Post on 02-Jul-2015
description
Modeling Spin Torque Device
M→
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FMI
MRAM
V
→ττττ||||||||,m
Deepanjan Datta
Dept of ECE, Purdue University
Fert, Nature Mat. (2007)
1
Motivation
Magnetics
∑
Reading (MR)
Writing Spin Torque
Spintronics
Very Low M.R. (~ 2%)
Spin ValveMagnetic
Tunnel Junction
All Spin Logic
M→
m→
Cu
M→
m→
MgO
2
Purdue Group
Nature NANO 2010
TOSHIBAGRANDIS
Outline of the Work
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FMI
1. Quantum-Transport Modeling of MTJ device with NEGF
2. Quantitative agreement with Experiments
1. Explains Bias dependence of Torque
2. Asymmetric ST device & Non-reciprocal torque
1. Spin Transport + 1-LLG; Switching asymmetry
2. Spin Transport + multi-LLG; model for Oscillator
IEEE Trans Nano 2012
Current WorkIEDM 2010
3
Outline of the Work
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FMI
1. Quantum-Transport Modeling of MTJ device with NEGF
2. Quantitative agreement with Experiments
1. Explains Bias dependence of Torque
2. Asymmetric ST device & Non-reciprocal torque
1. Spin Transport + 1-LLG; Switching asymmetry
2. Spin Transport + multi-LLG; model for Oscillator
IEEE Trans Nano 2012
Current WorkIEDM 2010
4
Magnetic Tunnel Junction
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FMIMTJ:
z
x
y
Spin Transport Model:
Spin Transport: NEGF Model
Ef ∆ bU *oxm *
FMm
SII
M, m
VR
τ
MR (Reading)
Writinginput
Fitting parameters
output
τ⊥5
Modeling Magnetic Tunnel Junction
( )* *L, R f b ox FMH, Σ E , , U , m , mf = ∆
Ef Ef
mox*
mFM* mFM
*
∆ ∆
UbbUV
M→
m→[H]
[ ]LΣ [ ]RΣ
S, LI
S, RI
I
Spin Torque:
S, L S, Rτ = I - I
S, Rˆ I || m
( )( )
S, L S, L
S, L
ˆ ˆτ = I - I .m m
ˆ ˆ = - m m I × ×
∆ ∆C, L E
Spin Transport: NEGF Model
Ef ∆ bU *oxm *
FMm
SII
mV
R
τ
Fitting parameters
τ⊥
S, FMI
6
Experiment
Resistance vs. VoltageSankey, Nature Phys. (2008)
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FM
-0.5 0 0.5
3
4
5
6
7
8
9
dV/d
I (k
ΩΩ ΩΩ)
Voltage (V)
-0.5 0 0.5
50
100
150
TM
R (%
)
Voltage (V)
71o
0o (Parallel)52o
180o
(Anti-Parallel)
×××× ××××
Theory
Ef = 2.25 eV∆ = 2.15 eVmFM
* = 0.8 mo
mox* = 0.18 mo
Ub = 0.77 eV
Spin Transport: NEGF Model
Ef ∆ bU *oxm *
FMm
SII
mV
R
τ
τ⊥
7
Torque vs. Voltage
-200 0 200-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Fie
ld-L
ike
Tor
que
(10
-19 J
)
Experiment
τ⊥
-1
0
1
2
3
4S
pin-
Tra
nsfe
r T
orqu
e (1
0-1
9 J)
-200 0 200
Experiment
||τ
Kubota, Nature Phys. (2008)
-200 0 200-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Fie
ld-L
ike
Torq
ue (1
0-1
9 J)
Vb (mV)
Theory
-200 0 200Vb (mV)
8-200 0 200-1
0
1
2
3
4
Spi
n-T
rans
fer
Tor
que
(10
-19 J
)
Vb (mV)
Theory
-200 0 200Vb (mV)
Proc. IEDM, 2010
TNANO, 2012
vs. Voltagedτ dV
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO Proc. IEDM, 2010
TNANO, 2012
Ralph, PRB (2009)Ralph, PRB (2009)
9
Outline of the Work
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FMI
10
1. Quantum-Transport Modeling of MTJ device with NEGF
2. Quantitative agreement with Experiments
1. Explains Bias dependence of Torque
2. Asymmetric ST device & Non-reciprocal torque
1. Spin Transport + 1-LLG; Switching asymmetry
2. Spin Transport + multi-LLG; model for Oscillator
IEEE Trans Nano 2012
Current WorkIEDM 2010
Bias Dependence of
V
M→
→ττττ||||||||,m
m→
MgO
Fixed FM Free FM
-1
0
1
2
3
4
Spi
n-T
rans
fer
Tor
que
(10
-19 J
)
-200 0 200
||τ (V)
( )ˆ ˆ
Kubota, Nature Phys. (2008)
||τ
C
G - GP =
G + G
↑ ↓
↑ ↓
||,m CMτ P (E)∝
Polarization:PC
0 1
EF
∆∆∆∆
0
E (e
V)
-200 0 200Vb (mV)
11
( )sˆ ˆˆ ˆI ~ M + m + M ma b c ×
CM Pa ∝
(1) When V > 0 is applied to Fixed FM
V > 0
M→
→ττττ||||||||,m
m→
MgO
Fixed FM Free FM
Fixed layer (M) Free layer (m)→ →
+ -
E (e
V)
12
EF
0 1
µR
0
qV > 0
0
|τ||,m (V > 0)|
+ -
µL = Ef
PCM
∆∆
M→
m
→ττττ||||||||,m
→MgO
V < 0
(2) When V < 0 is applied to Fixed FM
Fixed FM Free FM
Fixed layer (M) Free layer (m)→ →
+-
E (e
V)
13
0 1
µL =
µR
00
|τ||,m (V < 0)|
qV < 0
+-
µL = Ef
PCM
∆ ∆
,m ,mτ (V<0) > τ (V>0)
-1
0
1
2
3
4
Spi
n-T
rans
fer
Tor
que
(10
-19 J
)
-200 0 200Vb (mV)
||τ||,m CMτ P (E)∝
E (e
V)
Fixed layer (M) Free layer (m)→ →
14IEEE Trans Nano 2012
|τ||,m (V < 0)|
|τ||,m (V > 0)|
EF
0 1
µL =
0
(2)
(1)
PCM
µL = Ef
µR
µR
qV < 0
0
qV > 0
∆ ∆
Non-reciprocal Torque
1.5x 10
14
→→→→
1.5x 10
14
ττττ→→→→
M→
m
→ττττ||||||||,m
→MgO
V
→ττττ||||||||,M
M→
MgO
V
→ττττ||||||||,M
m
→ττττ||||||||,m
→Non-magnetic
metal
-0.2 -0.1 0 0.1 0.2-1.5
-1
-0.5
0
0.5
1
ττ ττ || (x
10-1
9 J.m
-2)
-Vb (Volt)
ττττ||||||||,m
ττττ||||||||,M
→→→→
→→→→
-0.2 -0.1 0 0.1 0.2-1.5
-1
-0.5
0
0.5
1
ττ ττ || (x
10-1
9 J.m
-2)
-Vb (Volt)
ττττ||||||||,m
ττττ||||||||,M
→→→→
→→→→
15IEEE Trans Nano 2012
Bias Dependence of
V
M→
m→
MgO →ττττ⊥⊥⊥⊥,m
Fixed FM Free FM
-200 0 200-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Fie
ld-L
ike
Tor
que
(10
-19 J
)
τ⊥
τ (V)⊥
, m CM Cmτ P (E) P (E) ⊥ ∝
-200 0 200Vb (mV)
CM Cm P P c ∝
16
( )sˆ ˆˆ ˆI ~ M + m + M ma b c ×
(1) When V > 0 is applied to Fixed FM
V > 0
M→
m→
MgO →ττττ⊥⊥⊥⊥,m
Fixed FM Free FM
E (e
V)
E (e
V)
Fixed layer (M) Free layer (m)→ →
+ -
17
µR
µL = EF
0 1 00
qV > 0
01
PCm
+ -
µL = Ef
PCM
∆ ∆
(2) When V < 0 is applied to Fixed FM
M→
MgO
V < 0
m→
→ττττ⊥⊥⊥⊥,m
Fixed FM Free FM
Fixed layer (M) Free layer (m)→ →
+-
E (e
V)
E (e
V)
18
µR
µL = EF
0 1 0 1qV < 0
+-
µL = Ef
PCmPCM
00
∆ ∆
, m CM Cmτ P (E) P (E) ⊥ ∝
-200 0 200Vb (mV)
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Fiel
d-Li
ke T
orqu
e (1
0-1
9 J)
τ⊥
E (e
V)
E (e
V)
Fixed layer (M) Free layer (m)→→
V > 0
,m ,mτ (V 0) τ (V 0) ⊥ ⊥< = >
0 1
µL = EF
0 1
V > 0
V < 0
19IEEE Trans Nano 2012
µR
µR
PCmPCM
µL = Ef
qV > 0
00
∆∆
qV < 0
Outline of the Work
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FMI
20
1. Quantum-Transport Modeling of MTJ device with NEGF
2. Quantitative agreement with Experiments
1. Explains Bias dependence of Torque
2. Asymmetric ST device & Non-reciprocal torque
1. Spin Transport + 1-LLG; Switching asymmetry
2. Spin Transport + multi-LLG; model for Oscillator
IEEE Trans Nano 2012
Current WorkIEDM 2010
StandardSTT Device
Coupling of Spins and Magnets
V I • Magnets
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Fixed FM Free FM
Purdue GroupNature NANO 2010
APL 2011
TNANO 2012
V I
Dynamics of Magnets:
LLG EquationSpin-
TorqueMagnetization
m sI
• Magnets
inject spins
• Spins
turn magnets
21
Spin Transport:NEGF
V
M→
→ττττ||||||||,m
→ττττ⊥⊥⊥⊥,m
m→
MgO
Spin Transport + LLG
Oscillator
Voltage
m1
m2
STTSTT
Switching
22-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-1
-0.5
0
0.5
1
m
Voltage (V)
VC-
VC+
P
AP
AP →→→→ P P →→→→ AP
Voltage (V) -0.27 V 0.38 V
Nat. Phys ’08
GND
m1
m3dipolar
V
Proposal for Asymmetric STT device
||,m ||,Mτ ( V) τ ( V) ± ≠ ∓
Explanation of Bias dependence for Spin
TorqueQuantitative model for R(V), TMR (V), (V)
and (V)τ
τ⊥
Summary
Spin Transport:NEGF
mI
I
23
Switching Asymmetry for AP → P & P → AP
New Model for Oscillator with
Transport + multi-LLG
Dynamics of Magnets:
LLG Equation
m
Magnetization Spin-Torque
sI
Please refer
D. Datta et. al., “Voltage Asymmetry of Spin-Transfer Torques,”
24
D. Datta et. al., “Voltage Asymmetry of Spin-Transfer Torques,” IEEE Trans on Nanotechnology, vol. 11, pp. 261-272 (2012)
Back-up Slides
25
Back-up Slides
Free Layer
Voltage
Tunnel Barrier
Co60Fe20B20
Co60Fe20B20
MgO
Ta
Ti
MTJ Device Stack
26
AFM Layer
GND
Pinned layerCo70Fe30
Ru
PtMn/ IrMn
Ta
TaN/ SiO2
Assumptions:m *Effective mass inside
Band Diagram of MTJ
V
M→
m→[H]
[ ]LΣ [ ]RΣ
I
( )* *L, R f b ox FMH, Σ E , , U , m , mf = ∆
27
1. PBC along transverse direction so that all k||are decoupled as parallel1-D wire.
2. k|| for each mode is conserved throughoutthe device.
∆EFM,t
Ef
∆ ∆
mFM* mFM
*
mox*
Ub
Ef
∆Eox,t
Equilibrium Fermi Level
Effective mass insideFerromagnet
Barrier height of insulator
Effective mass insideinsulator
Asymmetry of τ (V)⊥
0
0.1
0.2
τ ⊥ /
Hk
0
0.1
0.2
τ ⊥ /
Hk
Theory EC, R - EC, L = δ
δ > 0δ < 0
Se-Chung Oh, Nature Phys. (2009)
τ ⊥ /
Hk
28
Cm , m CMif P (E) ~ constant τ P (E)⊥ ∝
Like-wise in , introduces an asymmetry in ||τ (V) CMP (E) τ (V)⊥
-0.4 -0.2 0 0.2 0.4Applied Voltage (V)
-0.4 -0.2 0 0.2 0.4Applied Voltage (V)
δ < 0
Applied Voltage (V)
, m CM Cmτ P (E) P (E) ⊥ ∝
Asymmetric Device: ,m ,mτ (V 0) τ (V 0) ⊥ ⊥< ≠ >
-0.4 -0.2 0 0.2 0.4
0
0.1
0.2
τ ⊥ /
Hk
Applied Voltage (V)
0
0.1
0.2
τ ⊥ /
Hk
-0.4 -0.2 0 0.2 0.4Applied Voltage (V)
Theory EC, R - EC, L = δ
δ > 0δ < 0
Free layer (m)→
E (e
V)
E (e
V)
29
EFµL =
|ττττ⊥⊥⊥⊥,m (V > 0)|
|ττττ⊥⊥⊥⊥,m (V < 0)|
µR
µR
0
qV < 0
qV > 0 δδδδ
∆∆∆∆
∆∆∆∆
V
00 1
0 1
Fixed layer (M)→
PCm
PCM