Damping of magnetization dynamics Andrei Kirilyuk � Radboud University, Institute for Molecules and Materials, Nijmegen, The Netherlands 1 ESM Cluj-Napoca - August 2015
2 ESM Cluj-Napoca - August 2015
Landau-Lifshitz equation energy gain: H eff � N torque equation: S Landau & Lifshitz, 1935 3 ESM Cluj-Napoca - August 2015
Landau-Lifshitz equation energy gain: H eff � N torque equation: S Landau & Lifshitz, 1935 3 ESM Cluj-Napoca - August 2015
Damping: Landau-Lifshitz vs Gilbert 4 ESM Cluj-Napoca - August 2015
Damping: Landau-Lifshitz vs Gilbert 4 ESM Cluj-Napoca - August 2015
Damping: Landau-Lifshitz vs Gilbert Landau-Lifshitz vs Gilbert 4 ESM Cluj-Napoca - August 2015
Damping: Landau-Lifshitz vs Gilbert Landau-Lifshitz vs Gilbert Since the second result is in agreement with the fact that a very large damping should produce a very slow motion while the first is not, one may conclude that the Landau-Lifshitz-Gilbert equation is more appropriate to describe magnetization dynamics. 4 ESM Cluj-Napoca - August 2015
To remember: magnetization = angular momentum Einstein – de Haas & Barnett effects A. Einstein & W.J. de Haas, Experimenteller Nachweis der Amperèschen Molekülströme, Verhandl. Deut. Phys. Ges. 17 , 152 (1915) S.J. Barnett, Magnetization by rotation , Phys. Rev. 6 , 239 (1915) 5 ESM Cluj-Napoca - August 2015
Angular momentum transfer and two ways of reversal usual (practical) precessional (fast) ! ! M M ! H ! H dM dM dM dM α α & # & # ( ) ( ) eff eff M H M M H M = − γ × + × = − γ × + × $ ! $ ! dt M dt dt M dt % " % " from spins to field 6 ESM Cluj-Napoca - August 2015
Angular momentum transfer and two ways of reversal usual (practical) precessional (fast) ! ! M M ! H ! H dM dM dM dM α α & # & # ( ) ( ) eff eff M H M M H M = − γ × + × = − γ × + × $ ! $ ! dt M dt dt M dt % " % " from spins to field from spins to lattice 6 ESM Cluj-Napoca - August 2015
Angular momentum transfer and two ways of reversal usual (practical) precessional (fast) ! ! M M ! H ! H dM dM dM dM α α & # & # ( ) ( ) eff eff M H M M H M = − γ × + × = − γ × + × $ ! $ ! dt M dt dt M dt % " % " from spins to field from spins to lattice 6 ESM Cluj-Napoca - August 2015
measuring the damping 7 ESM Cluj-Napoca - August 2015
measuring the damping 7 ESM Cluj-Napoca - August 2015
Example 1: thin film configuration from the condition that the net torque on M is zero: 8 ESM Cluj-Napoca - August 2015
FMR resonance 9 ESM Cluj-Napoca - August 2015
FMR resonance 9 ESM Cluj-Napoca - August 2015
FMR resonance 9 ESM Cluj-Napoca - August 2015
FMR versus applied field angle isotropic out of plane easy axis easy plane 10 ESM Cluj-Napoca - August 2015
FMR linewidth 11 ESM Cluj-Napoca - August 2015
FMR linewidth 11 ESM Cluj-Napoca - August 2015
Example 2: optical pump-probe measurement Damping in a Bi:YIG garnet film as a function of temperature pump probe 12 ESM Cluj-Napoca - August 2015
Example 2: optical pump-probe measurement Damping in a Bi:YIG 370 K garnet film as a function 380 K of temperature 390 K Faraday rotation 395 K pump 400 K probe 405 K 410 K 415 K T C 420 K 0 200 400 600 800 1000 1200 1400 Delay time (ps) 12 ESM Cluj-Napoca - August 2015
Energy flow via spin waves?? 13 ESM Cluj-Napoca - August 2015
Semi-quantitative analysis 14 ESM Cluj-Napoca - August 2015
Semi-quantitative analysis radius laser spot ~20 µ m; km v 100 ⇒ > s observed τ < 200 ps; 14 ESM Cluj-Napoca - August 2015
Semi-quantitative analysis radius laser spot ~20 µ m; km v 100 ⇒ > s observed τ < 200 ps; ω k 14 ESM Cluj-Napoca - August 2015
Semi-quantitative analysis radius laser spot ~20 µ m; km v 100 ⇒ > s observed τ < 200 ps; ω d ω v g = dk 0 ≈ k 14 ESM Cluj-Napoca - August 2015
Semi-quantitative analysis radius laser spot ~20 µ m; km v 100 ⇒ > s observed τ < 200 ps; ω d ω v g = dk 0 ≈ k Magnetostatic modes; picture from Demokritov & Hillebrands 14 ESM Cluj-Napoca - August 2015
Semi-quantitative analysis radius laser spot ~20 µ m; km v 100 ⇒ > s observed τ < 200 ps; ω d ω v g = dk 0 ≈ k Magnetostatic modes; picture from km Demokritov & Hillebrands v g 10 ≤ s 14 ESM Cluj-Napoca - August 2015
µ -magnetic simulations [Eilers et al, PRB 74, 054411 (2006)] 0 . 4 m µ km v 6 ≈ ≈ s 70 ps 15 ESM Cluj-Napoca - August 2015
Experiment: propagation of spin waves ! H J 0.5 ns, 40 Oe pulse part with T. Korn & U. Ebels, SPINTEC, Grenoble 16 ESM Cluj-Napoca - August 2015
Experiment: propagation of spin waves ! H J 0.5 ns, 40 Oe pulse part with T. Korn & U. Ebels, SPINTEC, Grenoble 16 ESM Cluj-Napoca - August 2015
Experiment: propagation of spin waves ! H J 0.5 ns, 40 Oe pulse 500 m µ part with T. Korn & U. Ebels, km v 140 ≈ ≈ SPINTEC, Grenoble s 3 . 5 ns 16 ESM Cluj-Napoca - August 2015
Conclusion 1 � not everything what you measure is damping! 17 ESM Cluj-Napoca - August 2015
Damping channels: intrinsic vs extrinsic 18 ESM Cluj-Napoca - August 2015
damping via magnetoelastic interactions breathing Fermi-surface in metals extrinsic: two-magnon scattering 19 ESM Cluj-Napoca - August 2015
damping via magnetoelastic interactions breathing Fermi-surface in metals extrinsic: two-magnon scattering 19 ESM Cluj-Napoca - August 2015
Phenomenology based on magneto-elasticity 20 ESM Cluj-Napoca - August 2015
‘Dissipative’ part of magnetic field 21 ESM Cluj-Napoca - August 2015
‘Dissipative’ part of magnetic field so that the total effective field is 21 ESM Cluj-Napoca - August 2015
Heating rate 22 ESM Cluj-Napoca - August 2015
Heating rate 22 ESM Cluj-Napoca - August 2015
Heating rate 22 ESM Cluj-Napoca - August 2015
Magnetostriction the adiabatic magnetostriction coefficients are defined as 23 ESM Cluj-Napoca - August 2015
Magnetostriction the adiabatic magnetostriction coefficients are defined as the time-varying magnetostrictive strain is then 23 ESM Cluj-Napoca - August 2015
Finally: the Gilbert damping tensor thus, a changing M produce a changing strain; the crystal viscosity tensor determines the heating rate per unit volume 24 ESM Cluj-Napoca - August 2015
Finally: the Gilbert damping tensor thus, a changing M produce a changing strain; the crystal viscosity tensor determines the heating rate per unit volume 24 ESM Cluj-Napoca - August 2015
Finally: the Gilbert damping tensor thus, a changing M produce a changing strain; the crystal viscosity tensor determines the heating rate per unit volume from this, the Gilbert damping tensor is rigorously given by 24 ESM Cluj-Napoca - August 2015
Experiments vs theory 25 ESM Cluj-Napoca - August 2015
Experiments vs theory the theoretical prediction is that 25 ESM Cluj-Napoca - August 2015
Theoretical vs measured damping parameters 26 ESM Cluj-Napoca - August 2015
Theoretical vs measured damping parameters 27 ESM Cluj-Napoca - August 2015
damping via magnetoelastic interactions breathing Fermi-surface in metals extrinsic: two-magnon scattering 28 ESM Cluj-Napoca - August 2015
damping via magnetoelastic interactions breathing Fermi-surface in metals extrinsic: two-magnon scattering 28 ESM Cluj-Napoca - August 2015
Ferromagnetism of metals 29 ESM Cluj-Napoca - August 2015
‘breathing’ Fermi-surface following Steiauf and Fähnle, PRB 72 , 0064450 (2005); see Kambersky, Can J. Phys. 48 , 2906 (1970); Kunes and Kambersky, PRB 65 , 212411 (2002) 30 ESM Cluj-Napoca - August 2015
1. Adiabatic regime we confine the treatment to the adiabatic regime: several ps to nanoseconds (single-electron spin fluctuations can be integrated out): 31 ESM Cluj-Napoca - August 2015
2. Dissipative free-energy functional the existence of such functional is postulated: 32 ESM Cluj-Napoca - August 2015
2. Dissipative free-energy functional the existence of such functional is postulated: 32 ESM Cluj-Napoca - August 2015
3. Translate this to the electronic level as outputted from the density functional theory 33 ESM Cluj-Napoca - August 2015
3. Translate this to the electronic level as outputted from the density functional theory 33 ESM Cluj-Napoca - August 2015
3. Translate this to the electronic level as outputted from the density functional theory as the total number of states is conserved 33 ESM Cluj-Napoca - August 2015
3. Translate this to the electronic level as outputted from the density functional theory as the total number of states is conserved 33 ESM Cluj-Napoca - August 2015
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