From magneto-optics From magneto optics to ultrafast manipulation - - PowerPoint PPT Presentation

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From magneto-optics From magneto optics to ultrafast manipulation of magnetism

Andrei Kirilyuk

Radboud University Nijmegen, The Netherlands

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Outline of the lecture

Light as a probe linear magneto optics linear magneto-optics nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 3

Outline of the lecture

Light as a probe linear magneto optics linear magneto-optics nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Optics

1.5–3.2 eV

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Why are certain wavelengths “visible”?

1 km

Transmission through water

UV X ray wave IR

1 km

X-ray Radio Microw

1 m 1 mm 1 µm 1 km 1 m 1 mm 1 µm 1 nm

visible spectrum

wavelength

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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spectrum

SLIDE 6

Optics

1.5–3.2 eV

E D r r ˆε ε = E P r r ˆε χ = r r r

• r

) ( t r k i

e E E

ω −

=

r r

r r

P E D r r r + = ε

χ ε ˆ 1 ˆ + =

2

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

6

2

n = ε

SLIDE 7

Anisotropic media

⎟ ⎞ ⎜ ⎛

xz xy xx

ε ε ε ⎟ ⎟ ⎟ ⎠ ⎜ ⎜ ⎜ ⎝ =

yz yy yx

ε ε ε ε ˆ

E r

⎟ ⎠ ⎜ ⎝

zz zy zx

ε ε ε

E r

y

E

⎞ ⎛

if H = 0

x

E

⎟ ⎟ ⎞ ⎜ ⎜ ⎛ =

xx

ε ε ε ˆ ⎟ ⎟ ⎠ ⎜ ⎜ ⎝

zz yy

ε ε ε

i.e. one could chose such a coordinate system

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Driven oscillator model t E ω sin

ω

F x dt x d m = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +

2 2 2

ω dt ⎠ ⎝

t eE F ω sin =

t E e x x d ω ω sin

2 2

= + t E m x dt ω ω sin

2

= +

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Driven oscillator model

solution in the form:

( )

e

x t r ( ) E t r

( )

t m eE t x x ω ω ω ω sin sin

2 2

− = =

( )

lit d

amplitude depends on ω

amplitude

ω

x

ω ω ω ω

°

phase

damped oscillator

°

−180 p

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Sum of the two waves:

Δz

incoming + outgoing

amplitude

( )

E E i

phase

( )

t E z E ω sin = =

phase

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Phase of the light after transmission

Δz

( )

⎟ ⎞ ⎜ ⎛ z t E E i

( )

⎟ ⎠ ⎜ ⎝ − = c t E z E ω sin

z Δ

extra time because of n:

c z n Δ − ) 1 ( ⎞ ⎛ Δ Δ

( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ − − − = c z n c z t E z E ) 1 ( sin ω

phase delay:

c z n Δ − ) 1 ( ω

z

z = 0

( )

t E E i

thus if a phase delay occurs

( )

t E z E ω sin = =

thus if a phase delay occurs, this is equivalent to the refractive index

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Absorption en refractive index

multiple resonances:

amplitude = absorption phase = refractive index

2 2

/ 2 1 Ne Ne ω ω γ −

2 2 2 2 0 0

1 2 ( ) ( / 2) 4 ( ) ( / 2)

e e

n c m m γ α ε ω ω γ ε ω ω ω γ = − = − + − +

t f d i

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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γ accounts for damping

SLIDE 13

Kramers-Kronig relations

ε ε ε i + =

( )

∞

2 1

ε ε ε i + =

ik n n + = ~

( ) ( )du

u u

∫

∞

− − =

2 2 1 2

1 2 ω ε π ω ω ε

ik n n + =

( ) ( ) d

u u u

∫

∞ 2

2 ε ω π

2 2 1

k n − = ε k 2

( ) ( ) du

u u u

∫

− =

2 2 2 1

ω ε π ω ε

nk 2

2 =

ε

real and imaginary parts are not independent!

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Dispersion of glass

ω

λ

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Optical constants of metals

Ni Au Ni Au

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Interaction of light with magnetic solids

How does magnetic field (magnetization) modify dielectric tensor? dielectric tensor?

r r

xx

⎥ ⎤ ⎢ ⎡ε

y

E D r r εε =

2

n

yy xx

= ⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ = ε ε ε

x

H=0

if isotropic

zz ⎥

⎦ ⎢ ⎣ ε

z

if isotropic

⎥ ⎥ ⎤ ⎢ ⎢ ⎡ = ? ? ? ? ? ? ε

M or H

H≠0

E r

⎥ ⎥ ⎦ ⎢ ⎢ ⎣ = ? ? ? ? ? ? ε

H≠0

E

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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How does magnetic field modify conductivity? g y y

H 0 y

⎥ ⎤ ⎢ ⎡

xx

σ

E j H=0 x

⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ =

zz yy xx

σ σ σ

E j r r σ =

E j H y x

FL=e[V×H]

Lorentz force

⎦ ⎣

zz

x

FL e[V H]

Lorentz force H E j

Ey → jx Ex → jy

j H

⎥ ⎤ ⎢ ⎡

xy xx

σ σ

E

⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ =

zz yy yx

σ σ σ σ

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Onsager principle: symmetry of kinetic coefficients symmetry of kinetic coefficients

⎥ ⎤ ⎢ ⎡

xy xx

ε ε

⎥ ⎤ ⎢ ⎡

xx

ε

⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ =

zz yy yx

ε ε ε ε

⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ =

zz yy

ε ε ε H=0 H≠0

X f W ∂ ∂

f S X

ji ij

S S =

t f t ∂ = ∂

j ij i

f S X =

X - response If S is a function of magnetic field

S (H) S (H) S ( H)

f - stimulus W - energy

Sij(H)=-Sji(H)=Sji(-H)

t D E t W ∂ ∂ = ∂ ∂

Onsager principle is applicable to ε

εij(H)=-εji(H)=εji(-H)

j ij i

E D ε =

in non-absorbing media

εij=εji*

L d & Lif hi Th i l Ph i 5 d 8

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Landau & Lifshitz, Theoretical Physics, vv. 5 and 8.

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Faraday effect – 1

⎞ ⎛

Isotropic medium in a magnetic field:

⎟ ⎟ ⎟ ⎞ ⎜ ⎜ ⎜ ⎛ − =

xy xy

i i ε ε ε ε ε ˆ

z xy

M ∝ ε

⎟ ⎟ ⎠ ⎜ ⎜ ⎝ +

zz xy

ε ε 0

2 z zz

M ∝ ε

H H r r =

E r

y x in

E j E i E r r r + =

z

H H =

in

E r

• ut

E

x

??? =

• ut

E r

y z

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Faraday effect – 2

E i ⎞ ⎛ ⎞ ⎛

To find the eigenvalues of the problem:

E n E E i i E D

y x xy xy

r r r

2

ˆ = ⎟ ⎟ ⎟ ⎞ ⎜ ⎜ ⎜ ⎛ ⎟ ⎟ ⎟ ⎞ ⎜ ⎜ ⎜ ⎛ − = = ε ε ε ε ε

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −

y x y x xy xy

E E n E E i i

2

ε ε ε ε

⎟ ⎠ ⎜ ⎝ ⎟ ⎠ ⎜ ⎝ ε

⎠ ⎝ ⎠ ⎝ ⎠ ⎝

y y xy

2 2

= − − − n i i n

xy

ε ε ε ε

⇒

2

1 ε ε ε

xy

n ± =

n i

xy

ε ε

2 1 ε ε ε

xy

n ± ≅

4 3

10 10 ~

− − − xy

ε

y x

iE E ± =

⎟ ⎟ ⎞ ⎜ ⎜ ⎛1 ⎟ ⎟ ⎞ ⎜ ⎜ ⎛ 1

eigenmodes and ,

• r

y x

iE E ±

⎟ ⎟ ⎠ ⎜ ⎜ ⎝i ⎟ ⎟ ⎠ ⎜ ⎜ ⎝−i

g and , or

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Faraday effect – 3

1 ε xy

y x

iE E ± =

Two circularly polarized waves ith diff t f ti i di

2 1 ε ε

xy

n ± ≅

±

with different refractive indices:

r

−

E

+

E

• ut

E r

in

E r

−

E

+

E

l

F

α

=

+ +

=

F

2 ε πl

Faraday rotation:

2 ε ε λ π α

xy F

l =

• M. Faraday, On the magnetization of light and the illumination of magnetic

lines of force, Phil. Trans. R. Soc. Lond. 136, 104 (1846).

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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f f ( )

SLIDE 22

Kerr effect: various geometries

θ θ θ θ θ

M r M r M r H r

• >>

θ

• ≈

θ

• >>

θ polar longitudinal transverse

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Magnetic linear birefringence

r r

light propagates along x axis, so that

z y in

E k E j E r r r + =

z

H

x y ⎟ ⎟ ⎞ ⎜ ⎜ ⎛ − =

xy

i i ε ε ε ε ε ˆ y ⎟ ⎟ ⎠ ⎜ ⎜ ⎝ + =

zz xy

i ε ε ε ε ε

2

zz

ε ε + , ε

Eigenvalues

2

M

zz ∝

ε

Eigenmodes

z y E

E r r ,

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 24

• rbits

light wave spins

• rbits

light wave spins

exchange + spin-orbit

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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What could be measured?

0.3

(deg)

'up' 0.0

tization" (

B i l PRL 76 4250 (1996)

• 3

3

• 0.3

'down'

"Magnet

Beaurepaire et al, PRL 76, 4250 (1996).

3 3

Field (kOe)

dynamics hysteresis

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

25

dynamics hysteresis

SLIDE 26

Outline of the lecture

Light as a probe linear magneto optics linear magneto-optics nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

26

SLIDE 27

Electromagnetic wave equation and source term

E r r r ∂

2 2 2 2P

∂ r r

2 2

ˆ Q M P ∂ ∂ ∂ r r r S E c t E = ∇ ⋅ − ∂ ∂

2 2 2 2

t P S ∂ ∂ = r

2 2

t Q t M t P S ∂ ∂ ∇ − ∂ ∂ × ∇ + ∂ ∂ =

ω ωE

E

d ) 1 (

1 Φ

( )

) , 1 ( ) , 1 ( ) , 1 ( ω ω ω ω ω ω

χ χ χ E E H E E E

d m d

∇ + + − = Φ

ω ω

χ E E

d ) , 1 (

• r

2 − = Φ

( )

• r

, ... 1

ω ω ω

γ β α E H E + ∇ + + + ×

ω ω

χ E P

d ) , 1 (

• r

= Φ ∂ − =

E r

• r

) , 1 ( ) , 1 ( ) , 1 ( ... ω ω ω ω

χ χ χ E H E P

q m d

+ ∇ + + = χ E ∂ ...

) , 2 ( ) , 2 ( ) , 2 ( ω ω ω ω ω ω

χ χ χ E E H E E E

q m d

∇ + + +

electric dipole approximation magnetic dipole electric quadrupole

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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magnetic dipole electric quadrupole

SLIDE 28

Harmonic oscillator

U(x)

(L)

Linear response U(x) P(L) x E

2 1

) ( x k x U = k x dU F ) (

1

) ( x k x U kx dx Fel = = ) (

2

E F x e dt d m

el =

+

2 2

) ( ) ( ) (

) (

ω ω χ ω

j ij L i

E P =

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Linear vs nonlinear optics?

Linearity in optics:

• Properties of a medium do not depend on light intensity
• Properties of a medium do not depend on light intensity
• Principle of superposition holds
• Frequency of light is not altered by its passage through the medium
• Frequency of light is not altered by its passage through the medium
• Light does not interact with light. A control of light by light is impossible.

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Nonlinear oscillator

Anharmonism

) ( ) ( NL L

P P P + = P(NL) U(x)

2ω + DC

E x

ω

3 2 2 1

) ( x k x k x U + =

ω

) ( ) ( ) 2 ( ) 2 (

) (

ω ω ω χ ω

NL

E E P =

2 2 1

3 2 ) ( x k x k dx x dU Fel + = =

) ( ) ( ) ( ) (

) (

ω ω χ

k j ijk NL i

E E P =

) ( ) ( ) 2 ( ) 2 ( ω ω ω χ ω

k j ijk i

E E P =

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 31

Nonlinear polarization and symmetry

( )

...

) 2 ( ) 1 (

+ ⋅ + ⋅ ∝

ω ω ω

χ χ ω E E E P

(electric dipole approximation)

t i

e ω

t i t i t i

e e e

ω ω ω 2

= ⋅

second-harmonic generation

t i t i t i

e e e

⋅ −

= ⋅

ω ω

• ptical rectification

inversion symmetry:

( ) ( )

ω ω

χ ω E E P ⋅ ∝

) 2 (

2

−1 −1 −1 1 1 1

( )

2 ≡ ω P(

)

except at surface/interface

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Magnetization-sensitive SHG

( )

) ( ) ( 2 ω ω ω

χ

k j ijk i

E E P =

( )

) ( ) ( ) ( ) ( ω ω

χ χ

k j m ijk cr ijk

E E ± =

crystallographic ± magnetic

space inversion:

g

P E r r , H M r r ,

p

polar vector axial vector

time reversal:

vector vector

time reversal:

i d R.R. Birss, Symmetry and Magnetism (North-Holland, Amsterdam, 1966).

• A. Kirilyuk and Th. Rasing,
• J. Opt. Soc. Am. B 22, 148 (2005)

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 33

Example: surface/interface sensitivity

ultrathin Co/Cu(001) films

t

Fe(110) surface

C (001) Co (x ML)

ast (%) total mag

Cu(001)

tic contra gnetizatio G magnet

• n (arb. u

SHG units)

at 4 ML, both interfaces are formed

• Phys. Rev. Lett. 74, 1462 (1995);
• J. Phys. D – Appl. Phys. 35, R189 (2002)

Reif et al, Phys. Rev. Lett. 67, 2878 (1991)

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 34

General phenomenology

... : :

) 3 ( ) 2 ( ) 1 (

+ + + ⋅ ∝ E E E E E E P r r r r r r r χ χ χ χ χ χ

( )

[ ]

3 ) ( mmm mem mee nl

r r r r r r r r r

( )

[ ]

3 ) (

, : : : H E

• H

H H E E E P

emm eem eee nl

r r r r r r r r r + + + ∝ χ χ χ

( )

[ ]

3 ) (

, : : : H E

• H

H H E E E M

mmm mem mee nl

+ + + ∝ χ χ χ

( )

[ ]

3 ) (

, : : : ˆ H E

• H

H H E E E Q

qmm qem qee nl

r r r r r r r r + + + ∝ χ χ χ

( )

[ ]

, Q χ χ χ

Source term:

sum- and difference frequency generation, including SHG and including SHG and

• ptical rectification

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 35

Outline of the lecture

• Light as a probe

linear magneto optics

• linear magneto-optics

nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

35

SLIDE 36

Outline of the lecture

Light as a probe linear magneto optics linear magneto-optics nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

36

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E i t l k h Experimental know-how: time-resolved pump-probe setup time resolved pump probe setup

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

37

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What you need: a femtosecond laser

Model Model Model TISSA20 TISSA50 TISSA100 Pump Power1) 3-5 W 3-7 W 5-10 W Output Power at 800 nm 150 - 250 mW 150-500 mW >10% efficiency Pulse Duration2) <20 fs 3) < 50 fs <100 fs Pulse Duration2) <20 fs 3) < 50 fs <100 fs Tuning Range 800 ± 20 nm 740 - 950 nm4) 720 - 980 nm4)

Interferometric autocorrelation function

Repetition Rate 70 - 140 MHz

te e o et c autoco e at o u ct o

• f 16 fs pulse obtained with external

group velocity dispersion compensation

you have some choice!

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

38

you have some choice!

SLIDE 39

pump & probe technique: stroboscopic, needs repeatable process! needs repeatable process!

time base pump adjustable delay delay probe

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 40

Stroboscopic magneto-optical pump-probe measurements

Ti:Sapphire 1 KHz 100 fs 805 nm 100 fs, 805 nm

delay τ delay τ

Delay line 0 1 μm = 0 7 fs

delay τ

Polarization change

( )

r

0.1 μm = 0.7 fs

• f the probe beam

is detected

( )

τ M ∝

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Optical pump-probe measurements of FMR

before pump pulse arrives after pump has arrived external field

s ani ext eff

H H H H r r r r + + =

Pump pulse affected by the laser

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

41

SLIDE 42

All-optical magnetic resonance in antiferromagnets

175 K, 433 GHz (x6)

1.0

u n i t s )

0.7

1

un.)

Z

δM

155 K, 406 GHz (x6) 135 K, 372 GHz (x3)

0.5

A m p l i t u d e ( a r b . u

0 5 0.6

0.01 0.1

plitudes (arb. u

Z Y X

δM

115 K, 327 GHz (x3) 95 K, 271 GHz (x3)

25 50 75 0.0

A Pulse fluence (mJ/cm

2)

0.4 0.5

(deg)

450

20 50 80 110 140 170

Amp Temperature (K)

Y X

k

σ

+

quasi-FM mode

z)

75 K, 211 GHz 60 K, 175 GHz

0.3

y rotation

300

Z

ncy (GHz

, 50 K, 159 GHz 40K 153 GH z

0.2

Faraday

δM S2

Y Z

k S1

quasi-AFM mode

Frequen

40 K, 153 GH z 30 K, 151 GHz 18K 151 GH

0.1

150 25 50 75 100 125 150 175

Y

k

σ

+

X

18 K, 151 GH z

50 100 150 200 250 300 0.0

25 50 75 100 125 150 175

Temperature (K)

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

42

Time delay (ps)

SLIDE 43

Outline of the lecture

Light as a probe linear magneto optics linear magneto-optics nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

43

SLIDE 44

Effects of the laser pulse: classification

• I. Thermal effects:

change of M is a result of change of T change of M is a result of change of T

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 45

Thermal laser-induced effects

ultrafast phase transitions

excitation and study

• f spin waves

laser-induced collapse of magnetization

Tex

ex 1

T S ×

S1 Tex Tex S2

A 1

H S ×

A 2

H S ×

Ju et al., PRL 82, 3705 (1999) van Kampen et al, PRL 88, 227201 (2002) Beaurepaire et al, PRL 76, 4250 (1996) Kimel et al., Nature 429, 850 (2004) Ju et al, PRL 93, 197403 (2004) Thiele et al, APL 85, 2857 (2004)

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

45

, , ( )

SLIDE 46

Effects of the laser pulse: classification

I. Thermal effects: change of M is a result of change of T change of M is a result of change of T

• II. Nonthermal photo-magnetic effects:

based on photon absorption

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 47

Photo-magnetic effects: modification of anisotropy

polarization-dependent polarization-dependent effect => nonthermal!

Hansteen et al., PRL 95, 047402 (2005);

• Phys. Rev. B 73, 014421 (2006).

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 48

Circular polarization, photon spin, and absorption

1 S

1 + =

z

S

2 1 =

z

S

1 − =

z

S

1 2 1 − =

z

S

1 h t / it 20000 K ΔT very fast and easy? ~0.01 phot/site max 1 photon / site = 20000 K ΔT ff 10 4 p ≤0.01 efficiency effect ≤ 10-4

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 49

Effects of the laser pulse: classification

I. Thermal effects: change of M is a result of change of T change of M is a result of change of T

• II. Nonthermal photo-magnetic effects:

based on photon absorption III N th l t ti ff t

• III. Nonthermal opto-magnetic effects:

do not require absorption

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 50

Extended introduction in laser-induced dynamics

everything you ever wanted to know about everything you ever wanted to know about laser-induced magnetization dynamics...

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 51

Thermodynamics of magneto-optics

( ) ( )

ω ω εε

*

E E = Φ

( ) ( ) ( ) ( )

E E H ∂ − = Φ ∂ − = ε ω ω ε

*

1

σ

+

( ) ( ) ( ) ( ) M

E E M H ∂ ∂ ω ω μ μ

σ

−

σ

⎞ ⎛

δH

+

δH

−

( )⎟

⎟ ⎟ ⎞ ⎜ ⎜ ⎜ ⎛ + − = ˆ M i M i

yy xx

ε α α ε ε

Inverse Faraday effect

δH δH

( )⎟

⎠ ⎜ ⎝ +

2

M O

zz

ε

( ) ( ) ( )

[ ]

ω ω α ε

*

E E H r r r × =

( ) ( ) ( )

[ ]

μ0

Pitaevskii, Sov. Phys. JETP 12, 1008 (1961). van der Ziel Phys. Rev. Lett. 15, 190 (1965).

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 52

Faraday effect Inverse

F d t ti

2 α π θ M l =

Faraday rotation:

ε λ θF =

no absorption required!

( ) ( ) ( )

[ ]

ω ω α ε

*

E E H r r r × =

no angular momentum transfer!

( ) ( ) ( )

[ ]

μ0

−

E

+

E

in

E r

−

E

+

E

l

• ut

E r + +

= =

F

α

H r

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

52

H

SLIDE 53

Effect for opposite pulse helicities

it works!!!

i l t t 100 f equivalent to a 100 fs magnetic field pulse of some 0.5–1 Tesla!

[ ]

ε

( ) ( ) ( )

[ ]

ω ω α μ ε

*

E E H r r r × =

100 1 . ~ −

IFE

H

Tesla

Hansteen et al., PRL 95, 047402 (2005);

• Phys. Rev. B 73, 014421 (2006).

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

53

y , ( )

SLIDE 54

Works everywhere! (almost)

+ 1.0

σ

+

(deg.)

σ

−

σ

+

0.2

• b. units)

σ

tation (

δM

+

0.1

δM

−

0.5

plitude (ar

day rot

25 50 75 0.0

Amp

DyFeO T = 95 K

3

σ

−

Farad

0.0

25 50 75

Pulse fluence (mJ/cm

2)

T = 95 K

σ

15 30 45 60

Time delay (ps)

( ) ( ) ( )

[ ]

ω ω α ε

*

E E H r r r × =

Time delay (ps)

( ) ( ) ( )

[ ]

ω ω α μ0 E E H

Kimel et al., Nature 435, 655 (2005)

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 55

Microscopic mechanism of the inverse Faraday effect

Stimulated Raman scattering on magnons (2 h t )

[Shen et al, Phys. Rev. (1966)]

(2-photon process)

L=1 Number of photons is conserved hω2 hω2 hω1 h(ω1−Ω) Process can be fast

τ ~ 1 / ω ~ 1 fs

L=0

hΩ light helicity (= angular momentum) is also conserved!

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 56

Manipulating pulse frequencies

picture courtesy Th.Baumert

Amplitudes and phases

• f 320 components
• f 320 components

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 57

Opto-magnetic effect with “shaped” pulse

ΩAFMR ΩAFMR

AFMR

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 58

Outline of the lecture

Light as a probe linear magneto optics linear magneto-optics nonlinear (magneto-)optics Example: all-optical FMR Light as an excitation classification of effects classification of effects basics of opto-magnetism coherent control local control of spins p can this become too-ultrafast?

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 59

Higher frequency component?

• A. Reid et al.,
• Phys. Rev. Lett. 105, 107402 (2010).

Hi h f High frequency: 650 GHz Phase change with pump helicity. p p y

Kaplan–Kittel exchange resonance

• J. Kaplan and C. Kittel, J. Chem Phys. 21 760-761 (1953).

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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p , y ( )

SLIDE 60

Garnet structure [Lu1.69Y0.65Bi0.66](Fe3.85Ga1.15)O12

“d”–sites ferrimagnetic ferrimagnetic

• rder

“a”–sites different local environment!

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 61

Exchange Resonance

Shouldn’t be able to see it. Neither OM nor MO necessarily correlate with M.

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 62

Correlation with the IFE

• A. Reid et al.,
• Phys. Rev. Lett. 105, 107402 (2010).

The same spectral dependence

locally driven spin dynamics!

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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locally driven spin dynamics!

SLIDE 63

Outline of the lecture

• Light as a probe

linear magneto optics

• linear magneto-optics

nonlinear (magneto-)optics

• Example: all-optical FMR
• Light as an excitation

classification of effects

• classification of effects

basics of opto-magnetism

• coherent control

local control of spins

• p

can this become too-ultrafast?

• Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

63

SLIDE 64

Transient magneto-optical response

Transient complex (Kerr or Faraday) rotation

( ) ( ) ( ) ( )

t M t F t G t + = θ ~

( ) ( ) ( ) ( )

t M F t F M t G t

T

Δ + Δ + Δ = Δ ~ θ

Pump-induced change

( ) ( )

t M F G t ~ + = θ

( ) ( )

G G F t F ≡

If, by some chance , then

( ) ( ) ( )

G t G ≡

( ) ( ) ( )

, y , then

( ) ( ) ( )

M t M t t Δ = Δ = Δ ε ε θ θ

and

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 65

( ) ( ) ( )

t M t t Δ Δ Δ ε θ( )

( ) ( )

M t M t t Δ = Δ = Δ ε ε θ θ

system out of equilibrium system out of equilibrium

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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SLIDE 66

Optical effects?

nonmagnetic magnetic magnetic

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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Messages to take home

not everything you measure is magnetization t ti ff t l d t l h

• pto-magnetic effects lead to real change
• f M during the pulse

it is a challenge to show whether there is an

• ther nonthermal mechanism to do this!

any other nonthermal mechanism to do this!

Andrei Kirilyuk, Targoviste – August 2011

Radboud University Nijmegen

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