Spin transfer torque and magnetization dynamics in in-plane and out-of-plane magnetized spin valves

Transcription

1 Spin transfer torque and magnetization dynamics in in-plane and out-of-plane magnetized spin valves Pavel Baláž Institute of Molecular Physics in Poznań Polish Academy of Sciences and Faculty of Physics A. Mickiewicz University in Poznań Univerzita Karlova, 5 December 2013 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

2 Nanoscale spin torque devices for spin electronics Joint research project under the framework of Polish-Swiss research programme Partners nanospin.agh.edu.pl AGH University of Science and Technology in Kraków T. Stobiecki coordinator Institute of Molecular Physics in Poznań, Polish Academy of Sciences J. Dubowik experiment, J. Barnaś theory Ecolé Polytechnique Fédérale in Lausanne J.-Ph. Ansermet Objectives jointly developing novel nanoscale spintronic devices based on the spin transfer torque effect, which promises unrivaled future scaling, flexibility and low power consumption P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

3 1 Introduction 2 Spin-torque in metallic spin valves 3 Dual spin valve 4 Nonlinear magnetoresistance in dual spin vales 5 Current-induced switching in metallic spin valves with perpendicular polarizers P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

4 Introduction Outline 1 Introduction 2 Spin-torque in metallic spin valves 3 Dual spin valve 4 Nonlinear magnetoresistance in dual spin vales 5 Current-induced switching in metallic spin valves with perpendicular polarizers P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

5 spin spin Introduction Spin valves and Giant magnetoresistance M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices Phys. Rev. Lett. 61, (1988) G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange Phys. Rev. B 39, (1989) R. E. Camley and J. Barnaś Theory of giant magnetoresistance effects in magnetic layered structures with antiferromagnetic coupling Phys. Rev. Lett. 63, (1989) T. Valet and A. Fert Theory of the perpendicular magnetoresistance in magnetic multilayers Phys. Rev. B 48, (1993) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

6 Introduction Current-induced dynamics and magnetization switching Magnetization can be switched by electric current without need of magnetic field Slonczewski s model (ballistic) J. Magn. Magn. Mater. 159, L1-L7 (1996) g(θ) sin(θ) (Co) 0.3 (Py) 0.2 where θ/ g(θ)= τ Sloncz = Ig(θ) ŝ ( ŝ Ŝ ) e [ 4+(1+P) 3 3+cos θ ] 1 4P 3/2 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

7 Introduction Current-induced dynamics and magnetization switching Magnetization can be switched by electric current without need of magnetic field Slonczewski s model (ballistic) J. Magn. Magn. Mater. 159, L1-L7 (1996) g(θ) sin(θ) where (Co) 0.3 (Py) θ/ g(θ)= τ Sloncz = Ig(θ) ŝ ( ŝ Ŝ ) e [ 4+(1+P) 3 3+cos θ ] 1 4P 3/2 Unified description (diffusive) Description of spin-transfer torque should be consistent with description of giant magnetoresistance (Valet-Fert model) J. Barnaś, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev From giant magnetoresistance to current-induced switching by spin transfer Phys. Rev. B 72, (2005) Spin-transfer torque τ θ = a(θ)i ŝ ( ŝ Ŝ ) τ φ = b(θ)i ŝ Ŝ P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

8 Introduction Equation of motion Landau-Lifshitz-Gilbert equation dŝ dt = γ g µ 0 ŝ H eff α ŝ dŝ dt + γ g M s d ( τθ + τ φ ) Effective magnetic field H eff = H ext ê z H ani (ŝ ê z )ê z + H demag Spin-transfer torque τ θ = a(θ)i ŝ ( ŝ Ŝ ) τ φ = b(θ)i ŝ Ŝ P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

9 Spin-torque in metallic spin valves Outline 1 Introduction 2 Spin-torque in metallic spin valves 3 Dual spin valve 4 Nonlinear magnetoresistance in dual spin vales 5 Current-induced switching in metallic spin valves with perpendicular polarizers P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

10 Mathematical description Spin-torque in metallic spin valves Two channels model bulk resistivities ρ ( ) = 2ρ (1 β) interface resistances R ( ) = 2R (1 γ) Diffusive transport 2 ( µ µ ) x 2 = 1 l 2 ( µ µ ) sf 2 ( µ + µ ) x 2 = η 2 ( µ µ ) x 2 β bulk asymmetry paramters γ interfacial asymmetry parameter J. Barnaś, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev From giant magnetoresistance to current-induced switching by spin transfer Phys. Rev. B 72, (2005) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

11 Mathematical description Spin-torque in metallic spin valves Two channels model bulk resistivities ρ ( ) = 2ρ (1 β) interface resistances R ( ) = 2R (1 γ) β bulk asymmetry paramters γ interfacial asymmetry parameter Diffusive transport 2 ( µ µ ) x 2 = 1 l 2 ( µ µ ) sf 2 ( µ + µ ) x 2 = η 2 ( µ µ ) x 2 for electrochemical potentials we get [ ] µ =(1+η) Ae x/l sf + Be x/l sf + Cx+G [ ] µ =(η 1) Ae x/l sf + Be x/l sf + Cx+G J. Barnaś, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev From giant magnetoresistance to current-induced switching by spin transfer Phys. Rev. B 72, (2005) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

12 Mathematical description Spin-torque in metallic spin valves µ 0 = µ + µ 2 Magnetic layer ˇ µ = µ 0 ˇ1+g ˇσ z, g= µ µ 2 with g being spin accumulation ǰ= ρ(e F )Ď ˇ µ x ǰ= 1 ( ) j0 ˇ1+j z ˇσ z 2 with j z being spin current Diffusive transport 2 ( µ µ ) x 2 = 1 l 2 ( µ µ ) sf 2 ( µ + µ ) x 2 = η 2 ( µ µ ) x 2 for electrochemical potentials we get [ ] µ =(1+η) Ae x/l sf + Be x/l sf + Cx+G [ ] µ =(η 1) Ae x/l sf + Be x/l sf + Cx+G J. Barnaś, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev From giant magnetoresistance to current-induced switching by spin transfer Phys. Rev. B 72, (2005) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

13 Mathematical description Spin-torque in metallic spin valves Nonmagnetic layer has no natural quantization axis where ˇ µ = µ 0 ˇ1+g. ˇσ ǰ= 1 ( j0 ˇ1+j. ˇσ ) 2 g=(g x,g y,g z ), j=(j x,j y,j z ) are 3D vectors written in the coordinate system of one of the adjacent magnetic layers Diffusive transport 2 ( µ µ ) x 2 = 1 l 2 ( µ µ ) sf 2 ( µ + µ ) x 2 = η 2 ( µ µ ) x 2 for electrochemical potentials we get [ ] µ =(1+η) Ae x/l sf + Be x/l sf + Cx+G [ ] µ =(η 1) Ae x/l sf + Be x/l sf + Cx+G J. Barnaś, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev From giant magnetoresistance to current-induced switching by spin transfer Phys. Rev. B 72, (2005) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

14 Spin-torque in metallic spin valves Boundary conditions at N/F interface particle current is continuous across all interfaces e 2 j 0 =(G + G )( µ F 0 µn 0 )+(G G )(g F z gn z ) spin current component parallel to the magnetization is continuous across the interface e 2 j z =(G G )( µ F 0 µn 0 )+(G + G )(g F z gn z ) transversal component of the spin current vanishes in the magnetic layer jump at the interface e 2 j x = 2Re{G }g N x + 2Im{G }g N y e 2 j y = 2Re{G }g N y 2Im{G }g N x A. Brataas, Yu.V. Nazarov, G.E.W. Bauer Spin-transport in multi-terminal normal metal-ferromagnet systems with non-collinear magnetizations Eur. Phys. J. B 22, 99 (2001) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

15 Spin-torque in metallic spin valves Boundary conditions at N/F interface particle current is continuous across all interfaces e 2 j 0 =(G + G )( µ F 0 µn 0 )+(G G )(g F z gn z ) spin current component parallel to the magnetization is continuous across the interface e 2 j z =(G G )( µ F 0 µn 0 )+(G + G )(g F z gn z ) transversal component of the spin current vanishes in the magnetic layer jump at the interface e 2 j x = 2Re{G }g N x + 2Im{G }g N y e 2 j y = 2Re{G }g N y 2Im{G }g N x Spin-transfer torque τ = h 2 (j L j R ) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

16 Spin-torque in metallic spin valves Boundary conditions at N/F interface particle current is continuous across all interfaces e 2 j 0 =(G + G )( µ F 0 µn 0 )+(G G )(g F z g N z ) spin current component parallel to the magnetization is continuous across the interface e 2 j z =(G G )( µ F 0 µn 0 )+(G + G )(g F z g N z ) transversal component of the spin current vanishes in the magnetic layer jump at the interface e 2 j x = 2Re{G }g N x + 2Im{G }g N y e 2 j y = 2Re{G }g N y 2Im{G }g N x Components in-plane out-of-plane τ θ = h 2 j y N/F τ φ = h 2 j x N/F P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

17 Results Calculations for real structures Spin-torque in metallic spin valves Standard spin valve Py(20)/Cu(10)/Py(8) STT / (h I / e ) τ θ 10 2 τ φ /4 /2 3 /4 θ Nonstandard spin valve Co(8)/Cu(10)/Py(8) STT / (h I / e ) τ θ τ φ /4 /2 3 /4 θ P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

18 Dual spin valve Outline 1 Introduction 2 Spin-torque in metallic spin valves 3 Dual spin valve 4 Nonlinear magnetoresistance in dual spin vales 5 Current-induced switching in metallic spin valves with perpendicular polarizers P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

19 What is a dual spin valve?

20 Dual spin valve Spin accumulation in dual spin valve spin accumulation in single spin valve spin accumulation x P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

21 Dual spin valve Spin accumulation in dual spin valve spin accumulation in single spin valve spin accumulation in dual spin valve spin accumulation 0.2 spin accumulation x x L. Berger Multilayer Configuration for Experiments of Spin Precession Induced by a DC Current J. Appl. Phys. 93, 7683 (2003) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

22 Dual spin valve Enhancement of switching single vs. dual spin valve Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20) Spin-transfer torque 0.2 STT / (h I / e ) Dual SV Single SV θ / P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

23 Dual spin valve Enhancement of switching single vs. dual spin valve Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20) Spin-transfer torque 0.2 STT / (h I / e ) 0.16 Dual SV Single SV θ / Switching time switching time [ns] Dual SV Single SV I / (10 8 A cm -2 ) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

24 Dual spin valve Enhancement of switching single vs. dual spin valve Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20) Spin-transfer torque 0.2 STT / (h I / e ) 0.16 Dual SV Single SV θ / Switching time switching time [ns] Dual SV Single SV I / (10 8 A cm -2 ) Is this all? P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

25 Question: How torque changes in non-collinear configurations? I>0

26 Dual spin valve Noncollinear configurations in dual spin valves Co(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8) P.B., M. Gmitra, J. Barnaś Current-induced dynamics in non-collinear dual spin-valves Phys. Rev. B 80, (2009) I>0 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

27 Dual spin valve Noncollinear configurations in dual spin valves Co(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8) P.B., M. Gmitra, J. Barnaś Current-induced dynamics in non-collinear dual spin-valves Phys. Rev. B 80, (2009) I>0 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

28 Dual spin valve Noncollinear configurations in dual spin valves Co(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8) P.B., M. Gmitra, J. Barnaś Current-induced dynamics in non-collinear dual spin-valves Phys. Rev. B 80, (2009) Current-induced dynamics I>0 We calculated average 1 tend s z = s z dt t end t eq teq and dispersion s D(s z)= 2 z sz 2 for each couple of I and Ω to map the dynamic behaviour. P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

29 Dual spin valve Noncollinear configurations in dual spin valves Co(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8) I>0 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

30 Nonlinear magnetoresistance in dual spin vales Outline 1 Introduction 2 Spin-torque in metallic spin valves 3 Dual spin valve 4 Nonlinear magnetoresistance in dual spin vales 5 Current-induced switching in metallic spin valves with perpendicular polarizers P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

31 Nonlinear magnetoresistance in dual spin vales Nonlinear magnetoresistance in dual spin vales Experimental works A. Aziz, O. P. Wessely, M. Ali, D. M. Edwards, C. H. Marrows, B. J. Hickey, and M. G. Blamire Nonlinear giant magnetoresistance in dual spin valves Phys. Rev. Lett. 103, (2009) N. Banerjee, A. Aziz, M. Ali, J. W. A. Robinson, B. J. Hickey, and M. G. Blamire Thickness dependence and the role of spin transfer torque in nonlinear giant magnetoresistance of permalloy dual spin valves Phys. Rev. B 82, (2010) N. Banerjee, J. W. A. Robinson, A. Aziz, M. Ali, B. J. Hickey, and M. G. Blamire Nonlocal Magnetization Dynamics in Ferromagnetic Hybrid Nanostructure Phys. Rev. B 86, (2012) Experimental results [Aziz et al, PRL (2009)]: (b) minor loops for Co 90 Fe 10 (6)/Cu(4)/Py(1)/Cu(2)/Co 90 Fe 10 (6)/IrMn(10) (c) Py thickness: 1 nm (blue), 2 nm (red), and 8 nm (magenta) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

32 Nonlinear magnetoresistance in dual spin vales Nonlinear magnetoresistance in dual spin vales Model s assumptions Spin accumulation in the central layer changes density of states on Fermi level This may change bulk/interfacial material parameters in the central layer We extended the diffusion transport model J. Barnaś, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev From giant magnetoresistance to current-induced switching by spin transfer Phys. Rev. B 72, (2005) Bulk contribution ρ = ρ 0 + q g β = β 0 + ξ g Interfacial contribution R = R 0 + q g(x i ) γ = γ 0 + ξ g(x i ) where g(x) is spin accumulation ρ0 and R 0 are zero-current bulk resistivity and interfacial resistance β 0 and γ 0 are zero-current bulk/interfacial asymmetry parameters q, ξ, q, ξ are phenomenological parameters P. Baláž, and J. Barnaś Nonlinear magnetotransport in dual spin valves Phys. Rev. B 82, (2010) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

33 Nonlinear magnetoresistance in dual spin vales Nonlinear magnetoresistance in dual spin vales Calculations for Cu - Co(6) / Cu(4) / Py(2) / Cu(2) / Co(6) / IrMn(10) - Cu R [fω m 2 ] R [fω m 2 ] Bulk parameters i = 3 i = θ / 0.04 (1) 0.02 only ρ * only β Reduced current density P. Baláž, and J. Barnaś Nonlinear magnetotransport in dual spin valves Phys. Rev. B 82, (2010) R [fω m 2 ] R [fω m 2 ] Interfacial parameters i = 3 i = θ/ d = 2 nm d = 8 nm d = 16 nm Reduced current density for q= 0.1, ξ = 0.1, I 0 = 10 8 Acm 2 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

34 Nonlinear magnetoresistance in dual spin vales Nonlinear magnetoresistance in dual spin vales Calculations for Cu - Co(6) / Cu(4) / Py(2) / Cu(2) / Co(6) / IrMn(10) - Cu iξ ~ Bulk parameters R > 0 R < iq ~ R [fω m 2 ] iξ ~ Interfacial parameters R > 0 R < iq ~ R [fω m 2 ] for interfaces R is symmetric with current density P. Baláž, and J. Barnaś Nonlinear magnetotransport in dual spin valves Phys. Rev. B 82, (2010) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

35 Perpendicular polarizer Outline 1 Introduction 2 Spin-torque in metallic spin valves 3 Dual spin valve 4 Nonlinear magnetoresistance in dual spin vales 5 Current-induced switching in metallic spin valves with perpendicular polarizers P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

36 Perpendicular polarizer Model of the polarizer (a) PP NL FL NR IP I>0 P. Baláž, M. Zwierzycki, J. Barnaś Spin-transfer torque and current-induced switching in metallic spin valves with perpendicular polarizers Phys. Rev. B 88, (2013) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

37 Perpendicular polarizer Transport through the polarizer We considered the perpendicular polarizer as a magnetized ballistic scaterrer in frame of coherent transport regime To calculate the transport properties of the polarizer we used Ab initio wave function matching method M. Zwierzycki et al Calculating scattering matrices by wave function matching Phys. Stat. Sol. (b) 245, (2008) In our formalism the scaterrer coresponds to a single interface. P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

38 Perpendicular polarizer Transport through the polarizer We considered the perpendicular polarizer as a magnetized ballistic scaterrer in frame of coherent transport regime To calculate the transport properties of the polarizer we used Ab initio wave function matching method M. Zwierzycki et al Calculating scattering matrices by wave function matching Phys. Stat. Sol. (b) 245, (2008) In our formalism the scaterrer coresponds to a single interface. P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

39 Perpendicular polarizer Transport through the polarizer We considered the perpendicular polarizer as a magnetized ballistic scaterrer in frame of coherent transport regime To calculate the transport properties of the polarizer we used Ab initio wave function matching method M. Zwierzycki et al Calculating scattering matrices by wave function matching Phys. Stat. Sol. (b) 245, (2008) In our formalism the scaterrer coresponds to a single interface. Outputs of the calculation: channel conductances G, G mixing conductance G = g r + ig i mixing transmission conductance T = tr + it i Differences in definitions G σσ = nn T σσ = nn t σ nn [δ nn r σ nn ( r σ nn ) ] ( t σ nn ) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

40 Perpendicular polarizer Boundary conditions Longitudinal components e 2 j 0 G = + G j z G G G G G + G µr 0 µl 0 µ R z µ L z Transverse components e 2 j R = G T µ R j L T G µ L where j R/L = j R/Lx µ R/L = µ R/Lx j R/Ly µ R/Ly and G=2 g r g i g i g T=2 i t r t i t i tr Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I. Halperin Nonlocal Magnetization Dynamics in Ferromagnetic Hybrid Nanostructure Rev. Mod. Phys 77, 1375 (2005) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

41 Perpendicular polarizer Spin transfer torque Spin torque acting on the free layer τ = Iŝ [ Ŝ OP ( a OP Ŝ OP + a IP Ŝ IP )] τ = Iŝ ( b OP Ŝ OP + b IP Ŝ IP ) a OP = h 2 a IP = h 2 where cosθ OP = ŝ Ŝ OP and cosθ IP = ŝ Ŝ IP j 1y N 1 /F 1 b I sinθ OP = h j 1x N 1 /F 1 OP 2 I sinθ OP j 2y F 1 /N 2 b IP = h j 2x F 1 /N 2 I sinθ IP 2 I sinθ IP P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

42 Perpendicular polarizer Studied structures Cu - PP / Cu(6) / Py(5) / Cu(12) / Py(20) - Cu Perpendicular polarizer PP 1 = Co(2 ML) / [Cu(2 ML)/Co(2 ML)] L 1 PP 2 = Pt(6 ML) / [Co(2 ML)/Pt(3 ML)] L / Co(3 ML) / Cu(2 ML) / Co(3 ML) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

43 Perpendicular polarizer Results for PP 1 Spin transfer torque Co(2 ML) / [Cu(2 ML)/Co(2 ML)] L 1 Spin torque τ Spin torque 10 τ PP polarizer L=1 L=3 L= (a) (c) (b) IP polarizer (d) angle θ P / angle θ I / wavelike angular dependence for the perpendicular polarizer P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

44 Perpendicular polarizer Results for PP 1 Current-induced switching from to at T = 300K Co(2 ML) / [Cu(2 ML)/Co(2 ML)] L 1 P sw P sw L=1 L=3 L=5 t p = 50 ps t p = 1 ns t p = 10 ns t p = 100 ps I m / [Am ] I m / [Am -2 ] P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

45 Perpendicular polarizer Switching mechanism For I < 0 For I > 0 P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

46 Perpendicular polarizer Results for PP 2 Spin transfer torque Pt(6 ML) / [Co(2 ML)/Pt(3 ML)] L / Co(3 ML) / Cu(2 ML) / Co(3 ML) Clean PP Disordered PP L=1 L= L= L= L= L= (a) (b) Spin torque τ Spin torque 10 τ (c) (d) angle θ P / angle θ P / P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

47 Perpendicular polarizer Results for PP 2 Current-induced switching from to Pt(6 ML) / [Co(2 ML)/Pt(3 ML)] L / Co(3 ML) / Cu(2 ML) / Co(3 ML) P sw P sw L=1 L=3 L=5 t p = 50 ps t p = 1 ns t p = 100 ps t p = 10 ns I m / [Am ] I m / [Am -2 ] P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

48 Perpendicular polarizer Summary Noncollinear diffusive model is an useful and flexible framework for dealing with spin dependent electronic transport in metalic multilayers spin tranfer torque and magnetoresistance in single and dual spin valves nonlinear effects in magnetoresistance spin transfer torque due to a perpendicular polarizer also spin torque and dynamics in composite free layers (synthetic ferro- or antiferromagnets) P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35

49 Perpendicular polarizer Thank you for your attention P. Baláž (AMU, Poznań) Spin transfer torque and magnetization dynamics Prague, December / 35