The Ultrafast Einstein-de Haas effect Steve Johnson Dornes et al., Nature 565, 209 (2019)
B B M Monday, January 29, 2019 Taming Nonequilibirum - ICTP
B B M Monday, January 29, 2019 Taming Nonequilibirum - ICTP
How does this happen dynamically? Assume provisionally: (1) M changes “arbitrarily” fast, spatially uniform (2) dM change in a volume dV → local torque 0 τ 3 − τ 2 0 σ M = − τ 3 τ 1 0 τ 2 − τ 1 Monday, January 29, 2019 Taming Nonequilibirum - ICTP
How does this happen dynamically? Assume provisionally: (1) M changes “arbitrarily” fast, spatially uniform (2) dM change in a volume dV → local torque ~ f = r · � M ⇒ force density non-zero only at surfaces!! Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Transverse displacement wave Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Assume provisionally: (1) M changes “arbitrarily” fast, spatially uniform (2) dM change in a volume dV → local torque Monday, January 29, 2019 Taming Nonequilibirum - ICTP
APPLIED PHYSICS LETTERS 89 , 122502 � 2006 � Einstein–de Haas effect in a NiFe film deposited on a microcantilever T. M. Wallis, a � J. Moreland, and P. Kabos National Institute of Standards and Technology, Boulder, Colorado 80305 � Received 31 May 2006; accepted 27 July 2006; published online 18 September 2006 � A method is presented for determining the magnetomechanical ratio g � in a thin ferromagnetic film deposited on a microcantilever via measurement of the Einstein–de Haas effect. An alternating magnetic field applied in the plane of the cantilever and perpendicular to its length induces bending oscillations of the cantilever that are measured with a fiber optic interferometer. Measurement of g � provides complementary information about the g factor in ferromagnetic films that is not directly available from other characterization techniques. For a 50 nm Ni 80 Fe 20 film deposited on a silicon nitride cantilever, g � is measured to be 1.83±0.10. � DOI: 10.1063/1.2355445 � PHYSICAL REVIEW B 79 , 104410 � 2009 � Dynamics of the Einstein–de Haas effect: Application to a magnetic cantilever Reem Jaafar, E. M. Chudnovsky, and D. A. Garanin Department of Physics, Lehman College, City University of New York, 250 Bedford Park Boulevard West, Bronx, New York 10468-1589, USA � Received 17 November 2008; revised manuscript received 26 January 2009; published 11 March 2009 � The local time-dependent theory of Einstein–de Haas effect is developed. We begin with microscopic interactions and derive dynamical equations that couple elastic deformations with internal twists due to spins. The theory is applied to the description of the motion of a magnetic cantilever caused by the oscillation of the dM/dt limited by domain domain wall. Theoretical results are compared with a recent experiment on the Einstein–de Haas effect in a wall motion microcantilever. PACS number � s � : 75.80. � q, 72.55. � s, 07.55.Jg DOI: 10.1103/PhysRevB.79.104410 ~ 20 kHz … assumption (1) violated! Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Ultrafast Demagnetization Ni ) 1996 s § Intense fs laser excitation of Ni → fast drop in magnetization § Subsequently seen in Fe, Co, alloys § Significant drop in M over ~ 10-30 fs § Where does the angular momentum go? e.g. Stamm et al. Nature Mater. 6, 740 (2007); § Orbitals? Hennecke et al. PRL 122, 157202 (2019) § EM field? Koopmans et al. J. Phys. Cond. Mat. 15, S723 (2003) “Superdiffusion” § Elsewhere in space, but still in spins? Battiato et al. § Lattice / phonons? PRL 105, 027203 (2010) Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Coupling of magnetism to lattice: ultrafast Einstein-de Haas effect force / movement during ultrafast demagnetisation initial magnetisation / external field § Fast demagnetization → in-plane force on all surfaces with a normal not parallel to Δ M (f ∝ n x dM/dt) § Leads to a transverse strain wave from surface § Sign of force/displacement depends on sign of M Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Thin film sample Al (~1.5 nm) MgO (~2nm) Fe (15 nm) MgAl 2 O 4 Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Simulated transverse strain dynamics Simulated atomic displacements (atomistic model, Born-von Karman) peak strain ~ 1.2 x 10 -4 (assumes all lost angular momentum goes to lattice) … a tiny change!! compare to longitudinal strain from heating, up to ~ 1 x 10 -2 Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Coupling of magnetism to lattice: ultrafast Einstein-de Haas effect erse strain xit cs § Can see transverse strain by x-ray diffraction § Look at a crystal truncation rod (CTR) of an in- plane reflection § Position along CTR selects momentum § Coherent strain gives oscillating intensity contribution, sign depends on sign of M Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Measurement of truncation rod Al (~1.5 nm) MgO (~2nm) Fe (15 nm) MgAl 2 O 4 erse strain xit Q z cs Dornes et al., Nature 565, 209 (2019) (220) truncation rod Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Q z § Pump-probe for time resolution § Pulser + electromagnet sets +/- M § Sort data by polarity § M + + M - : “even” effects (heat, magnetostriction) § M + - M - : “odd” effects (EdH transverse strain) Dornes et al., Nature 565, 209 (2019) Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Experiment Simulation Experiment Simulation a) c) 0.8 1.1 q z 0.7 1 diffraction intensity normalised sum q z = 0.0737 0.0737 0.6 0.9 0.5 0.8 0.8 1.1 (Longitudinal) 1 q z 0.7 1 q z = 0.0482 q 0.5 0 2 4 0.0482 M + + M - 0.6 0.9 0.5 0.8 (even) 0.8 1.1 q z q z = 0.0236 0.7 1 0.0236 0.6 0.9 0.5 0.8 1 2 3 4 1 2 3 4 10 -3 10 -3 b) d) diffraction intensity normalised asymmetry 2 2 q z q z = 0.0737 0 0 0.0737 -2 -2 (Transverse) t [ps] t [ps] 2 2 M + - M - q q z = 0.0482 q z 0 0 0.0482 (odd) -2 -2 t [ps] t [ps] 2 2 q z = 0.0236 q z 0 0 0.0236 -2 -2 0 1 2 3 4 0 1 2 3 4 t [ps] t [ps] Dornes et al., Nature 565, 209 (2019) Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Dispersion 10 11 Experiment 10 11 Simulation 16 16 x sum x sum 14 14 x difference x difference 12 12 Frequency [Hz] Frequency [Hz] v L = 4750 100 m/s v L = 5150 150 m/s 10 10 8 8 6 6 4 4 v T = 3700 200 m/s v T = 3900 100 m/s 2 2 0 0 0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08 q z [r.l.u.] q z [r.l.u.] § Consistency check: “odd” M oscillations vs. q agree with transverse sound velocity (3875 ± 20 m/s) Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Quantitative analysis χ 2 map, coarse timescale χ 2 map, fine timescale 1000 800 0 0 1 1 2 2 780 3 3 950 4 4 5 5 6 6 760 7 7 900 Absolute demagnetisation [%] Absolute demagnetisation [%] 8 8 9 9 740 10 10 11 11 850 12 12 720 13 13 14 14 15 15 800 700 16 16 17 17 18 18 19 19 680 750 20 20 21 21 22 22 660 23 23 700 24 24 25 25 640 26 26 27 27 650 28 28 620 29 29 30 30 10 25 50 100 250 500 1000 2500 100 140 180 220 260 300 340 380 Demagnetisation time [fs] Demagnetisation time [fs] § Best fit of simulation to data consistent with 200 fs time scale of torque, 80% of lost angular momentum § Large uncertainties, could easily be any time scale below 300 fs and as much as 100% § Limited mostly by S/N at high wavevectors Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Mechanisms: Local vs. superdiffusion vs § Is angular momentum transferred to lattice on fast time YES ! scales? § Appears as a coherent strain wave in < 0.3 ps § Outstanding question: how does it get there? § Via incoherent phonons? § More direct path? § Needs better time & q resolution Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Theory … § Some theories predict a fast (~ 10 fs) transfer via spin- orbit coupling / non-perpturbative coupling to phonons Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Outlook 1.5 ∆ t = - 1ps 1 ∆ M /M 0.7 ps Z 1 0 0.1 ∆ M /M -1 Z 0 -0.2 0 0.2 500 ps 0.5 Field (T) 0.6 ∆ M z / M -0.1 ∆ M /M -0.2 0 0.2 Z 0 Field (T) 0 -0.6 -0.2 0 0.2 0.5 ps 200 ps Field (T) 0.4 -0.5 ∆ M /M 0.1 ∆ M / M Z Z 0 0 -0.1 -1 -0.4 [Stanciu et al. PRL 99, 047601 (2007) -0.2 0 0.2 -0.2 0 0.2 Field (T) Field (T) -1 0 1 2 400 800 1200 Delay time ∆ t (ps) & PRL 99, 217204 (2007)] GdFeCo alloys § All optical switching of magnetism in ferrimagnets § Demagnetization is an intermediate: role/constraints from Einstein-de Haas coupling? Monday, January 29, 2019 Taming Nonequilibirum - ICTP
Conclusions § Experimental evidence for a coupling of dM/dt to antisymmetric stress in response to strong electronic excitation § Not magnetostriction (odd in M, depends on dM/dt not M) § Makes transverse strain wave propagating from interfaces § May play a role in ultrafast switching of ferrimagnets Monday, January 29, 2019 Taming Nonequilibirum - ICTP
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