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


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

http://www.phys.msu.su/


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)


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:


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


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


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


-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


FL

Houssameddine

et al. Nat. Mat. 6, 447 (2007)


-200

0

200

400

600

-1 0 1 H

beff (Oe)

IDC (mA)

IRLIRL

shou

lder

AP

P

Static

current-

field

diagram


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)



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)


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


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


Transport equation

0=+×+∂∂

sf

sdm Jz τ

mMmjη


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


Transport equation


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



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


-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


-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


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


PO

LFL

z

AN

OPS

IPS

OPP

IPP

POL-FL-AN


-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


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


PO

LFL

z

AN

POL-FL-AN

Happ

=0


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


-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


Freq

uenc

y (G

Hz)

Japp (A/m2)

OPP frequency No applied field


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


Freq

uenc

y (G

Hz)

Japp (A/m2)

No applied field

POL-FL-ANPOL-FL


-2x1010 -1x1010 0 1x10100

4

8

12

16

20


Freq

uenc

y (G

Hz)

Japp (A/m2)


POL-FL-ANPOL-FL



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.


-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)


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


Freq

uenc

y (G

Hz)

Japp (A/m2)

→ µmag

simulation

Temperature effects No applied field

before jump

after jump

T=400K


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

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