Modeling spin torque device
29
Modeling Spin Torque Device M → → τ τ τ ⊥ ⊥ ⊥,m m → MgO Fixed FM Free FM I MRAM V → τ τ τ || || || || ,m Deepanjan Datta Dept of ECE, Purdue University Fert, Nature Mat. (2007) 1
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Spin Torque Transfer (STT) devices that can switch the magnetization of a ferromagnetic layer using spin polarized electrons have generated much interest due to their write information without any external magnetic field. The bias behavior of spin torque applied to Magnetic Tunnel Junctions (MTJs) is critical for applications including high density magnetic random access memory (MRAM) devices. In this slides, we will present a Non-Equilibrium Green’s Function based transport for MTJ to investigate the bias dependence of torques. First, we use our model to show quantitative agreement with the diverse experimental aspects of STT devices namely (i) differential resistances, (ii) Tunnel magneto-resistance (TMR), and (iii) in-plane and (iv) out-of-plane torques. Second, based on our model, we analyze the reason why one of the ferromagnetic layers (free) experiences a larger torque when negative voltage is applied to the other magnetic layer (fixed). Third, we also propose an asymmetric STT structure that can lead to significant difference in the torques on two ferromagnetic contacts, even if they are identical. We couple our spin transport model with magnetization dynamics to explore the switching behavior of the MTJ device. Our preliminary results demonstrates the switching voltage asymmetry.
Transcript of Modeling spin torque device
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
