. JACS 135(2013)16545

Energy level diagram

Current ProfileCu
Resonant tunneling through MOs
Nakamura, Ohto, et al. JACS 135(2013)16545

Ru

G and S•

Many narrow states•

Sign change of S

1 ò dE ( E - EF )t (E) ( - ¶ f ¶E )S=T
ò dEt (E)( - ¶ f ¶E )Nakamura, Ohto, et al. JACS 135(2013)16545

Wiedemann-Franz and ZT

Wiedemann-Franz is broken
Wiedemann-Franz則k
LZ == const.
sT

LWF =p 2 kBAt a temperature, ZT=03

Nakamura, Ohto, et al. JACS 135(2013)16545

Metal-complex-based
thermoelectric devices

Fe[(H2Bpz2) 2bipy]

D. Ghosh et al.
Appl. Phys. Lett. 106 (2015) 193105

N. Liu et al.
J. Phys. D: Appl. Phys. 51 (2018) 145102

5. Organic Magnetoresistance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 TRIPLET

P. 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

Bipolarons

Excitons 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 )V
Z= =I I 0ei (t + )Measurement

Equivalent circuit

Capacitance vs frequency

1= G + i CZ

Nyquistdiagram,Phase.
Give information on electronicprocesses

Capacitance

Fitting of the data
SingleDoubleSign : 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 1Al
α-6T
ITO

Region 3Region 2HFE-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 2

Region 3C > 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-6T

PentaceneAl

4.8

4.92
5.3

Pen onlyOMAR results
α-6T only

HFEHFEΔg 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SummarySingle carriers

Double carriers

Disorder
α-6TBipolarons
hhExcitons and e/h pairsheheΔg mechanism-MC+MC with HFE

The mechanism is identified.

Magnitude and shape ofOMAR is tuned.

Song-Toan Pham, Marine Fayolle, Tatsuhiko Ohto, Hirokazu Tada
Appl. Phys. Lett. 111, 203303 (2017)

Perspective
Single carriers
Bipolarons
hh-MC・Bipolaron is a
deep mid-gap state

・How much defective
are organic
semiconductors?

Realistic landscape↓
Carrier dynamics
simulation

W. Nie, et al, Adv. Sci., 2, 1500024 (2015)

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

Surface Green’s Function
M. P. Lopez Sancho et al. J. Phys. F 14(1984)1205

Recursive Method




H =





H0H10

H −10

H0
H −1

H1
H00 0 H −10
H10H0

H1 0𝑡0 = (𝐸 − 𝐻0 ) −1 𝐻0+𝑡෥0 = (𝐸 − 𝐻0 ) −1 𝐻0











Lead

Z-1

Z+1J

H1H0

H1
H0H0−1 𝑡 2𝑡𝑖 = (𝐼 − 𝑡𝑖−1 𝑡෦
𝑖−1 − 𝑡෦𝑖−1 𝑡𝑖−1 )𝑖−12𝑡෥ = (𝐼 − 𝑡 𝑡෦ − 𝑡෦ 𝑡 ) −1 𝑡෪
𝑖𝑖−1 𝑖−1𝑡𝑛 -𝑡𝑛−1 < ε𝑇 = 𝑡0 + 𝑡෥0 𝑡1 + 𝑡෥0 𝑡෥1 𝑡2 + ⋯ + 𝑡෥0 … 𝑡෧
𝑛−1 𝑡𝑛𝐺0 = (𝐸 − 𝐻0 − 𝐻1 𝑇) −1

Z

𝑖−1 𝑖−1𝑖−1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† lll

l =1llH1l

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)