Time scales in magnetism Jan Vogel Institut Nel, CNRS and Universit - PowerPoint PPT Presentation

Time scales in magnetism Jan Vogel Institut Néel, CNRS and Université Joseph Fourier Grenoble, France http://neel.cnrs.fr

Overview timescales Magneti- Electronic Thermally activated magnetization dynamics zation processes precession 10 -15 10 -12 10 -9 10 -6 10 -3 10 9 1 Photoelectric interactions J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Different time-related parameters or derivated parameters are used : Frequency = time -1 1 nanosecond ↔ 1 Gigahertz J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Different time-related parameters or derivated parameters are used : Frequency = time -1 1 nanosecond ↔ 1 Gigahertz Energy = h * frequency 1GHz ↔ 6.63 x 10 -25 J = 4.14 µeV h = 6.63 x 10 -34 J.s = 4.136 x 10 -15 eV.s J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Different time-related parameters or derivated parameters are used : Frequency = time -1 1 nanosecond ↔ 1 Gigahertz Energy = h * frequency 1GHz ↔ 6.63 x 10 -25 J = 4.14 µeV h = 6.63 x 10 -34 J.s = 4.136 x 10 -15 eV.s Energy = k * temperature 1 meV ↔ 11.6 K k = 1.38 x 10 -23 J.K -1 = 8.617 x 10 -5 eV.K -1 J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Small magnetic particle, with uniaxial magnetic anisotropy constant K (two stable orientations) Stoner-Wohlfarth model : macrospin, energy barrier ΔE = KV (V : volume of particle) J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Average time between two magnetization flips (Néel-Arrhenius law) : τ Ν = τ 0 e KV/kT Example : Co particle, K = 45 x 10 4 J/m 3 Room temperature 293 K : kT = 4 x 10 -21 J τ 0 ≈ 10 -9 s 0.1 x 0.1 x 0.1 µm 3 : τ Ν ≈ ∞ J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Average time between two magnetization flips (Néel-Arrhenius law) : τ Ν = τ 0 e KV/kT Example : Co particle, K = 45 x 10 4 J/m 3 Room temperature 293 K : kT = 4 x 10 -21 J τ 0 ≈ 10 -9 s 0.1 x 0.1 x 0.1 µm 3 : τ Ν ≈ ∞ 10 x 10 x 10 nm 3 : τ Ν ≈ 7 x 10 39 s (1 year ≈ 3 x 10 7 s) J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Average time between two magnetization flips (Néel-Arrhenius law) : τ Ν = τ 0 e KV/kT Example : Co particle, K = 45 x 10 4 J/m 3 Room temperature 293 K : kT = 4 x 10 -21 J τ 0 ≈ 10 -9 s 0.1 x 0.1 x 0.1 µm 3 : τ Ν ≈ ∞ 10 x 10 x 10 nm 3 : τ Ν ≈ 7 x 10 39 s (1 year ≈ 3 x 10 7 s) 8 x 8 x 8 nm 3 : τ Ν ≈ 1 x 10 16 s J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Average time between two magnetization flips (Néel-Arrhenius law) : τ Ν = τ 0 e KV/kT Example : Co particle, K = 45 x 10 4 J/m 3 Room temperature 293 K : kT = 4 x 10 -21 J τ 0 ≈ 10 -9 s 0.1 x 0.1 x 0.1 µm 3 : τ Ν ≈ ∞ 10 x 10 x 10 nm 3 : τ Ν ≈ 7 x 10 39 s (1 year ≈ 3 x 10 7 s) 8 x 8 x 8 nm 3 : τ Ν ≈ 1 x 10 16 s 6 x 6 x 6 nm 3 : τ Ν ≈ 870 s J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Average time between two magnetization flips (Néel-Arrhenius law) : τ Ν = τ 0 e KV/kT Example : Co particle, K = 45 x 10 4 J/m 3 Room temperature 293 K : kT = 4 x 10 -21 J τ 0 ≈ 10 -9 s 0.1 x 0.1 x 0.1 µm 3 : τ Ν ≈ ∞ 10 x 10 x 10 nm 3 : τ Ν ≈ 7 x 10 39 s (1 year ≈ 3 x 10 7 s) 8 x 8 x 8 nm 3 : τ Ν ≈ 1 x 10 16 s 6 x 6 x 6 nm 3 : τ Ν ≈ 870 s 4 x 4 x 4 nm 3 : τ Ν ≈ 9.6 µs J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics 2 x 2 x 2 nm 3 : τ Ν ≈ 2.4 ns Same particle, decreasing temperature : T = 150 K : τ Ν ≈ 5.7 ns T = 100 K : τ Ν ≈ 13.6 ns T = 50 K : τ Ν ≈ 184 ns J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics 2 x 2 x 2 nm 3 : τ Ν ≈ 2.4 ns Same particle, decreasing temperature : T = 150 K : τ Ν ≈ 5.7 ns T = 100 K : τ Ν ≈ 13.6 ns T = 50 K : τ Ν ≈ 184 ns T = 20 K : τ Ν ≈ 462 µs J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics 2 x 2 x 2 nm 3 : τ Ν ≈ 2.4 ns Same particle, decreasing temperature : T = 150 K : τ Ν ≈ 5.7 ns T = 100 K : τ Ν ≈ 13.6 ns T = 50 K : τ Ν ≈ 184 ns T = 20 K : τ Ν ≈ 462 µs T = 10 K : τ Ν ≈ 214 s J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics 2 x 2 x 2 nm 3 : τ Ν ≈ 2.4 ns Same particle, decreasing temperature : T = 150 K : τ Ν ≈ 5.7 ns T = 100 K : τ Ν ≈ 13.6 ns T = 50 K : τ Ν ≈ 184 ns T = 20 K : τ Ν ≈ 462 µs T = 10 K : τ Ν ≈ 214 s T = 5 K : τ Ν ≈ 4.6 x 10 13 s Particle is 'superparamagnetic' above a certain 'blocking temperature' that depends on the measuring time J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Slow dynamics : Spin glasses Materials with frustrated ferro/antiferromagnetic interactions, short and long range order : many different states with equivalent energies, separated by energy barriers. Relaxation over long times scales (days or more) E J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Domain nucleation + domain wall propagation Thermally assisted reversal of nucleation volume (>1ns) Propagation of domain walls over pinning barriers, maximum speeds ~1000 m/s J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics J. Vogel, Targoviste, 22/08/2011

Thermally activated magnetization dynamics Pt/Co multilayer µ 0 H (mT) Reversal mode and coercivity are dynamical properties of a sample (depend on field sweep rate, temperature) J. Vogel, Targoviste, 22/08/2011

Beyond thermal activation : Landau-Lifshitz- Gilbert equation : precession and damping d M /dt = γ M x H eff + α/ M S ( M x d M /dt) J. Vogel, Targoviste, 22/08/2011

Beyond thermal activation : Landau-Lifshitz- Gilbert equation : precession and damping d M /dt = γ M x H eff + α/ M S ( M x d M /dt) Larmor precession frequency : f = γΒ/2π γ = 176 GHz/T (for g=2) τ = 1/f = 36 ps f (1T) = 28 GHz γ : gyromagnetic ratio g : Landé factor J. Vogel, Targoviste, 22/08/2011

Precession and damping : ferromagnetic resonance Calculation for Ferromagnetic resonance (FMR) of µ 0 M S = 1T ; µ 0 H eff = 0.01T NiFe @ f = 9.77 Ghz 2 PyZI30_0deg_26Nov10b 1,5 1 0,5 0 -0,5 0,06 0,07 0,08 0,09 0,1 0,11 0,12 Field (Tesla) µ 0 ΔH = 2(α/γ)ω res Ph.D. thesis C. Bilzer J. Vogel, Targoviste, 22/08/2011

Beyond thermal activation : precessional switching Precessional switching with 140 ps pulses of µ 0 H = 15.5 mT pulses τ = 1/f L = 2.3 ns ? Switching by demagnetizing field H.W. Schumacher et al., Phys. Rev. Lett. 90, 017201 (2003) ; 017204 (2003) J. Vogel, Targoviste, 22/08/2011

Ultrafast magnetization dynamics (femtomagnetism) Beaurepaire et al., Phys. Rev. Lett. 76, 4250 (1996). J. Vogel, Targoviste, 22/08/2011

Ultrafast magnetization dynamics (femtomagnetism) Beaurepaire et al., Bigot et al., Nature Phys. 5, 515 (2009) Phys. Rev. Lett. 76, 4250 (1996). J. Vogel, Targoviste, 22/08/2011

Ultrafast magnetization dynamics I : Initial equilibrium II : Fast demagnetization + thermalization, changing M and anisotropy III : Precession around new equilibrium M. van Kampen et al. Phys. Rev. Lett. 88, 227201 (2002). J. Vogel, Targoviste, 22/08/2011

Ultrafast magnetization dynamics A.V. Kimel et al., Nature 435, 655 (2005) J. Vogel, Targoviste, 22/08/2011

Ultrafast magnetization dynamics Magnetization reversal with one 40fs circularly polarized laser pulse C.D. Stanciu, A. Kirilyuk, Th. Rasing et al., A.V. Kimel et al., Nature 435, 655 (2005) Phys. Rev. Lett. 99, 047601 (2007) J. Vogel, Targoviste, 22/08/2011

Summary time scales 10 -15 – 10 -12 s (femto- to picosecond) Electronic processes : electron-photon interactions, exchange interaction, spin-orbit interaction, spin-flips, electron-phonon interactions 10 -12 – 10 -9 s (pico- to nanosecond) Magnetization precession, ferromagnetic resonance, spin waves 10 -9 s – ∞ Thermally acivated magnetization processes : relaxation, domain nucleation, domain wall propagation J. Vogel, Targoviste, 22/08/2011

Magnetization dynamics for applications - Permanent magnets - Transformers - Magnetic recording - Magnetic Random Access Memories - Oscillators

Applications : permanent magnets 60 480 50 400 Nd-Fe-B Sm-Fe-N metres… (BH) max [MGOe] 40 320 (BH) max [kJm -3 ] Sm-Co 30 240 hand held tools, 60 480 Steel appliances… 20 160 Alnico 50 400 Steels Ferrites Nd-Fe-B 10 80 Sm-Fe-N (BH) max [MGOe] 40 320 (BH) max [kJm -3 ] 0 Sm-Co 0 30 240 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 20 160 Alnico Steels Ferrites 10 80 0 0 ↑ (BH) max → ↓ magnet volume 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Ferrite Alnico Sm-Co Nd-Fe-B Courtesy : Nora Dempsey

Applications : permanent magnets High performance permanent magnets need to operate at T ≤ 180°C 3 180°C 2,5 2 H C < H A (anisotropy field) : improve microstructure µ 0 H c (T) 1,5 Better understanding of coercivity--> modelling 1 0,5 0 300 400 500 600 T (K) 5 µm thick NdFeB films (µ 0 H c = 2.6 T) as model systems for coercivity analysis ( Institut Néel, IFW Dresden, NIMS, U. Sheffield, Toyota Motor Corporation) J. Vogel, Targoviste, 22/08/2011