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.

1. Modeling Spin Torque Device
I
Fixed FM → →
Free FM MRAM
M m
→
MgO τ⊥,m
→
τ||
||,m
V
Fert, Nature Mat. (2007)
Deepanjan Datta
Dept of ECE, Purdue University 1

2. Motivation
Spintronics Magnetics
∑
Reading Writing
(MR) Spin Torque
Very Low M.R. (~ 2%)
→ →
M m
Magnetic
Cu All Spin
Spin Valve Tunnel
Logic Purdue Group
Junction
Nature NANO 2010
→ →
M m
MgO
2
GRANDIS TOSHIBA

3. Outline of the Work
Fixed FM I Free FM
→ →
M m
→
MgO τ⊥,m
→
τ||
||,m
V
1. Quantum-Transport
1. Spin Transport + 1-LLG;
Modeling of MTJ device with
Switching asymmetry
NEGF
2. Spin Transport + multi-LLG;
2. Quantitative agreement with
model for Oscillator
Experiments
IEDM 2010 1. Explains Bias dependence Current Work
of Torque
2. Asymmetric ST device &
Non-reciprocal torque
IEEE Trans Nano 2012 3

4. Outline of the Work
Fixed FM I Free FM
→ →
M m
→
MgO τ⊥,m
→
τ||
||,m
V
1. Quantum-Transport
1. Spin Transport + 1-LLG;
Modeling of MTJ device with
Switching asymmetry
NEGF
2. Spin Transport + multi-LLG;
2. Quantitative agreement with
model for Oscillator
Experiments
IEDM 2010 1. Explains Bias dependence Current Work
of Torque
2. Asymmetric ST device &
Non-reciprocal torque
IEEE Trans Nano 2012 4

5. Magnetic Tunnel Junction
Fixed FM I Free FM
MTJ:
→ →
M m
z
→
MgO τ⊥,m
y
→
τ||
x
||,m
V
Spin Transport Model:
Fitting parameters
Ef ∆
* *
U b m ox m FM
output R MR (Reading)
V Spin Transport: I
input τ
M, m NEGF Model IS Writing
τ⊥
5

6. Modeling Magnetic Tunnel Junction
I  H, Σ  = f ( E , ∆, U , m
 
*
, m* )
[ΣL ] [ΣR ]
L, R f b ox FM
→
M mox*
[H]
→
m mFM* mFM*
V U
Ubb
Ef Ef
IS, L IS, R
∆ ∆
IS, FM C, L E
Spin Torque:
Fitting parameters
τ = IS, L - IS, R
Ef ∆
* *
U b m ox m FM
R ˆ
IS, R || m
V I
( )
Spin Transport: τ
m NEGF Model IS ˆ ˆ
τ = IS, L - IS, L .m m
τ⊥
ˆ ˆ (
= - m × m × IS, L ) 6

7. Resistance vs. Voltage
Sankey, Experiment (2008)
Nature Phys.
Fixed FM Free FM
→ →
M m
→
MgO τ⊥,m
→
τ||
||,m
V
Ef ∆
* *
U b m ox m FM
R Theory
150
9
V Spin Transport: I
T MR (% )
τ 100
× ×
8
m NEGF Model IS 50
180o
τ⊥ 7
(Anti-Parallel)
-0.5 0 0.5
dV /dI (kΩ )
Voltage (V)
6
Ef = 2.25 eV
∆ = 2.15 eV
5
71o
mFM* = 0.8 mo 4
52o
mox* = 0.18 mo 3 o
0 (Parallel)
-0.5 0 0.5
Ub = 0.77 eV Voltage (V)
7

8. Torque vs. Voltage
Experiment Experiment
4 0.2
Spin-Transfer Torque (10 -19 J)
Kubota,
0 Nature Phys. (2008)
J)
3
τ||
-19
-0.2 τ⊥
Field-Like Torque (10
2 -0.4
-0.6
1
-0.8
0
-1
-1 -1.2
-200 0 200 -200 0 200
Vb (mV) Vb (mV)
Theory Theory
4 0.2
Proc. IEDM, 2010
Spin-Transfer Torque (10 -19 J)
0
J)
3 TNANO, 2012
-19
-0.2
Field-Like Torque (10
2 -0.4
-0.6
1
-0.8
0
-1
-1 -1.2
-200 0 200 -200 0 200 8
Vb (mV) Vb (mV)

9. d τ dV vs. Voltage
→ →
M m
→ Proc. IEDM, 2010
MgO τ⊥,m
TNANO, 2012
→
τ||
||,m
Ralph, PRB (2009) V Ralph, PRB (2009)
9

10. Outline of the Work
Fixed FM I Free FM
→ →
M m
→
MgO τ⊥,m
→
τ||
||,m
V
1. Quantum-Transport
1. Spin Transport + 1-LLG;
Modeling of MTJ device with
Switching asymmetry
NEGF
2. Spin Transport + multi-LLG;
2. Quantitative agreement with
model for Oscillator
Experiments
IEDM 2010 1. Explains Bias dependence Current Work
of Torque
2. Asymmetric ST device &
Non-reciprocal torque
IEEE Trans Nano 2012 10

11. Bias Dependence of τ|| (V)
Kubota, Nature Phys. (2008)
Fixed FM Free FM 4
→ →
Spin-Transfer Torque (10 -19 J)
M m 3
MgO 2
τ||
1
→
τ||
||,m
0
V
( )
-1
-200 0 200
Is ~ a M + b m + c M × m
ˆ ˆ ˆ ˆ Vb (mV)
E (eV)
a ∝ PCM
τ||,m ∝ PCM (E)
EF
∆
G↑ - G↓ 0
Polarization: PC = ↑ 0 1
G + G↓ PC 11

12. (1) When V > 0 is applied to Fixed FM
Fixed FM Free FM
→ →
M m
MgO
→
τ||
||,m
E (eV)
V >+ -
0
→ →
Fixed layer (M) Free layer (m)
|τ||,m (V > 0)|
µR
µL = EfEF
∆ ∆
qV > 0
0 0
0 1
PCM
12
+ -

13. (2) When V < 0 is applied to Fixed FM
→
τ||
||,m
Fixed FM Free FM
→
M
MgO
→
m
E (eV)
V<0 +
-
→ →
Fixed layer (M) Free layer (m)
µLµL = f
=E
∆ ∆ µR
|τ||,m (V < 0)|
0 0
0 1
PCM qV < 0
13
- +

14. τ ,m (V<0) > τ ,m (V>0)
4
τ||,m ∝ PCM (E)
J)
-19
3
τ||
Spin-Transfer Torque (10
2
1
0
-1
-200 0 200
E (eV)
Vb (mV)
→ →
Fixed layer (M) Free layer (m)
|τ||,m (V > 0)|
µR
(1)
µLµL = fEF
=E
∆ ∆ µR
(2)
|τ||,m (V < 0)|
qV > 0
0 0
0 1
PCM qV < 0
14
IEEE Trans Nano 2012

15. Non-reciprocal Torque
→ →
τ → →
τ
||,m
|| ||,m
||
M M
→
τ MgO →
τ MgO Non-magnetic
||,M
|| ||,M
||
metal
→ →
m m
V V
14
14
x 10 x 10
1.5 1.5
→
1
τ||
||,m →
τ||
1 ||,m
10 -19 J.m -2)
10 -19 J.m -2)
0.5 0.5
→
τ||
||,M
0 0 →
τ||
||,M
τ || (x
-0.5
τ || (x
-0.5
-1 -1
-1.5 -1.5
-0.2 -0.1 0 0.1 0.2 -0.2 -0.1 0 0.1 0.2
-V b (Volt) -V b (Volt)
15
IEEE Trans Nano 2012

16. Bias Dependence of τ ⊥ (V)
Fixed FM Free FM 0.2
→ → 0
J)
M m
-19
-0.2 τ⊥
Field-Like Torque (10
MgO -0.4
→
τ⊥,m -0.6
-0.8
-1
V
-1.2
-200 0 200
Vb (mV)
ˆ ˆ ˆ ˆ (
Is ~ a M + b m + c M × m )
c ∝ PCM PCm τ ⊥, m ∝ PCM (E) PCm (E)
16

17. (1) When V > 0 is applied to Fixed FM
Fixed FM → → Free FM
M m
MgO
→
τ⊥,m
V >+ -
E (eV)
0
E (eV)
→ →
Fixed layer (M) Free layer (m)
µR
µL =L EfEF
µ =
∆ ∆
qV > 0
0 0
0 1 0 1
PCM PCm
17
+ -

18. (2) When V < 0 is applied to Fixed FM
Fixed FM → → Free FM
M m
MgO
→
τ⊥,m
V < -0 +
E (eV)
E (eV)
→ →
Fixed layer (M) Free layer (m)
µL µL EfE
==
∆ ∆
F
µR
0 0
0 1 0 1
PCM qV < 0 PCm
- + 18

19. τ ⊥,m (V < 0) = τ ⊥,m (V > 0)
0.2
τ ⊥, m ∝ PCM (E) PCm (E) 0
Field-Like Torque (10 -19 J)
-0.2 τ⊥
-0.4
-0.6
-0.8
-1
E (eV)
-1.2
E (eV)
-200 0 200
Vb (mV)
→ →
Fixed layer (M) Free layer (m)
V> 0
µR
µL =L EfEF
µ =
∆ ∆ µR
V< 0
qV > 0
0 0
0 1 0 1
PCM qV < 0 PCm
19
IEEE Trans Nano 2012

20. Outline of the Work
Fixed FM I Free FM
→ →
M m
→
MgO τ⊥,m
→
τ||
||,m
V
1. Quantum-Transport 1. Spin Transport + 1-LLG;
Modeling of MTJ device with Switching asymmetry
NEGF
2. Spin Transport + multi-LLG;
2. Quantitative agreement with model for Oscillator
Experiments
IEDM 2010 1. Explains Bias dependence Current Work
of Torque
2. Asymmetric ST device &
Non-reciprocal torque
IEEE Trans Nano 2012 20

21. Coupling of Spins and Magnets
Fixed FM Free FM
Standard →
M
→
m
Purdue Group
STT Device Nature NANO 2010
→
MgO τ⊥,m APL 2011
TNANO 2012
→
τ||
||,m
V
V Spin Transport: I • Magnets
NEGF inject spins
ˆ
m Is
Dynamics of
Magnets: Spin- • Spins
Magnetization LLG Equation Torque
turn magnets
21

22. Spin Transport + LLG
Switching Oscillator
→ → Voltage
M m
→
MgO τ⊥,m
→
τ||
||,m m2
V STT STT
m1
Nat. Phys ’08 AP → P P → AP
dipolar
Voltage (V) -0.27 V 0.38 V m3
1
P
0.5 VC+
m
0
GND
-0.5 VC-
-1
AP
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
22
Voltage (V)

23. Summary
Explanation of Bias
dependence for Spin Proposal for
Quantitative model for
Torque Asymmetric STT device
R(V), TMR (V), τ (V)
and τ ⊥ (V) τ||,m ( ± V) ≠ τ||,M ( ∓ V)
V Spin Transport: I
NEGF
ˆ
m Is
Magnetization Dynamics of Spin-Torque
Magnets:
LLG Equation
New Model for
Switching Asymmetry
Oscillator with
for AP → P & P → AP
Transport + multi-LLG
23

24. Please refer
D. Datta et. al., “Voltage Asymmetry of Spin-Transfer Torques,”
IEEE Trans on Nanotechnology, vol. 11, pp. 261-272 (2012)
24

25. Back-up Slides
25

26. MTJ Device Stack
Voltage
Ti
Ta
Co60Fe20B20 Free Layer
MgO Tunnel Barrier
Co60Fe20B20
Ru Pinned layer
Co70Fe30
PtMn/ IrMn AFM Layer
Ta
TaN/ SiO2
GND 26

27. Band Diagram of MTJ
I
[ΣL ] →
M
[ΣR ]
[H]
→
m
V
 H, Σ L, R  = f ( E f , ∆, U b , m , m
 
*
ox
*
FM )
Assumptions:
Effective mass inside mox *
insulator 1. PBC along transverse
direction so that all k||
∆Eox,t
are decoupled as parallel
Effective mass inside 1-D wire.
mFM* mFM*
Ferromagnet
2. k|| for each mode is
Barrier height of insulator Ub conserved throughout
Equilibrium Fermi Level Ef E the device.
f
∆EFM,t ∆ ∆
27

28. Asymmetry of τ ⊥ (V)
Se-Chung Oh, Nature Phys. (2009) Theory EC, R - EC, L = δ
τ⊥ / H k
0.2
0.2
ττ⊥ //Hkk
0.1
0.1
H
⊥
0
0
δ>0
δ<0
-0.4
-0.4 -0.2
-0.2 0 0.2 0.4
0.4
Applied Voltage (V) Applied Voltage (V)
Applied
τ ⊥, m ∝ PCM (E) PCm (E)
if PCm (E) ~ constant τ ⊥, m ∝ PCM (E)
Like-wise in τ|| (V) , PCM (E) introduces an asymmetry in τ ⊥ (V) 28

29. Asymmetric Device: τ ⊥,m (V < 0) ≠ τ ⊥,m (V > 0)
Theory EC, R - EC, L = δ
0.2
0.2
ττ⊥ //Hkk
0.1
0.1
H
⊥
0
0
E (eV)
δ>0
δ<0
-0.4
-0.4 -0.2
-0.2 0 0.2 0.4
0.4 →
Free layer (m)
Applied Voltage (V)
Applied
E (eV)
→
Fixed layer (M)
τ
|τ⊥,m (V < 0)|
∆ µR
µL = EF
qV < 0
∆ µR
0
τ
|τ⊥,m (V > 0)| 0 1
qV > 0 δ PCm
0
0 1
PCM
V 29