Spin Torque Oscillator from micromagnetic point of view

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1 Spin Torque Oscillator from micromagnetic point of view Liliana BUDA-PREJBEANU Workshop on Advance Workshop Magnetic on Materials Advance / Cluj-Napoca Magnetic (Romania) Materials 16/9/27 / Cluj-Napoca (Romania) 16/9/27 1/27

Modeling & simulation Daria Gusakova Ioana Firastrau Anatoly Vedyayev Jean-Christophe Toussaint Fabrication & characterization Dimitri Houssameddine Ursula

2 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 2/27

3 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) 3/27

4 Starting point The magnetization acts on the current GMR / TMR phenomena Action-reaction principle: Every action has an equal and opposite reaction. The polarized current acts on the magnetization Spin torque phenomena 4/27

5 Starting point Basic picture ( J<) Cu Co Cu Co 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 - 5/27

6 Starting point Landau-Lifshitz-Gilbert equation + polarized current M = γ t 2 M = 1 [ M H ] eff + α M M t M + t ST H eff H eff Gilbert torque M Gilbert torque M spin torque spin torque antidamping steady oscillation 6/27

7 Perpendicular spin torque oscillator Main goal generate steady oscillations without applying field Pt / (Co/Pt)/PEL /Cu/Py/Cu/Co/ Co/IrMn I DC 57,6 Low current R(H b ) AP AN R (Ohm) 57,5 FL AN POL FL J. C. Slonczewski US K. J. Lee APL 86 (25) O. Redon US6,532,164 B2 57,4 P -1, -,5,,5 1, H b (koe) Ellipse of 6x7 nm² I DC =.15 ma ΔR =.19Ω MR=.3% Houssameddine et al. Nat. Mat. 6, 447 (27) 7/27

8 Perpendicular spin torque oscillator FL Shoulder R (Ohm) 57,6 57,5 57,4 I =.15 ma P AP -1, -,8 -,6 -,4 -,2,,2 H b (koe) Intermediate resistance level (IRL) I = 1.1 ma P -1, -,8 -,6 -,4 -,2,,2 H b (koe) AP R (Ω).4 Ω -,2,,2,4 H beff (koe) I DC There are two magnetoresistive states Houssameddine et al. Nat. Mat. 6, 447 (27) 8/27

9 Perpendicular spin torque oscillator Static current- field diagram AP IRL IRL P -1 1 I DC (ma) shoulder Hbeff (Oe) PSD (nv 2 /Hz) I DC < I DC > f (Ghz) H beff = 9 Oe f (GHz) I DC Houssameddine et al. Nat. Mat. 6, 447 (27) 9/27

10 Perpendicular spin torque oscillator Static current- field diagram Dynamic current- field diagram AP IRL IRL P -1 1 I DC (ma) shoulder Hbeff (Oe) f1 f2 f3 AP P P? -1 1 I DC (ma)?? Hbeff (Oe) Houssameddine et al. Nat. Mat. 6, 447 (27) 1/27

E ex + E [ M H ] s anis eff δe δm + E dem M + α M t + E app M b)the

11 Micromagnetic model Full 3D integration of H eff a)the Landau-Lifshitz-Gilbert (LLG) equation M = γ t M H E 2 eff = = 1 1 = µ M E ex + E [ M H ] s anis eff δe δm + E dem M + α M t + E app M b)the magnetostatic equations H dem V m ( r' ) dv' G( r r' ) σ ( ) ( r) = G ( r r' ) ρ r' ds' S m 11/27

12 Micromagnetic model (2) c) Addition term due to the spin torque transfer M = γ t 2 M = 1 [ M H ] eff M + α M t + M t ST M t ST = γ a J [ M ( M )] m PL M t ST = c [ m M] J. C. Slonczewski JMMM. 159, L1 (1996) A. Vedyeyev, D. Gusakova «ballistic transport model» «diffusive transport model» ST-GLFFT LLG_SA 12/27

13 Micromagnetic model (3) Transport equation j z m + J η sd m M + m τ sf = electron current j e = j +j = σ E z D z n D β (M z m) spin current j m => j j =σ E z βm D z m D β M z n M t ST = J μ sf B m M 13/27

14 Micromagnetic model (4) Transport equation m x m y m z POL FL AN, 25 5,x1-7 1,x1-6 1,5x1-6 2,x1-6 2,5x1-6 3,x , 5,x1-7 1,x1-6 1,5x1-6 2,x1-6 2,5x1-6 3,x , 5,x1-7 1,x1-6 1,5x1-6 2,x1-6 2,5x1-6 3,x1-6 z (m) 2nm 4nm 3.5nm 3nm 3nm 45 14/27

15 Perpendicular spin torque oscillator z Micromagnetic parameters AN Fixed layer circular disk 6nm, thickness 3.5nm POL FL y x M s K u = 866 ka/m = 664.5J/m 3 Ox (H u =15Oe) A ex = J/m α =.1 Mesh size 2 x 2 x 3.5 nm 3 Fixed layer 15/27

Macrospin current-field diagram z POL-FL POL FL applied magnetic field, Oe 15 12 9 IPS 6 3

16 Macrospin current-field diagram z POL-FL POL FL applied magnetic field, Oe IPS 6 3 OPS OPP ,3 -,2 -,1,,1,2,3 current density, 1 7 A/cm 2 Daria Gusakova 16/27

17 Macrospin current-field diagram AN z POL-FL-AN POL FL applied magnetic field, Oe IPP IPS 6 3 OPS OPP ,3 -,2 -,1,,1,2,3 current density, 1 7 A/cm 2 Daria Gusakova 17/27

18 Macrospin current-field diagram AN z POL-FL-AN POL FL applied magnetic field, Oe ,3 -,2 -,1,,1,2,3 current density, 1 7 A/cm 2 H app = Daria Gusakova 18/27

19 OPP frequency No applied field 2 16 Frequency (GHz) macro micro POL-FL POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 19/27

20 OPP frequency No applied field µmag simulation experimental data 2 4, H bias =-371Oe 16 3,5 Frequency (GHz) 12 8 Frequency (GHz) 3, 2,5 4 macro micro POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 2, 1,5-1,5-1, -,5,,5 1, 1,5 I app (ma) 2/27

21 OPP frequency No applied field Frequency (GHz) Frequency (GHz) macro micro POL-FL POL-FL POL-FL-AN -2x1-2x x1-1x x1 1 1x1 1 J app (A/m 2 app (A/m ) 21/27

22 OPP frequency No applied field 2 16 Frequency (GHz) macro micro POL-FL POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 22/27

23 OPP frequency No applied field 2 16 Frequency (GHz) macro micro POL-FL POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 23/27

24 Perpendicular spin torque oscillator Static current- field diagram Dynamic current- field diagram AP IRL IRL P -1 1 I DC (ma) shoulder Hbeff (Oe) f1 f2 f3 AP P P -1 1 I DC (ma)? Hbeff (Oe) Houssameddine et al. accepted Nat. Mat. 24/27

25 IPP frequency experimental data µmag simulation 6 H beff (Oe) Freq (GHz) -1 1 I DC (ma) 4 3 f H beff (Oe) Frequency (Hz) 7,x1 9 6,x1 9 5,x1 9 4,x1 9 3,x1 9 2,x1 9 J app =,8*1 1 A/m 2 micro macro POL-FL-AN µ H app (mt) 25/27

26 Temperature effects No applied field µmag simulation 2,1 16,5, Frequency (GHz) macro micro POL-FL POL-FL-AN <M z > -,5 -,1 -,15 -,2 before jump,47*1 1 A/m 2,48*1 1 A/m 2 (CH) after jump,48*1 1 A/m 2,47*1 1 A/m 2 T=4K T=4K -2x1 1-1x1 1 1x1 1 J app (A/m 2 ), 1,x1-8 2,x1-8 3,x1-8 4,x1-8 time (s) 26/27

27 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 27/27

Injection locking at zero field in two free layer spin-valves

Injection locking at zero field in two free layer spin-valves Mario Carpentieri, 1 Takahiro Moriyama, 2 Bruno Azzerboni, 3 Giovanni Finocchio 3 1 Department of Ingegneria Elettrica e dell Informazione,