Ultrafast magnetization dynamics: U t a ast ag et at o dy a cs the role of angular momentum Andrei Kirilyuk Radboud University Nijmegen The Netherlands Radboud University Nijmegen, The Netherlands Radboud University Nijmegen 1 Andrei Kirilyuk, Targiviste – August 2011
Magnetization dynamics and switching r r = − ⋅ E M H energy gain: r r N d L = torque: H T dt dt [ ] r r r r r = γ = × S M L T M H r [ [ ] ] r r d M Landau & Lifshitz, = γ ⋅ × M M H H 1935 dt e γ = ⋅ g 2 = 28 GHz/T mc ( ) α ⎛ ⎞ dM dM = − γ × + × ⎜ ⎟ eff M H M with damping: ⎝ ⎝ ⎠ ⎠ dt M dt Radboud University Nijmegen 2 Andrei Kirilyuk, Targiviste – August 2011
Consequence 1: Inertia-free motion r γ [ [ ] ] r r d M = γ ⋅ × × M M H H dt The motion happens only as long as the field is there Radboud University Nijmegen 3 Andrei Kirilyuk, Targiviste – August 2011
Consequence 2: conservation of angular momentum Einstein – de Haas effect A. Einstein & W.J. de Haas, Experimenteller Nachweis der Amperèschen Molekülströme, Verhandl. Deut. Phys. Ges. 17 , 152–170 (1915). S J Barnett Magnetization by Rotation Physical Review 6 239 270 (1915) S. J. Barnett, Magnetization by Rotation , Physical Review 6, 239–270 (1915). Radboud University Nijmegen 4 Andrei Kirilyuk, Targiviste – August 2011
Consequence 3: Precessional magnetization reversal Kaka et al, APL 80 , 2958 (2002); , , ( ); Gerrits et al, Nature 418 , 509 (2002); Schumaher et al, PRL 90 , 017201 (2003). The fastest way to reverse The fastest way to reverse the magnetization is via precession Radboud University Nijmegen 5 Andrei Kirilyuk, Targiviste – August 2011
Angular momentum transfer and two ways of reversal usual (practical) precessional (fast) r r M M M M r r H r r H ( ) α ( ) α ⎛ ⎞ ⎛ ⎞ dM dM dM dM = − γ × + × = − γ × + × ⎜ ⎟ ⎜ ⎟ eff eff M H M M H M ⎝ ⎠ ⎝ ⎠ dt M dt dt M dt from spins to field from spins to lattice Radboud University Nijmegen 6 Andrei Kirilyuk, Targiviste – August 2011
Outline of the lecture Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction Radboud University Nijmegen 7 Andrei Kirilyuk, Targiviste – August 2011
Outline of the lecture Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction Radboud University Nijmegen 8 Andrei Kirilyuk, Targiviste – August 2011
? Ballistic (inertial) magnetic dynamics? Radboud University Nijmegen i d ti ti l) Andrei Kirilyuk, Targiviste – August 2011 (i B lli ti 9
Consequence of the LL equation: Inertia-free motion r [ ] r r d d M M = γ ⋅ × M H dt dt The motion happens only as long as the field is there Inertia may appear when the angular momentum is gone! Inertia may appear when the angular momentum is gone! Radboud University Nijmegen 10 Andrei Kirilyuk, Targiviste – August 2011
Ferromagnet and antiferromagnet ω γ ω γ + ~ H H H H ~ ( ( ) ) H H A H H AFM A ex FM r r 1-10 GHz 100-1000 GHz 00 000 G M M M M 1 r r r = + ≈ m M M 0 r no inertia i ti 1 1 2 2 r r r M = − 2 l M M 1 2 inertia! Lagrangian Lagrangian Equation of motion f i A d Andreev and Marchenko, Sov. Phys. Usp. 23 , 21 (1980) d M h k S Ph U 23 21 (1980) Radboud University Nijmegen 11 Andrei Kirilyuk, Targiviste – August 2011
Magnetic phases in HoFeO 3 Γ 24 Γ 12 24 12 x x l M M M M H θ δϕ θ z z l y y Γ 12 Γ 24 Γ 12 Γ 24 δ t H(t) t Inertial Magnetic spin motion pulse Radboud University Nijmegen 12 Andrei Kirilyuk, Targiviste – August 2011
Inertia-driven spin reorientation in HoFeO 3 a) Theory b) Experiment 0.04 2 σ (+) 0.02 eg) 1 H H=+1.05H C 1.05H C ation (de 0 0.00 day rota ϕ (t) H=+0.95H C -1 σ (-) -0.02 Farad -2 H=-1.05H C -0.04 -3 3 Magnetic field T=50.5 K pulse -4 -0.06 -4 4 0 0 4 4 8 8 12 12 16 16 0 0 20 20 40 40 60 60 80 80 ω t/2 π Time delay (ps) Kimel et al Nature Physics 5 727 (2009) Kimel et al., Nature Physics 5 , 727 (2009) Radboud University Nijmegen 13 Andrei Kirilyuk, Targiviste – August 2011
Ultrafast reorientation in HoFeO 3 (+) σ 40 K H Γ 24 S 1 x σ ( ) (−) z 0.03 deg σ (+) m 44 K otation y S 2 σ (−) (+) σ σ δ H δ H aday ro 48 K 48 K Γ 12 x σ (−) ( ) Fara z z δ T σ (+) m 51 K σ S 1 (+) S 2 2 y (−) σ σ (-) (+) (+) σ (−) ( ) σ T T 52 K 55 K What route is faster? 0 0 400 400 800 800 1200 1200 Time (ps) Radboud University Nijmegen 14 Andrei Kirilyuk, Targiviste – August 2011
Heat driven vs field-driven dynamics 4 (a) z -HoFeO 3 (b) Heat-driven 48 K 48 K M Z /M Field- 3 Field-driven driven driven M 52 K %) Heat-driven Heat-driven M Z /M (% 2 2 40 60 80 Heat-driven ~ 400 ps Temperature (K) Field-driven ~ 3 ps Field driven 3 ps (c) 1 Laser pulse ~ 0.1 ps M M Z /M Field-driven 0 0 Heat-driven 0 0 400 400 800 800 1200 1200 0 0 5 5 10 10 15 15 Time delay (ps) Time delay (ps) Radboud University Nijmegen 15 Andrei Kirilyuk, Targiviste – August 2011
Outline of the lecture Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction Radboud University Nijmegen 16 Andrei Kirilyuk, Targiviste – August 2011
To reverse the magnetization fast(er): r [ [ ] ] r r d d M M = γ ⋅ × apply stronger torque M H dt or reduce associated angular momentum Radboud University Nijmegen 17 Andrei Kirilyuk, Targiviste – August 2011
Solution: make the field stronger? 2 ps, several Teslas end of ultrafast magnetism? d f lt f t ti ? Radboud University Nijmegen 18 Andrei Kirilyuk, Targiviste – August 2011
Radboud University Nijmegen Any way around? y Andrei Kirilyuk, Targiviste – August 2011 y 19
Ultrafast laser-induced demagnetization thi thin Ni film Ni fil Radboud University Nijmegen 20 Andrei Kirilyuk, Targiviste – August 2011
Ultrafast laser-induced demagnetization (Ni film) 3 3 ∝ + S L M 2 Beaurepaire et al. (1996) Beaurepaire et al (1996) Stamm et al (2007) Stamm et al. (2007) see any difference?? see any difference?? Radboud University Nijmegen 21 Andrei Kirilyuk, Targiviste – August 2011
Simple model to describe the process localized atomistic spin model with a Heisenberg exchange electron temperature is introduced electron temperature is introduced via stochastic field term exchange interaction Radboud University Nijmegen 22 Andrei Kirilyuk, Targiviste – August 2011
Example: thermalization of Gd spins in GdFe alloy temperature is applied as a step at t=0 T.A. Ostler et al., PRB (2011) , ( ) Radboud University Nijmegen 23 Andrei Kirilyuk, Targiviste – August 2011
Landau-Lifshitz-Bloch equation longitudinal transverse relaxation relaxation Assuming that the heat bath (phonons or electrons) acts much faster than the spins, the bath degrees of freedom can be averaged out. The ensemble-averaged spin polarization gives the magnetization m Garanin, Phys. Rev. B 55 , 3050 (1997). Radboud University Nijmegen 24 Andrei Kirilyuk, Targiviste – August 2011
to summarize here: laser does change M (and L) very fast laser does change M (and L) very fast but only to disorder the system can we still do something useful with it? Radboud University Nijmegen 25 Andrei Kirilyuk, Targiviste – August 2011
Ferrimagnet with a compensation point(s) samples in our experiments: Gd 20-30% Fe 65-75% Co 5% T M T T T A M RE (Gd) M RE SiN (60nm) GdFeCo (20 nm) A TM SiN (5nm) AlTi (10 nm) AlTi (10 ) T C ~500 K T 500 K M Glass substrate A A A RE 0.3 'up' n netization M TM TM (FeCo) 0.0 Mag 'down' Temperature -0.3 g Gd < g F C g Gd < g FeCo -3 0 3 Field (kOe) Radboud University Nijmegen 26 Andrei Kirilyuk, Targiviste – August 2011
Radboud University Nijmegen samples by A. Tsukamoto and A. Itoh y p GdFeCo – static measurements Andrei Kirilyuk, Targiviste – August 2011 T M 27
Ferrimagnetic resonance dM RE Landau – Lifshitz – Gilbert equation H dt eff for two sublattices: for two sublattices: r [ [ ] ] ( ( ) ) r r r d M = = γ γ × × − λ λ eff TM M M H H M M M R M R TM TM RE dt E r [ [ ] ] ( ( ) ) r r r d M = = γ γ × × − − λ λ eff RE M M H H M M RE RE TM x M TM dt y ( ) ( ) ( ) dM TM − ( ) M T M T M T γ = = dt RE TM T ( ) ( ) ( ) ( ) z ( ) ( ) eff M T M T A T − RE TM γ γ RE TM ω = γ →∞ = α → ∞ eff eff H T T also if FMR eff A Radboud University Nijmegen 28 Andrei Kirilyuk, Targiviste – August 2011
Radboud University Nijmegen Phys. Rev. B 73 , 220402 (2006) B 73 220402 (2006) Dynamics of magnetization in GdFeCo. R Ph H ext = 0.29 T Andrei Kirilyuk, Targiviste – August 2011 29
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