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Spin Torque Oscillator Spin Torque Oscillator from micromagnetic point of view from micromagnetic point of view Liliana BUDA-PREJBEANU Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 Workshop on Advance Magnetic

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Spin Torque Oscillator Spin Torque Oscillator from micromagnetic point of view from micromagnetic point of view

Liliana BUDA-PREJBEANU

Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007

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Daria Gusakova Ioana Firastrau Anatoly Vedyayev Jean-Christophe Toussaint Dimitri Houssameddine Ursula Ebels Betrand Delaët Bernard Rodmacq Fabienne Ponthenier Magalie Brunet Christophe Thirion Jean-Philip-Michel Marie-Claire. Cyrille Olivier Redon Bernard 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

  • n the magnetization

Spin torque phenomena 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 current Landau-Lifshitz-Gilbert equatio

[ ]

⎪ ⎩ ⎪ ⎨ ⎧ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ × + × − = ∂ ∂ 1

2

M M M M H M M

eff ST

t t t α γ

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 steady

  • scillations without applying field

Pt / (Co/Pt)/PEL /Cu/Py/Cu/Co/ Co/IrMn IrMn Ellipse of 60x70 nm² IDC = 0.15 mA

ΔR = 0.19Ω

MR=0.3% P AP

  • 1,0
  • 0,5

0,0 0,5 1,0 57,4 57,5 57,6 R (Ohm) Hb (kOe)

FL AN AN

Low current R(Hb )

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

  • J. C. Slonczewski

US5695864

  • K. 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 (Ohm) 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 0.1 0.3 0.5 0.7 0.9 1.1

  • 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

200 400 600

  • 1

1 Hbeff (Oe) IDC (mA) IRL IRL s h

  • u

l d e r AP P Static current- field diagram

Perpendicular spin torque oscillator

2 3 4 1 2 3 4 PSD (nV

2/Hz)

f (Ghz) 2 3 4 f (GHz) IDC < 0 IDC > 0 Hbeff = 9 Oe

0.3 1.2

|IDC|

0.7 0.8 0.9 1.0 1.1 0.6 0.5 0.4 1.3 1.4 1.5

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

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Perpendicular spin torque oscillator

P AP f1 f2 f3

  • 200

200 400 600

  • 1

1 Hbeff (Oe) IDC (mA)

Dynamic current- field diagram

  • 200

200 400 600

  • 1

1 Hbeff (Oe) IDC (mA) IRL IRL s h

  • u

l d e r 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

[ ]

app dem anis ex s

E E E E E E M µ t t + + + = − = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ × + × − = ∂ ∂ M H M M M H M M

eff eff

δ δ α γ

2

1 1

( ) ( )

∫∫ ∫

− ∇ − − ∇ − =

S m V m

dS G dV G ' ) ( ' ) ( ) ( r' r' r r' r' r r Hdem σ ρ

Heff M

Micromagnetic model

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  • c) Addition term due to the spin torque transfer

[ ]

⎪ ⎩ ⎪ ⎨ ⎧ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ × + × − = ∂ ∂ 1

2

M M M M H M M

eff ST

t t t α γ

  • J. C. Slonczewski
  • JMMM. 159, L1 (1996)

( ) [ ]

PL

m M M M × × − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂

J ST

a t γ

« ballistic transport model » ST-GLFFT

Micromagnetic model (2)

  • A. Vedyeyev, D. Gusakova

[ ]

M m M × = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ c t

ST

« diffusive transport model » LLG_SA

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Transport equation

= + × + ∂ ∂

sf sd m

J z τ m M m j η

Micromagnetic model (3)

M m M × = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂

B sf ST

J t μ

electron current

je = j↑+j↓ = σ0 Ez –D0 ∂z n–D0 β′(M·∂z m)

spin current

jm => 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
  • 50

50 100 150 200 250 300 350 400 0,0 5,0x10

  • 7

1,0x10

  • 6

1,5x10

  • 6

2,0x10

  • 6

2,5x10

  • 6

3,0x10

  • 6
  • 50

50 100 150 200 250 0,0 5,0x10

  • 7

1,0x10

  • 6

1,5x10

  • 6

2,0x10

  • 6

2,5x10

  • 6

3,0x10

  • 6
  • 250
  • 200
  • 150
  • 100
  • 50

50 100

mx my z (m) mz

20nm

3.5nm 3nm 3nm 4nm

45° POL FL AN

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Perpendicular spin torque oscillator

Fixed layer Fixed layer Micromagnetic parameters POL FL

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

30 60 90 120 150 applied magnetic field, Oe current density, 10

7 A/cm 2

Daria Gusakova

Macrospin current-field diagram

POL 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

30 60 90 120 150 applied magnetic field, Oe current density, 10

7 A/cm 2

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

30 60 90 120 150 applied magnetic field, Oe current density, 10

7 A/cm 2

POL FL z AN

OPS IPS OPP IPP POL-FL-AN

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  • 0,3
  • 0,2
  • 0,1

0,0 0,1 0,2 0,3

  • 150
  • 120
  • 90
  • 60
  • 30

30 60 90 120 150 applied magnetic field, Oe current density, 10

7 A/cm 2

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

30 60 90 120 150 applied magnetic field, Oe current density, 10

7 A/cm 2

POL FL z AN

POL-FL-AN Happ =0

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OPP frequency

  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro

Frequency (GHz) Japp (A/m2)

  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro micro

POL-FL POL-FL-AN

Frequency (GHz) Japp (A/m2)

No applied field

POL-FL-AN POL-FL

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  • 1,5
  • 1,0
  • 0,5

0,0 0,5 1,0 1,5 1,5 2,0 2,5 3,0 3,5 4,0

Hbias=-371Oe

Frequency (GHz)

Iapp (mA)

→ µmag

simulation

→ experimental data

  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro micro

POL-FL POL-FL-AN

Frequency (GHz) Japp (A/m2)

OPP frequency

No applied field

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OPP frequency

  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro

Frequency (GHz) Japp (A/m2)

  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro micro

POL-FL POL-FL-AN

Frequency (GHz) Japp (A/m2)

No applied field

POL-FL-AN POL-FL

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  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro micro

POL-FL POL-FL-AN

Frequency (GHz) Japp (A/m2)

OPP frequency

No applied field

POL-FL-AN POL-FL

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  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro micro

POL-FL POL-FL-AN

Frequency (GHz) Japp (A/m2)

OPP frequency

No applied field

POL-FL-AN POL-FL

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Perpendicular spin torque oscillator

P AP f1 f2 f3

  • 200

200 400 600

  • 1

1 Hbeff (Oe) IDC (mA)

Dynamic current- field diagram

  • 200

200 400 600

  • 1

1 Hbeff (Oe) IDC (mA) IRL IRL s h

  • u

l d e r AP P Static current- field diagram

?

P AP

Houssameddine et al. accepted

  • Nat. Mat.
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  • 300 0

300 1 2 3 4 Hbeff (Oe)

  • 200

200 400 600

  • 1

1

Hbeff (Oe)

IDC (mA) f3

IPP frequency

10 20 30 40 50 2,0x10

9

3,0x10

9

4,0x10

9

5,0x10

9

6,0x10

9

7,0x10

9

micro macro

Frequency (Hz)

µ0Happ (mT)

Japp=0,8*1010A/m2 POL-FL-AN

→ µmag

simulation

→ experimental data Freq (GHz)

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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*10

10A/m 2

0,47*10

10A/m 2

T=400K 0,48*10

10A/m 2(CH)

<Mz> time (s) 0,47*10

10A/m 2

  • 2x10

10

  • 1x10

10

1x10

10

4 8 12 16 20

macro micro

POL-FL POL-FL-AN

Frequency (GHz) 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

  • ptimization for future device integration