04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 11
Spin Dependent Electron Spin Dependent Electron Transport in Nanostructures Transport in Nanostructures
A. Ali YanikA. Ali Yanik††
DissertationDissertation
††Department of Physics Department of Physics &&
Network for Computational NanotechnologyNetwork for Computational NanotechnologyPurdue University, West Lafayette, IN 47907Purdue University, West Lafayette, IN 47907
April 2007April 2007
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 22
Spin + Electronics = Spin + Electronics = SpintronicsSpintronics
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 33
Spintronic DevicesSpintronic Devices
Non volatile RAM, Freescale,2006
Devices: GMR (read heads), TMR (MRAM), BMR Devices, etc..
MagnetoelectroniMagnetoelectronics cs
GateFM FM
2DEG
GateFM FM
2DEG
S. Datta & B. Das, APL. 56, 665 (1990)
Gate Voltage Control / Rashba Effect
Field Controlled SpintronicsDevices: Spin-FET (Datta), etc..
Contact Contact Injection/DetectionInjection/Detection
Gate Gate ContactContact
External B External B FieldField
Spin Spin DephasingDephasing
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 44
NEGF Formalism
Motivation-IMotivation-I
DeviceDevicess
Concepts
Physics Community
Spin Decoherence + QM
Equilibrium
Engineering Community
Transport + QM
Non-Equilibrium
Decoherence Physics Quantum Transport
Ph.D. Thesis: First formalized treatment of Quantum-Transport with Spin-Decoherence in NEGF
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 55
Motivation-IIMotivation-II
ContactsChannelElectrons
Ballistic Transport / NEGF FORMALISM
Phononsel
NEGF FORMALISM (Inelastic Transport)
Electron-phononrelaxation time
LocalizedSpins
es sl Spin-latticerelaxation time
EQUILIBRIUM PHYSICSEQUILIBRIUM PHYSICS
Challenges:
Physics Based Unified Treatment (not specialized for each device, geometry, etc)
Conservation Laws (angular momentum, total energy, particles)
Numerically Treatable
Benchmark against experiment.
State of Art Modelling
Averaging of Coherent Processes
Doesn’t Capture the Physics
Not straightforward to include dissipative interactions
NON-EQUILIBRIUM TRANSPORT
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 66
A Unified Quantum A Unified Quantum Transport Model Transport Model
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 77
Unified Approach to Nanoscale DevicesUnified Approach to Nanoscale Devices
Quantum
Device
Source Drain
Gate
Scatterer
Molecule (Gosh et al)
MTJ (Yanik et al)
L R
Scattering
Source Drain
Gate
QuantumDevice
H U
Spin Torque (Prabhakar et al)
Nanotubes (IBM, Kosawatta et al)
Nuclear Spin Polarization(Salahuddin et al)
MOSFET (Damle et al)
RTD (Klimeck et al)
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 88
Magnetic Tunnel Magnetic Tunnel JunctionsJunctions
Availability of Experimental DataAvailability of Experimental Data
Technological ImportanceTechnological Importance
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 99
Coherent RegimeCoherent Regime
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1010
Junction MagnetoresistanceJunction Magnetoresistance Potential Barrier + Magnetic Contacts
Soft Layer & Hard Layer (fixed)
Exchange shifted two current model
Parallel Contacts Anti-parallel Contacts
0
0F AF F AF
AF F
I IR R G GRJMR
R R G I
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
ΔΔ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ
Parallel Contacts Anti-parallel Contacts
0
0F AF F AF
AF F
I IR R G GRJMR
R R G I
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
ΔΔ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ
F AF F AF
AF AF
R R G GRJMR
R R G
Parallel ContactsAntiparallel Contacts
T.M. Maffit et al IBM J. Res. & Dev. 50, 25 (2006)
Barrier
FE
minoritycE
majoritycE
FE
minoritycE
majoritycE
barrU
Barrier
FE
minoritycE
majoritycE
FE
minoritycE
majoritycE
barrU
Stearns M. B., J. Magn. Magn. Mater. 5, 167 (1977)
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1111
Junction MagnetoresistanceJunction Magnetoresistance Potential Barrier + Magnetic Contacts
Soft Layer & Hard Layer (fixed)
Exchange shifted two current model
Parallel Contacts Anti-parallel Contacts
0
0F AF F AF
AF F
I IR R G GRJMR
R R G I
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
ΔΔ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ
Parallel Contacts Anti-parallel Contacts
0
0F AF F AF
AF F
I IR R G GRJMR
R R G I
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Soft Layer
Hard Layer
Tunneling Oxide
F
F
Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
ΔΔ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ Δ
FE
minoritycE
majoritycE
FEminoritycE
majoritycE
Δ
F AF F AF
AF AF
R R G GRJMR
R R G
Parallel ContactsAntiparallel Contacts
T.M. Maffit et al IBM J. Res. & Dev. 50, 25 (2006)
Spin polarization is conserved
Rectangular potential barrier & exchange shifted parabolic bands.
Qualitatively correct and widely used by experimentalists
2
2F F F F
FM
F F F F
k k k kP
k k k k
22 barr Fm U E
Slonczewski’s Formula:
Fails for Thin Tunneling Barriers!!!
J.C. Slonczewski PRB 39, 6995 (1989)
Practical Interest
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1212
Coherent Regime (NEGF)Coherent Regime (NEGF)
F z AF zz
F z
I E I EJMR E
I E
Weighting Factor
JMR for Different Incoming Energies
z
z F z F zE
E I E I E
majoritycE
minoritycE FE
EF=2.2eV, ∆=1.45eV and Vbias=1meV after Stearns et al.
ω(Ez) shifts towards higher energies with increasing barrier thicknesses
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1313
Coherent Regime (NEGF)Coherent Regime (NEGF)
F z AF zz
F z
I E I EJMR E
I E
Weighting Factor
JMR for Different Incoming Energies
z
z F z F zE
E I E I E
EF=2.2eV, ∆=1.45eV and Vbias=1meV after Stearns et al.
ω(Ez) shifts towards higher energies with increasing barrier thicknesses
( )z z zJMR E JMR E dE
Experimentally Measured JMR
ω(Ez) shifts towards higher energies with increasing barrier thicknesses
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1414
Incoherent RegimeIncoherent Regime
Impurity Concentration
Barrier Thickness
Barrier Height
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1515
MTJs with Magnetic Impurity LayersMTJs with Magnetic Impurity LayersR. Jansen & J. S. Moodera, J. Appl. Phys. 83, 6682 (1998)
Hard Layer
FTunneling Oxide
Impurity Layer
Tunneling Oxide
Soft Layer
F
Barrier
FE
minoritycE
majoritycE
FE
minoritycE
majoritycE
barrU
Impurity Layer
Barrier
FE
minoritycE
majoritycE
FE
minoritycE
majoritycE
barrU
Barrier
FE
minoritycE
majoritycE
FE
minoritycE
majoritycE
barrU
Impurity Layer
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1616
MTJs with Magnetic Impurity LayersMTJs with Magnetic Impurity Layers
Normalized JMR ratios are barrier thickness independent
JMR(Ez) ratios reduces at all energies
Elastic spin scattering doesn’t effect normalized ω(Ez)
Decreasing JMRs with increasing impurity concentrations
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1717
MTJs with Magnetic Impurity LayersMTJs with Magnetic Impurity Layers
A universal trend independent from the barrier heights
Minimal Fitting Parameters
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1818
Pd & Ni Impurity LayersPd & Ni Impurity Layers
<J2>2D exchange coupling used as a fitting parameter
Minimal temperature dependence
Close <J2>2D coupling constants estimated for Pd and Ni impurities
+1 spin state is believed to be the dominant state.
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 1919
High-Spin/Low-Spin Phase TransitionHigh-Spin/Low-Spin Phase Transition
J exchange coupling used as a fitting parameter
Large temperature dependence
Thermally driven low-spin/high-spin phase transitions
d4-d7 systems:t2g set → low spin state
eg set → high spin case.
S. W. Biernacki et al, PRB. 72, 024406 (2005).
Crystal Field Theory
-The Pairing energy (P) Coulombic repulsion Exchange Energy-The eg - t2g Splitting
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2020
Details of the TheoryDetails of the Theory
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2121
Spin Array
L RSource
LΣ
SΣ
RΣ
Drain
Gate
QuantumDevice
H U
Spin Array
L RSource
LΣ
SΣ
RΣ
Drain
Gate
QuantumDevice
H U
Exchange Interaction Spin ScatteringExchange Interaction Spin Scattering
Hamiltonian: , ch L R IH H H H
chH Effective mass description†
k k kk
c c
,L RH Modeled through contact self energy
IHModeled using self consistent Born approximation S
, L R
Magnetic Impurity Magnon ScatteringAranov-Bir-Pikus (Electron-Hole)Nuclei (Hyperfine Interaction)
, , ,, ;
,
, '; , '; , '; i j i j k l k l
k l
in out n p n pS r r E D r r G r r E d
Analogous to the Electron/Hole Density
Rate at which electrons/holes are scattered in/out of a state
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2222
Spin Scattering Self EnergySpin Scattering Self Energy
*, ' , ', 'nint intD H r t H r t
int -j
j jRH r J r R S
Interaction Hamiltonian:
† †1 1 1,
2 2 2int zH r t J r R aS t a S t a a S t
Spin Array
Spin Array
Channel
Spin Exchange Interaction
† 0a
0
†1 1
2 2x a a
†1 1
2 2y a ai i
† 1
2z a a
0
0 0
qi teS t d
0 0
0qi tS t d
e
1
2zS d d Imp
uri
ty
Op
era
tors
Ele
ctr
on
O
pera
tors
Preserves Angular Momentum
Jordan-Wigner
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2323
n,p 2
nsf
,
,
1 0 0 0D , '; '0 1 0 0
0 0 1 0
0 0 0 1
q
k l
i j
I qr r r r J N
Inelastic Spin Flip ScatteringInelastic Spin Flip Scattering
n,p 2 ,
sf
,
,
,
0 0 0D , '; '
0 0 0 0 0 0 0
0 0 0 0
q
k l
i j
u d qqI
d u q
Fr r r r J N
F
, , ,, '; , '; , '; n p n p n p
sf nsfD r r D r r D r r
Spin Flip Scattering
Non-Spin Flip Scattering
0
0u
d
F
F
Impurity Density Matrix
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2424
Elastic Spin Flip ScatteringElastic Spin Flip Scattering
2-D Translational Symmetry
Elastic Spin Flip Scattering
2 2
2
1'
q
I q IDr r J N J n
a
n,p 2Isf 2D
0 0 0,
0 0 0,D 0 n a
0 0 0 0
0 0 0 0
k l
i j
Fu d
Fd uJ
a
a
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2525
Spin Array
L RSource
LΣ
SΣ
RΣ
Drain
Gate
QuantumDevice
H U
Spin Array
L RSource
LΣ
SΣ
RΣ
Drain
Gate
QuantumDevice
H U
Unpolarized Spin EnsembleUnpolarized Spin Ensemble
0.5 0
0 0.5
Magnetic Impurity Layer
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2626
Self-consistent SolutionSelf-consistent Solution
Regular Contacts:
Channel: zH
Incoherent Scattering:
Hamiltonian
Transport Equations:
Green’s Function
L R SG E EI H U
2 , ,ln 1 expD z L R s z L R Bf E N E k T
Fix
ed
at
the
Ou
tset
Self
-con
sit
en
t S
ol.
2 2 z
D in D nL L z z L z z z
E
qI tr E A E tr E G E dE
h
; ; i j i k k l k l
i j
S D G E
Dir
ect
Sol
, 2 , ,inL R z D z L R L R zE f E E
, 2 , ,1outL R z D z L R L R zE f E E
12 2D n D n
z z zG E I P E S E
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2727
SummarySummary
Magnetic Impurity Layer
ContactsChannelElectrons Phononsel
Electron-phononrelaxation time
LocalizedSpins
es sl Spin-latticerelaxation time
NON-EQUILIBRIUM TRANSPORT
0.5 0
0 0.5
Magnetic Impurity LayerMagnetic Impurity Layer
ContactsChannelElectrons Phononsel
Electron-phononrelaxation time
LocalizedSpins
es sl Spin-latticerelaxation time
NON-EQUILIBRIUM TRANSPORT
0.5 0
0 0.5
ContactsContactsChannelElectronsChannelElectrons PhononsPhononsel
Electron-phononrelaxation time
LocalizedSpins
es sl Spin-latticerelaxation time
LocalizedSpins
LocalizedSpins
es sl Spin-latticerelaxation time
NON-EQUILIBRIUM TRANSPORT
0.5 0
0 0.5
Challenges:
Physics Based Unified Treatment
Conservation Laws (angular momentum, total energy, particles)
Numerically Treatable
Benchmarking against experiment
Contributions:
A Non-Equilibrium Quantum Transport model with Spin Decoherence is developed.
A Self Energy Calculation scheme is derived for Exchange Interaction Scattering.
A numerical implementation is shown in MTJ devices.
04/21/2304/21/23 A. Ali Yanik, Purdue UniversityA. Ali Yanik, Purdue University 2828
AcknowledgementAcknowledgement
Professors Supriyo Datta and Gerhard KlimeckProfessors Supriyo Datta and Gerhard Klimeck
Dr. Dmitri Nikonov – Intel corporationDr. Dmitri Nikonov – Intel corporation
Sayeef Salahuddin, Prabhakar Srivastava Sayeef Salahuddin, Prabhakar Srivastava
NSF funded Network for Computational NSF funded Network for Computational Nanotechnology (NCN) and MARCONanotechnology (NCN) and MARCO
Recommended