[PPT] - The Ultrafast Einstein-de Haas effect Steve Johnson Dornes et al., PowerPoint Presentation

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Steve Johnson

The Ultrafast Einstein-de Haas effect

Dornes et al., Nature 565, 209 (2019)

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Monday, January 29, 2019 Taming Nonequilibirum - ICTP

M B B

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M B B

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How does this happen dynamically?

σM =   τ3 −τ2 −τ3 τ1 τ2 −τ1  

Assume provisionally: (1) M changes “arbitrarily” fast, spatially uniform (2) dM change in a volume dV → local torque

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How does this happen dynamically?

~ f = r · M

⇒ force density non-zero only at surfaces!!

Assume provisionally: (1) M changes “arbitrarily” fast, spatially uniform (2) dM change in a volume dV → local torque

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Transverse displacement wave

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Assume provisionally: (1) M changes “arbitrarily” fast, spatially uniform (2) dM change in a volume dV → local torque

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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

scillations 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 Ni80Fe20 film deposited on a silicon nitride cantilever, g is measured to be 1.83±0.10. DOI: 10.1063/1.2355445

APPLIED PHYSICS LETTERS 89, 122502 2006

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 domain wall. Theoretical results are compared with a recent experiment on the Einstein–de Haas effect in a microcantilever. DOI: 10.1103/PhysRevB.79.104410 PACS numbers: 75.80.q, 72.55.s, 07.55.Jg PHYSICAL REVIEW B 79, 104410 2009

dM/dt limited by domain wall motion ~ 20 kHz

…assumption (1) violated!

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Ultrafast Demagnetization

§ 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? § Orbitals? § EM field? § Elsewhere in space, but still in spins? § Lattice / phonons?

Ni ) s

1996

Koopmans et al. J. Phys. Cond. Mat. 15, S723 (2003) e.g. Stamm et al. Nature Mater. 6, 740 (2007); Hennecke et al. PRL 122, 157202 (2019) “Superdiffusion” Battiato et al. PRL 105, 027203 (2010)

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Coupling of magnetism to lattice: ultrafast Einstein-de Haas effect

initial magnetisation / external field force / movement during ultrafast demagnetisation

§ Fast demagnetization → in-plane force on all surfaces with a normal not parallel to ΔM (f ∝ n x dM/dt) § Leads to a transverse strain wave from surface § Sign of force/displacement depends on sign of M

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Thin film sample

Fe (15 nm) MgAl2O4 Al (~1.5 nm) MgO (~2nm)

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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

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Coupling of magnetism to lattice: ultrafast Einstein-de Haas effect

§ 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

xit cs

erse strain

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Measurement of truncation rod

Fe (15 nm) MgAl2O4 Al (~1.5 nm) MgO (~2nm)

xit cs

erse strain

(220) truncation rod

Qz

Dornes et al., Nature 565, 209 (2019)

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Qz

§ 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)

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0.5 0.6 0.7 0.8 a) 0.5 0.6 0.7 0.8 1 2 3 4 0.5 0.6 0.7 0.8

t [ps]

2

2 10-3 b)

t [ps]

2

2 1 2 3 4

t [ps]

2

2 0.8 0.9 1 1.1 c) 0.8 0.9 1 1.1 1 2 3 4 0.8 0.9 1 1.1

t [ps]

2

2 10-3 d)

t [ps]

2

2 1 2 3 4

t [ps]

2

2

0.5 1 2 4

Experiment Simulation diffraction intensity normalised sum (Longitudinal) diffraction intensity normalised asymmetry (Transverse) qz 0.0737 qz 0.0737 qz 0.0482 qz 0.0482 qz 0.0236 qz 0.0236

M+ + M- q q qz = 0.0236 qz = 0.0482 qz = 0.0737 qz = 0.0236 qz = 0.0482 qz = 0.0737 M+ - M- (even) (odd) Experiment Simulation Dornes et al., Nature 565, 209 (2019)

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Dispersion

§ Consistency check: “odd” M oscillations vs. q agree with transverse sound velocity (3875 ± 20 m/s)

0.02 0.04 0.06 0.08

qz [r.l.u.]

2 4 6 8 10 12 14 16

Frequency [Hz]

1011 Experiment

vL = 4750 100 m/s vT = 3700 200 m/s

0.02 0.04 0.06 0.08

qz [r.l.u.]

2 4 6 8 10 12 14 16

Frequency [Hz]

1011

Simulation

vL = 5150 150 m/s vT = 3900 100 m/s

x sum x difference x sum x difference

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Quantitative analysis

§ 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

Demagnetisation time [fs] Absolute demagnetisation [%] χ2 map, fine timescale

100 140 180 220 260 300 340 380 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 620 640 660 680 700 720 740 760 780 800

Demagnetisation time [fs] Absolute demagnetisation [%] χ2 map, coarse timescale

10 25 50 100 250 500 1000 2500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 650 700 750 800 850 900 950 1000

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Mechanisms: Local vs. superdiffusion

§ Is angular momentum transferred to lattice on fast time 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

vs

YES!

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Theory…

§ Some theories predict a fast (~ 10 fs) transfer via spin-

rbit coupling / non-perpturbative coupling to phonons

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Outlook

§ All optical switching of magnetism in ferrimagnets § Demagnetization is an intermediate: role/constraints from Einstein-de Haas coupling?

[Stanciu et al. PRL 99, 047601 (2007)

1

1 2 400 800 1200

1
0.5

0.5 1 1.5

0.6

0.6

0.4

0.4

0.1

0.1

0.1

0.1

0.2

0.2

1

1 Field (T)

Delay time ∆t (ps) ∆Mz/ M

0.2 0

0.2

0.2 0

0.2

0.2

0.2

∆M / M Z

0.2

0.2 ∆t = - 1ps 0.7 ps 500 ps 0.5 ps 200 ps

∆M /M Z ∆M /M Z ∆M /M Z ∆M /M Z Field (T) Field (T) Field (T) Field (T)

& PRL 99, 217204 (2007)]

GdFeCo alloys

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§ 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

Conclusions

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Acknowledgments

ETHZ

E. Abreu
C. Dornes
V. Esposito
L. Huber*
M. Kubli
G. Lantz
M. J. Neugebauer
M. Savoini
Y. Acremann

PSI

A. Alberca
B. P. Beaud
M. Buzzi*
E. Bothschafter
H. Lemke
M. Porer
L. Rettig*
U. Staub
C. Vaz
Y. W. Windsor

SLAC/LCLS

D. Zhu
S. Song
J. M. Glownia