Spin Torque Oscillator from micromagnetic point of...
Transcript of Spin Torque Oscillator from micromagnetic point of...
1/27Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007
Spin Torque Oscillator Spin Torque Oscillator from micromagnetic point of viewfrom micromagnetic point of view
Liliana BUDA-PREJBEANU
Workshop on Advance Magnetic Materials / Cluj-Napoca
(Romania) 16/09/2007
2/27Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007
Daria
GusakovaIoana FirastrauAnatoly VedyayevJean-Christophe
Toussaint
Dimitri
HoussameddineUrsula EbelsBetrand
Delaët
Bernard RodmacqFabienne
Ponthenier
Magalie
BrunetChristophe
Thirion
Jean-Philip-MichelMarie-Claire. CyrilleOlivier RedonBernard Dieny
Modeling
& simulation
Fabrication & characterization
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What is a spin torque oscillator?
Why we are interested in ST oscillator?
Which are the modeling tools to describe them?
Out-of-plane precision (OPP)
In-plane precision (IPP)
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Starting point…
The polarized current acts on the magnetization
Spin torquephenomena
GMR / TMR phenomena
The magnetization acts on the current
“Every action has an equal and opposite reaction.”Action-reaction principle:
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Starting point…
Exchange interaction between injected polarized e-
↑and local magnetization causes the magnetization switching
in the direction parallel to the spin of the injected e-
Co Cu Co
Basic picture …
( J<0)
Cu Cu
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Gilbert torque
Starting point…Landau-Lifshitz-Gilbert equation + polarized currentLandau-Lifshitz-Gilbert equatio
[ ]⎪⎩
⎪⎨
⎧
=
⎟⎠⎞
⎜⎝⎛∂∂
+⎟⎠⎞
⎜⎝⎛
∂∂
×+×−=∂∂
12
0
M
MMMHMMeff
STtttαγ
Heff
M
spin torque
antidamping
Gilbert torque
Heff
spin torque
steady oscillation
M
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AN
IDC
Perpendicular spin torque oscillator
Main goal →
generate steadyoscillations without applying field
Pt / (Co/Pt)/PEL
/Cu/Py/Cu/Co/Co/IrMnIrMn
Ellipse of 60x70 nm²IDC
= 0.15 mAΔR = 0.19ΩMR=0.3%
P
AP
-1,0 -0,5 0,0 0,5 1,0
57,4
57,5
57,6
R (O
hm)
Hb (kOe)
FL ANAN
Low current R(Hb
)
Houssameddine
et al. Nat. Mat. 6, 447 (2007)
J. C. Slonczewski
US5695864K. J. Lee APL 86 (2005)O. Redon US6,532,164 B2
POL
FL
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-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2
57,4
57,5
57,6
R (O
hm)
Hb (kOe)-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2
Hb(kOe)
I = 0.15 mA I = 1.1 mA
P
AP
P
AP
Intermediate resistance level (IRL)
Shoulder
-0,2 0,0 0,2 0,4
R (Ω
)Hbeff (kOe)
( )
IDC-1.5
1.3
0.10.30.50.70.91.1
-1.3
-0.1-0.3-0.5-0.7-0.9-1.1
0.4 Ω
There are two magnetoresistive
states
Perpendicular spin torque oscillator
FL
Houssameddine
et al. Nat. Mat. 6, 447 (2007)
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-200
0
200
400
600
-1 0 1 H
beff (Oe)
IDC (mA)
IRLIRL
shou
lder
AP
P
Static
current-
field
diagram
Perpendicular spin torque oscillator
2 3 40
1
2
3
4
PSD
(nV
2 /Hz)
f (Ghz)2 3 4
f (GHz)
IDC
< 0 IDC
> 0Hbeff = 9 Oe
0.3
1.2
|IDC
|
0.70.80.91.01.1
0.60.50.4
1.31.41.5
Houssameddine
et al. Nat. Mat. 6, 447 (2007)
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Perpendicular spin torque oscillator
P
AP
f1f2f3
-200
0
200
400
600
-1 0 1 H
beff (Oe)
IDC (mA)
Dynamic
current-
field
diagram
-200
0
200
400
600
-1 0 1 H
beff (Oe)
IDC (mA)
IRLIRL
shou
lder
AP
P
Static
current-
field
diagram
?
??
P
AP
Houssameddine
et al. Nat. Mat. 6, 447 (2007)
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Full 3D integration of
a)the
Landau-Lifshitz-Gilbert (LLG) equation
b)the
magnetostatic equations
[ ]
appdemanisex
s
EEEEE
EMµ
tt
+++=
−=
=
⎟⎠⎞
⎜⎝⎛
∂∂
×+×−=∂∂
MH
M
MMHMM
eff
eff
δδ
αγ
0
2
0
11
( ) ( )∫∫∫ −∇−−∇−=S
mV
m dSGdVG ')(')()( r'r'rr'r'rrHdem σρ
Heff
M
Micromagnetic model
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c) Addition term due to the spin torque transfer
[ ]⎪⎩
⎪⎨
⎧
=
⎟⎠⎞
⎜⎝⎛∂∂
+⎟⎠⎞
⎜⎝⎛
∂∂
×+×−=∂∂
12
0
M
MMMHMMeff
STtttαγ
J. C. Slonczewski JMMM. 159, L1 (1996)
( )[ ]PLmMMM××−=⎟
⎠⎞
⎜⎝⎛∂∂
JST
at 0γ
«
ballistic transport model
»
ST-GLFFT
Micromagnetic model (2)
A. Vedyeyev, D. Gusakova
[ ]MmM×=⎟
⎠⎞
⎜⎝⎛∂∂
0ct ST
«
diffusive transport model
»
LLG_SA
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Transport equation
0=+×+∂∂
sf
sdm Jz τ
mMmjη
Micromagnetic model (3)
MmM×=⎟
⎠⎞
⎜⎝⎛∂∂
B
sf
ST
Jt μ
electron currentje
= j↑+j↓
= σ0
Ez
–D0
∂z
n–D0
β′(M·∂z
m)
spin currentjm
=> j↑–j↓=σ0
Ez
βM–D0
∂z
m–D0
β′M∂z
n
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Transport equation
Micromagnetic model (4)
0,0 5,0x10-7 1,0x10-6 1,5x10-6 2,0x10-6 2,5x10-6 3,0x10-6
-500
50100150200250300350400
0,0 5,0x10-7 1,0x10-6 1,5x10-6 2,0x10-6 2,5x10-6 3,0x10-6
-500
50100150200250
0,0 5,0x10-7 1,0x10-6 1,5x10-6 2,0x10-6 2,5x10-6 3,0x10-6-250-200-150-100
-500
50100
mx
my
z (m)
mz
20nm 3.5nm 3nm3nm4nm
45°
POL FL AN
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Perpendicular spin torque oscillator
Fixed layer
Fixed layer
Micromagnetic parameters
PO
LFL
z
x
y
AN
circular disk 60nm, thickness 3.5nm
Ms
= 866
kA/m
Ku
= 664.5J/m3
|| Ox (Hu
=15Oe)
Aex
= 2⋅10-11J/m
α
= 0.01
Mesh size 2 x 2 x 3.5 nm3
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-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3-150-120-90-60-30
0306090
120150
ap
plie
d m
agne
tic fi
eld,
Oe
current density, 107 A/cm2
Daria Gusakova
Macrospin
current-field diagramP
OL
FL
z
OPS
IPS
OPP
POL-FL
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-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3-150-120-90-60-30
0306090
120150
ap
plie
d m
agne
tic fi
eld,
Oe
current density, 107 A/cm2
Daria Gusakova
Macrospin
current-field diagram
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3-150-120-90-60-30
0306090
120150
ap
plie
d m
agne
tic fi
eld,
Oe
current density, 107 A/cm2
PO
LFL
z
AN
OPS
IPS
OPP
IPP
POL-FL-AN
18/27Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3-150-120-90-60-30
0306090
120150
ap
plie
d m
agne
tic fi
eld,
Oe
current density, 107 A/cm2
Daria Gusakova
Macrospin
current-field diagram
-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3-150-120-90-60-30
0306090
120150
ap
plie
d m
agne
tic fi
eld,
Oe
current density, 107 A/cm2
PO
LFL
z
AN
POL-FL-AN
Happ
=0
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OPP frequency
-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro
Freq
uenc
y (G
Hz)
Japp (A/m2)-2x1010 -1x1010 0 1x1010
0
4
8
12
16
20
macro micro POL-FL POL-FL-AN
Freq
uenc
y (G
Hz)
Japp (A/m2)
No applied field
POL-FL-ANPOL-FL
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-1,5 -1,0 -0,5 0,0 0,5 1,0 1,51,5
2,0
2,5
3,0
3,5
4,0Hbias=-371Oe
Freq
uenc
y (G
Hz)
Iapp (mA)
→ µmag
simulation → experimental data
-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro micro POL-FL POL-FL-AN
Freq
uenc
y (G
Hz)
Japp (A/m2)
OPP frequency No applied field
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OPP frequency
-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro
Freq
uenc
y (G
Hz)
Japp (A/m2)-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro micro POL-FL POL-FL-AN
Freq
uenc
y (G
Hz)
Japp (A/m2)
No applied field
POL-FL-ANPOL-FL
22/27Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007
-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro micro POL-FL POL-FL-AN
Freq
uenc
y (G
Hz)
Japp (A/m2)
OPP frequency No applied field
POL-FL-ANPOL-FL
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-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro micro POL-FL POL-FL-AN
Freq
uenc
y (G
Hz)
Japp (A/m2)
OPP frequency No applied field
POL-FL-ANPOL-FL
24/27Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007
Perpendicular spin torque oscillator
P
AP
f1f2f3
-200
0
200
400
600
-1 0 1 H
beff (Oe)
IDC (mA)
Dynamic
current-
field
diagram
-200
0
200
400
600
-1 0 1 H
beff (Oe)
IDC (mA)
IRLIRL
shou
lder
AP
P
Static
current-
field
diagram
?
P
AP
Houssameddine
et al. accepted
Nat. Mat.
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-300 0 3001
2
3
4
Hbeff (Oe)
-200
0
200
400
600
-1 0 1
Hbe
ff (O
e)
IDC (mA)
f3
IPP frequency
0 10 20 30 40 502,0x109
3,0x109
4,0x109
5,0x109
6,0x109
7,0x109
micro macro
Freq
uenc
y (H
z)
µ0Happ (mT)
Japp=0,8*1010A/m2
POL-FL-AN
→ µmag
simulation→ experimental dataFr
eq (G
Hz)
26/27Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007
0,0 1,0x10-8 2,0x10-8 3,0x10-8 4,0x10-8
-0,20
-0,15
-0,10
-0,05
0,00
0,05
0,10
0,48*1010A/m2
0,47*1010A/m2 T=400K
0,48*1010A/m2(CH)
<Mz>
time (s)
0,47*1010A/m2
-2x1010 -1x1010 0 1x10100
4
8
12
16
20
macro micro POL-FL POL-FL-AN
Freq
uenc
y (G
Hz)
Japp (A/m2)
→ µmag
simulation
Temperature effects No applied field
before jump
after jump
T=400K
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Conclusion Solving self-consistently the LLG equation and the spin dependant transport equation:
a)
accurate investigation of structures with 2, 3 or more coupled magnetic layers
b) qualitative good agreement with the experimental data
c) “A toy“
dedicated to the ST oscillator optimization for future device integration