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 Ebels Betrand Delaët Bernard Rodmacq Fabienne Ponthenier Magalie Brunet Christophe Thirion Jean-Philip-Michel Marie-Claire. Cyrille Olivier Redon Bernard Dieny 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) 3/27
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
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
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
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 US5695864 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
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 -1.5-1.3-1.1 -.9 -.7 -.5 -.3 -.1.1.3.5.7.9 1.1 1.3 There are two magnetoresistive states Houssameddine et al. Nat. Mat. 6, 447 (27) 8/27
Perpendicular spin torque oscillator Static current- field diagram AP IRL IRL P -1 1 I DC (ma) shoulder 6 4 2-2 Hbeff (Oe) PSD (nv 2 /Hz) 4 3 2 1 I DC < I DC > 2 3 4 f (Ghz) H beff = 9 Oe 2 3 4 f (GHz) I DC 1.5 1.4 1.3 1.2 1.1 1..9.8.7.6.5.4.3 Houssameddine et al. Nat. Mat. 6, 447 (27) 9/27
Perpendicular spin torque oscillator Static current- field diagram Dynamic current- field diagram AP IRL IRL P -1 1 I DC (ma) shoulder 6 4 2-2 Hbeff (Oe) f1 f2 f3 AP P P? -1 1 I DC (ma)?? 6 4 2-2 Hbeff (Oe) Houssameddine et al. Nat. Mat. 6, 447 (27) 1/27
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
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
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
Micromagnetic model (4) Transport equation m x m y m z 4 35 3 25 2 15 1 5-5 POL FL AN, 25 5,x1-7 1,x1-6 1,5x1-6 2,x1-6 2,5x1-6 3,x1-6 2 15 1 5-5, 5,x1-7 1,x1-6 1,5x1-6 2,x1-6 2,5x1-6 3,x1-6 1 5-5 -1-15 -2-25, 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
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 = 2 1-11 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 OPS OPP -3-6 -9-12 -15 -,3 -,2 -,1,,1,2,3 current density, 1 7 A/cm 2 Daria Gusakova 16/27
Macrospin current-field diagram AN z POL-FL-AN POL FL applied magnetic field, Oe IPP 15 12 9 IPS 6 3 OPS OPP -3-6 -9-12 -15 -,3 -,2 -,1,,1,2,3 current density, 1 7 A/cm 2 Daria Gusakova 17/27
Macrospin current-field diagram AN z POL-FL-AN POL FL applied magnetic field, Oe 15 12 9 6 3-3 -6-9 -12-15 -,3 -,2 -,1,,1,2,3 current density, 1 7 A/cm 2 H app = Daria Gusakova 18/27
OPP frequency No applied field 2 16 Frequency (GHz) 12 8 4 macro micro POL-FL POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 19/27
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
OPP frequency No applied field 2 2 16 16 Frequency (GHz) Frequency (GHz) 12 12 88 44 macro micro POL-FL POL-FL POL-FL-AN -2x1-2x1 1 1-1x1-1x1 1 1 1x1 1 1x1 1 J app (A/m 2 app (A/m ) 21/27
OPP frequency No applied field 2 16 Frequency (GHz) 12 8 4 macro micro POL-FL POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 22/27
OPP frequency No applied field 2 16 Frequency (GHz) 12 8 4 macro micro POL-FL POL-FL POL-FL-AN -2x1 1-1x1 1 1x1 1 J app (A/m 2 ) 23/27
Perpendicular spin torque oscillator Static current- field diagram Dynamic current- field diagram AP IRL IRL P -1 1 I DC (ma) shoulder 6 4 2-2 Hbeff (Oe) f1 f2 f3 AP P P -1 1 I DC (ma)? 6 4 2-2 Hbeff (Oe) Houssameddine et al. accepted Nat. Mat. 24/27
IPP frequency experimental data µmag simulation 6 H beff (Oe) 4 2-2 Freq (GHz) -1 1 I DC (ma) 4 3 f3 2 1-3 3 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 1 2 3 4 5 µ H app (mt) 25/27
Temperature effects No applied field µmag simulation 2,1 16,5, Frequency (GHz) 12 8 4 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
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