[PPT] - Ultrafast magnetization dynamics: U t a ast ag et at o dy a cs PowerPoint Presentation

SLIDE 1

Ultrafast magnetization dynamics: U t a ast ag et at o dy a cs the role of angular momentum

Radboud University Nijmegen The Netherlands

Andrei Kirilyuk

Radboud University Nijmegen, The Netherlands

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

1

SLIDE 2

Magnetization dynamics and switching

H M E r r ⋅ − =

energy gain:

r

N

H

torque:

T dt L d r =

S

dt

[ ]

H M T r r r × = L M r r γ =

[ ]

H M M d r r r

Landau & Lifshitz,

[ ]

H M dt × ⋅ =γ

1935

mc e g 2 ⋅ = γ

= 28 GHz/T

( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × + × − = dt dM M M H M dt dM

eff

α γ

with damping:

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

2

⎠ ⎝

SLIDE 3

Consequence 1: Inertia-free motion

[ ]

H M M d r r r × γ [

]

H M dt × ⋅ =γ

The motion happens only as long as the field is there

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 4

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)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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S. J. Barnett, Magnetization by Rotation, Physical Review 6, 239–270 (1915).

SLIDE 5

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

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

5

SLIDE 6

Angular momentum transfer and two ways of reversal

precessional (fast) usual (practical)

M r M r M

r

M

H r r H r

( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × + × − = dt dM M M H M dt dM

eff

α γ

( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × + × − = dt dM M M H M dt dM

eff

α γ

from spins to lattice from spins to field

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

6

SLIDE 7

Outline of the lecture

Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

7

SLIDE 8

Outline of the lecture

Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 9

B lli ti (i ti l) ti d i ? Ballistic (inertial) magnetic dynamics?

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 10

Consequence of the LL equation: Inertia-free motion

M d r

[ ]

H M dt M d r r × ⋅ =γ 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!

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 11

Ferromagnet and antiferromagnet

) ( H H H H ) ( ~ H H A

FM

+ γ ω

1-10 GHz

ex A AFM

H H γ ω ~

100-1000 GHz

M r

00 000 G

M

1

M

2 1

≈ + = M M m r r r

i ti

2

M r

2 1 2 1

M M l r r r − =

no inertia

Lagrangian

inertia!

Lagrangian Equation f i

f motion

A d d M h k S Ph U 23 21 (1980)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Andreev and Marchenko, Sov. Phys. Usp. 23, 21 (1980)

SLIDE 12

Magnetic phases in HoFeO3

Γ12 Γ24

12 24

x M M l x θ δϕ z M M z θ

H

y l y

δt

Γ12 Γ12 Γ24 Γ24

t

H(t)

Inertial spin motion Magnetic pulse

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 13

Inertia-driven spin reorientation in HoFeO3

0.04

b) Experiment a) Theory

0.02 1 2

eg)

σ(+)

H=+1.05HC 0.00

ation (de

H 1.05HC

0.02
1

day rota

σ(-)

H=+0.95HC

ϕ(t)

0.04

3

2

Farad

H=-1.05HC 20 40 60 80

0.06

4 4 8 12 16

4
3

T=50.5 K

Magnetic field pulse

20 40 60 80

4

4 8 12 16

Time delay (ps)

ωt/2π

Kimel et al Nature Physics 5 727 (2009)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Kimel et al., Nature Physics 5, 727 (2009)

SLIDE 14

Ultrafast reorientation in HoFeO3

40 K

σ

(+) ( )

H

x

Γ24

S1

44 K

0.03 deg

σ

(+)

σ

(−)

z

m 48 K

σ

(+)

σ

(−)

tation

δH

y

S2

48 K

σ

(−)

aday ro

δH

x z

Γ12

51 K

σ

(+)

σ

( )

Fara

σ

(+)

δT

z

m

S1 S2

(+)

σ

(−) ( )

σ(-)

T

y

2

What route is faster?

55 K

σ

(+)σ (−)

400 800 1200

T

52 K

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Time (ps)

400 800 1200

SLIDE 15

Heat driven vs field-driven dynamics

4

z-HoFeO3

48 K

Heat-driven

(b) (a)

3

Field-driven 48 K

Field- driven

MZ/M

2 %)

Heat-driven

driven

M

52 K

2

40 60 80

MZ/M (%

Heat-driven

Temperature (K)

Heat-driven ~ 400 ps Field driven 3 ps

1

M

(c)

Laser pulse ~ 0.1 ps Field-driven ~ 3 ps

Field-driven

MZ/M

400 800 1200

5 10 15

Heat-driven

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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400 800 1200

5 10 15

Time delay (ps) Time delay (ps)

SLIDE 16

Outline of the lecture

Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 17

To reverse the magnetization fast(er):

[ ]

M d r apply stronger torque

[ ]

H M dt M d r r × ⋅ =γ

r

reduce associated angular momentum

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 18

Solution: make the field stronger?

2 ps, several Teslas

d f lt f t ti ? end of ultrafast magnetism?

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 19

Any way around? y y

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 20

Ultrafast laser-induced demagnetization

thi Ni fil thin Ni film

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 21

Ultrafast laser-induced demagnetization (Ni film)

3

M

L S 2 3 + ∝

Stamm et al (2007) Beaurepaire et al (1996) Stamm et al. (2007) Beaurepaire et al. (1996)

see any difference?? see any difference??

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 22

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

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 23

Example: thermalization of Gd spins in GdFe alloy

temperature is applied as a step at t=0

T.A. Ostler et al., PRB (2011)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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, ( )

SLIDE 24

Landau-Lifshitz-Bloch equation

longitudinal relaxation transverse 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).

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 25

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?

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 26

Ferrimagnet with a compensation point(s)

T T samples in our experiments: Gd20-30%Fe65-75%Co5% TM TA RE (Gd)

MRE

M

ATM

T 500 K

SiN (5nm) AlTi (10 ) GdFeCo (20 nm) SiN (60nm)

M A

TC~500 K

AlTi (10 nm) Glass substrate

ARE A

0.3

n

'up'

TM (FeCo)

MTM

0.0

netization

Temperature

3

3

0.3

'down'

Mag

gGd < gF C

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Field (kOe)

gGd < gFeCo

SLIDE 27

GdFeCo – static measurements TM

samples by A. Tsukamoto and A. Itoh

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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p y

SLIDE 28

Ferrimagnetic resonance

Landau – Lifshitz – Gilbert equation for two sublattices:

dt dM RE

eff

H

for two sublattices:

MR

( )

[ ]

eff TM

M H M M d r r r r λ γ − × =

MR

E

( )

[ ]

( )

[ ]

eff RE RE TM TM

M H M M d M H M dt r r r r λ γ λ γ − × = × =

x

y

MTM

( )

[ ]

TM RE RE

M H M dt λ γ − × =

dt dMTM

z

( ) ( ) ( ) ( ) ( ) ( ) ( )

T A T M T M T M T M T M T

TM RE TM RE eff

= − = γ

( ) ( ) ( )

TM RE

− γ γ

eff FMR effH

ω γ = →∞

eff

α → ∞

A

T T =

if also

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 29

Dynamics of magnetization in GdFeCo. Hext = 0.29 T

Ph R B 73 220402 (2006)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Phys. Rev. B 73, 220402 (2006)

SLIDE 30

High frequency + high damping near TA

Fast switching Stop

Angular momentum compensation Angular momentum compensation is the key to increase the reversal speed

Ph R B 73 220402 (2006)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Phys. Rev. B 73, 220402 (2006)

SLIDE 31

Can this be realized in practice?

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 32

Temperature increase over Tcomp

Gd Fe Gd Mtot Fe

dynamics?

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 33

Hysteresis loops with pump laser on

Phys. Rev. Lett. 99, 217204 (2007)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 34

Laser-induced magnetization reversal

Contrast reverses in 0.7 ps Also MGd is affected by the laser pulse on a sub-ps time scale (?) pulse on a sub-ps time scale (?) Decrease of the angular g momentum does work!

Stanciu et al Phys Rev Lett 99 217204 (2007)

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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Stanciu et al, Phys. Rev. Lett. 99, 217204 (2007)

SLIDE 35

Outline of the lecture

Angular momentum gone, inertia recovered: antiferromagnets Tuning angular momentum in ferrimagnets: faster precession / switching Angular momentum conservation vs exchange interaction

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

35

SLIDE 36

To distinguish the two sublatices

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 37

XMCD contrast

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 38

Static hysteresis loops of Gd & Fe

Gd

loops of Gd & Fe

Gd Fe

Gd Gd Mtot Fe

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 39

Femto slicing (BESSY)

ptical pump – X-ray probe fs time-resolved measurements

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 40

Ultrafast dynamics of sublattices

Gd: 427±102 fs Fe: 100±23 fs

ferromagnetic GdFeCo!

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 41

Atomistic simulations

localized atomistic spin model with a Heisenberg exchange exchange parameters (Fe-Fe, Gd-Gd, and Fe-Gd) obtained by fitting static MFe,Gd(T) dependencies. stochastic term added to the effective field reversing field is present during the process

simulations by the group of R.W. Chantrell

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 42

Simulation results

ferromagnetic state reproduced!

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 43

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 44

Simulation results

ferromagnetic state reproduced!

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 45

different demagnetization times of Fe and Gd

L d L d

TM RE

r r − ≠

conservation of angular momentum FM state initiates the reversal

dt dt Gd

FM state initiates the reversal

L d L d r r Fe dt L d dt L d

TM RE

− ≈

t

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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SLIDE 46

Therefore:

angular momentum controls the switching g g different demagnetization times of the sublattices different demagnetization times of the sublattices exact compensation is not required exact compensation is not required

Andrei Kirilyuk, Targiviste – August 2011

Radboud University Nijmegen

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