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 Materials / Cluj-Napoca (Romania) 16/09/2007 1/27
Modeling & simulation Daria Gusakova Ioana Firastrau Anatoly Vedyayev Jean-Christophe Toussaint Fabrication & characterization Dimitri Houssameddine Ursula Ebels Betrand Delaët Bernard Rodmacq Fabienne Ponthenier Magalie Brunet Christophe Thirion Jean-Philip-Michel Marie-Claire. Cyrille Olivier Redon Bernard Dieny Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 2/27
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) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 3/27
Starting point… GMR / TMR The magnetization acts on the current phenomena Action-reaction principle: “Every action has an equal and opposite reaction.” Spin torque The polarized current acts on the magnetization phenomena Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 4/27
Starting point… Basic picture … ( J<0) Co Cu Co Cu Cu Exchange interaction between injected polarized e - ↑ and local magnetization causes the magnetization switching in the direction parallel to the spin of the injected e - Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 5/27
Starting point… Landau-Lifshitz-Gilbert equation + polarized current Landau-Lifshitz-Gilbert equatio ⎧ ∂ [ ] ∂ ∂ ⎛ ⎞ ⎛ ⎞ M M M = − γ × + α × + ⎜ ⎟ ⎜ ⎟ ⎪ M H M 0 ∂ ∂ ∂ eff ⎝ ⎠ ⎝ ⎠ ⎨ t t t ST ⎪ = 2 1 ⎩ M H eff H eff Gilbert torque Gilbert torque M M spin torque spin torque antidamping steady oscillation Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 6/27
Perpendicular spin torque oscillator Main goal → generate steady Pt / (Co/Pt)/PEL /Cu/ Py /Cu/ Co/ Co/IrMn IrMn oscillations without applying field Low current R(H b ) I DC AP 57,6 AN R (Ohm) FL AN AN 57,5 P 57,4 FL -1,0 -0,5 0,0 0,5 1,0 H b (kOe) POL Ellipse of 60x70 nm² I DC = 0.15 mA Δ R = 0.19 Ω J. C. Slonczewski US5695864 MR=0.3% K. J. Lee APL 86 (2005) O. Redon US6,532,164 B2 Houssameddine et al. Nat. Mat. 6, 447 (2007) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 7/27
Perpendicular spin torque oscillator Shoulder FL ( ) I DC I = 0.15 mA I = 1.1 mA -1.5 57,6 AP -1.3 AP -1.1 -0.9 R (Ohm) 57,5 -0.7 -0.5 -0.3 R ( Ω ) P P - 0.1 57,4 0.1 0.3 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0.5 H b (kOe) H b (kOe) 0.7 0.9 0.4 Ω 1.1 1.3 Intermediate -0,2 0,0 0,2 0,4 resistance level (IRL) H beff (kOe) There are two magnetoresistive states Houssameddine et al. Nat. Mat. 6, 447 (2007) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 8/27
Perpendicular spin torque oscillator Static current- field diagram I DC < 0 I DC > 0 4 H beff = 9 Oe 600 |I DC | 3 1.5 r 400 1.4 e 2 /Hz) d 1.3 l u 1.2 o AP h 1.1 2 s PSD (nV 200 H beff (Oe) 1.0 0.9 0.8 IRL 1 0.7 0 IRL 0.6 0.5 P 0.4 -200 0 0.3 -1 0 1 2 3 4 2 3 4 I DC (mA) f (Ghz) f (GHz) Houssameddine et al. Nat. Mat. 6, 447 (2007) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 9/27
Perpendicular spin torque oscillator Static current- field diagram Dynamic current- field diagram � f1 600 600 � f2 � f3 ? 400 r 400 e d l u o AP h AP AP ? s 200 200 H beff (Oe) H beff (Oe) ? IRL 0 IRL 0 P P P -200 -200 -1 0 1 -1 0 1 I DC (mA) I DC (mA) Houssameddine et al. Nat. Mat. 6, 447 (2007) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 10/27
Micromagnetic model � Full 3D integration of H eff a)the Landau-Lifshitz-Gilbert (LLG) equation ∂ ∂ ⎛ ⎞ [ ] M M M = − γ × + α × ⎜ ⎟ M H M 0 ∂ ∂ eff ⎝ ⎠ t t = 2 1 M δ 1 E = − H δ eff µ M M 0 s = + + + E E E E E ex anis dem app b)the magnetostatic equations ( ) ( ) ∫ ∫∫ = − ∇ − ρ − ∇ − σ ( ) ( ) ' ( ) ' H dem r G r r' r' dV G r r' r' dS m m V S Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 11/27
Micromagnetic model (2) c) Addition term due to the spin torque transfer ⎧ ∂ ∂ ∂ ⎛ ⎞ ⎛ ⎞ [ ] M M M = − γ × + α × + ⎜ ⎟ ⎜ ⎟ ⎪ M H M 0 ∂ ∂ ∂ eff ⎝ ⎠ ⎝ ⎠ ⎨ t t t ST ⎪ = 2 1 ⎩ M ∂ ∂ ⎛ ⎞ ⎛ ⎞ [ ] [ ] M ( ) M = − γ × × = × ⎜ ⎟ ⎜ ⎟ a M M m c m M 0 0 ∂ ∂ J PL ⎝ ⎠ ⎝ ⎠ t t ST ST J. C. Slonczewski A. Vedyeyev, D. Gusakova � � JMMM. 159, L1 (1996) « ballistic transport model » « diffusive transport model » ST-GLFFT LLG_SA Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 12/27
Micromagnetic model (3) � Transport equation ∂ m j J m + × + = 0 sd m M ∂ η τ z sf electron current j e = j ↑ +j ↓ = σ 0 E z –D 0 ∂ z n–D 0 β′ ( M · ∂ z m ) spin current j m => j ↑ – j ↓ = σ 0 E z β M –D 0 ∂ z m –D 0 β′ M ∂ z n ∂ ⎛ ⎞ J M = × ⎜ ⎟ sf m M ∂ μ ⎝ ⎠ t ST B Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 13/27
Micromagnetic model (4) � Transport equation POL FL AN 400 350 300 250 m x 200 150 100 50 0 -50 0,0 -7 -6 -6 -6 -6 -6 5,0x10 1,0x10 1,5x10 2,0x10 2,5x10 3,0x10 250 200 150 m y 100 50 0 -50 0,0 -7 -6 -6 -6 -6 -6 5,0x10 1,0x10 1,5x10 2,0x10 2,5x10 3,0x10 100 50 0 -50 m z -100 -150 -200 -250 0,0 -7 -6 -6 -6 -6 -6 5,0x10 1,0x10 1,5x10 2,0x10 2,5x10 3,0x10 z (m) 4nm 3.5nm 3nm 3nm 20nm 45° Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 14/27
Perpendicular spin torque oscillator z Micromagnetic parameters Fixed layer AN circular disk 60nm, thickness 3.5nm M s = 866 kA/m x K u = 664.5J/m 3 || Ox (H u =15Oe) FL y A ex = 2 ⋅ 10 -11 J/m = 0.01 α Mesh size 2 x 2 x 3.5 nm 3 POL Fixed layer Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 15/27
Macrospin current-field diagram POL-FL z POL FL 150 120 applied magnetic field, Oe 90 IPS 60 30 OPS 0 OPP -30 -60 -90 -120 -150 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 7 A/cm 2 current density, 10 Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 16/27 Daria Gusakova
Macrospin current-field diagram z POL-FL-AN AN POL FL IPP 150 150 120 120 applied magnetic field, Oe applied magnetic field, Oe 90 IPS 90 60 60 30 30 OPS 0 0 OPP -30 -30 -60 -60 -90 -90 -120 -120 -150 -150 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 7 A/cm 2 current density, 10 7 A/cm 2 current density, 10 Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 17/27 Daria Gusakova
Macrospin current-field diagram z POL-FL-AN AN POL FL 150 150 120 120 applied magnetic field, Oe applied magnetic field, Oe 90 90 60 60 30 30 H app =0 0 0 -30 -30 -60 -60 -90 -90 -120 -120 -150 -150 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 7 A/cm 2 current density, 10 7 A/cm 2 current density, 10 Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 18/27 Daria Gusakova
OPP frequency No applied field 20 20 16 16 Frequency (GHz) Frequency (GHz) 12 12 8 8 macro micro macro 4 4 POL-FL POL-FL POL-FL-AN POL-FL-AN 0 0 10 10 10 10 0 0 10 10 -2x10 -2x10 -1x10 -1x10 1x10 1x10 Japp ( A/m2 ) Japp ( A/m2 ) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 19/27
OPP frequency No applied field → experimental data → µmag simulation H bias =-371Oe 20 4,0 16 3,5 Frequency (GHz) 3,0 Frequency (GHz) 12 2,5 8 2,0 macro micro 4 POL-FL POL-FL-AN 1,5 0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 0 10 10 10 -2x10 -1x10 1x10 Japp ( A/m2 ) Iapp (mA) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 20/27
OPP frequency No applied field 20 20 16 16 Frequency (GHz) Frequency (GHz) 12 12 8 8 macro macro micro 4 4 POL-FL POL-FL POL-FL-AN POL-FL-AN 0 0 0 10 10 10 -2x10 -1x10 1x10 10 10 0 10 Japp ( A/m2 ) -2x10 -1x10 1x10 Japp ( A/m2 ) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 21/27
OPP frequency No applied field 20 16 Frequency (GHz) 12 8 macro micro 4 POL-FL POL-FL POL-FL-AN POL-FL-AN 0 10 10 0 10 -2x10 -1x10 1x10 Japp ( A/m2 ) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 22/27
OPP frequency No applied field 20 16 Frequency (GHz) 12 8 macro micro 4 POL-FL POL-FL POL-FL-AN POL-FL-AN 0 10 10 0 10 -2x10 -1x10 1x10 Japp ( A/m2 ) Workshop on Advance Magnetic Materials / Cluj-Napoca (Romania) 16/09/2007 23/27
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