スピントロニクスデザインコース
講義7

有機スピントロニクス

基礎工学研究科
大戸達彦

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・LSIetc…

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

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. Single Molecular Spin Valve

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

1. 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., NatureChem. 1, 635 (2009).
B. Capozzi et al., NatureNanotech. 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

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 Basis

TurbomoleNEGFH 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 )0Σ𝐿 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 iIntegral 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 GKeldysh-Kadanoff-Baym (KKB) Equation↑ lesser self energy

3. 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・TAMR

with 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
-2-1

01
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：電気伝導度
S ：ゼーベック係数
κ：熱伝導度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=E

分子軌道（HOMO）のスピン分極によりフェルミ準位より上に軌道が現れる⇒ゼーベック係数の符号が変わる

F

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=E

分子軌道（HOMO）のスピン分極によりフェルミ準位より上に軌道が現れる⇒ゼーベック係数の符号が変わる

F9Total
UpDown8765432Total
UpDown765432110-4-3-2-10E-EF (eV)123Hexa-faced structure(most stable)•••

8Transmission Coefficient

Transmission Coefficient

per spin

per spinNi(111)-C60-Ni(111)40-4-3-2-10E-EF (eV)12Penta-faced structure

安定と考えられる構造ではいずれも負のゼーベック係数（実験結果を再現）
フェルミ準位近くにあるLUMOが伝導に寄与（Au-C60-Auと同様）
スピン分極の様子は吸着構造によって異なるが、小さい

34熱起電力向上に向けて

without O
with O

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

量子干渉効果Papadopoulos et al. PRB 74(2006)193306

Fano共鳴単一分子における量子干渉効果

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

長距離伝導分子ワイヤー
Bis(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

共鳴トンネルによる長距離伝導？

Reddy et al, Science 315(2007) 1568

分子軌道の位置が電極のフェルミ準位に非常に近い（共鳴トンネルなら）熱電材料として有望

電気伝導計算HiRUNE module (NEGF-DFT), PBE functional

Au電極に架橋したBis-terPy(M) M=Cu, Fe, Ru, Vac etc.

γR, γL

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

準位図Current ProfileCu

Ru

d-metalによってフェルミ準位まで下がった分子軌道による共鳴トンネル
Nakamura, Ohto, et al. JACS 135(2013)16545

伝導度と熱起電力••

フェルミ準位付近に大量の状態
透過係数が鋭く、Sは大きい•

ある温度でSの符号が反転する

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

Wiedemann-Franz則の破れとZT

Wiedemann-Franz則の破れが大きなZTの一因

Wiedemann-Franz則k
LZ == const.
sT

LWF =p 2 kB

ZT=0となる温度が存在する

3

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

金属錯体分子を用いた熱電素子

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

4. 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 carriersBipolarons

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 electronic
processes

CapacitanceFitting 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 1

Al
α-6T
ITO

Region 3Region 2HFE-MC

α-6T

Region1 Region2 Region3

HFE–MC with HFE

HFE

HFE

+MC with HFE

How to explain the various OMAR shapes?

SingleCapacitance results
Region 1Region 2

Region 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-6T

Pentacene
Al

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SummarySingle carriers

Double carriers

Disorderα-6T

Bipolarons
hhExcitons and e/h pairs

heheΔg mechanism-MC+MC with HFE

The mechanism is identified.

Magnitude and shape ofOMAR is tuned.

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

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

・How much defective
are organicsemiconductors?

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 −1H1
H00 0 H −10
H10H0

H1 0

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

Lead

Z-1

Z+1J

H1H0

H1
H0

H0−1 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 =1Lead

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 =  lhlhll

H1H0H0

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)