From magnetoFrom magneto-optics to ultrafast manipulation of...

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From magneto-opticsFrom magneto optics to ultrafast manipulation of magnetism

Andrei KirilyukRadboud University Nijmegen, The Netherlands

Andrei Kirilyuk, Targoviste – August 2011 Radboud University Nijmegen1

Outline of the lecture

Light as a probelinear magneto opticslinear magneto-opticsnonlinear (magneto-)optics

Example: all-optical FMR

Light as an excitationclassification of effectsclassification of effectsbasics of opto-magnetismcoherent controllocal control of spinsp

can this become too-ultrafast?

Optics

1.5–3.2 eV

Why are certain wavelengths “visible”?

Transmission through water

UVX rayw

ave IR

Radio Mic

row1 m

1 km 1 m 1 mm 1 µm 1 nm

visiblespectrum

wavelength

spectrum

Optics

1.5–3.2 eV

0ε̂ε= EPrr

0ˆεχ=rrr

trkieEE ω−=rrrr PED

rrr+= 0ε χε ˆ1ˆ +=

Anisotropic media

⎟⎞

⎜⎛ xzxyxx εεε

⎟⎟⎟

⎠⎜⎜⎜

= yzyyyx εεεε̂

⎟⎠

⎜⎝ zzzyzx εεε

⎞⎛ 00if H = 0

⎟⎟⎞

⎜⎜⎛

ε 0000

ˆ⎟⎟

⎠⎜⎜

⎝ zz

εεε00

i.e. one could chose such a coordinate system

Driven oscillator model

tE ωsin0

xdm =⎟⎟⎠

⎞⎜⎜⎝

⎛+ 2

ωdt ⎠⎝

teEF ωsin0=

tEexxd ωω sin22

=+ tEm

ωω sin002 =+

Driven oscillator model

solution in the form:

( )ex tr( )E tr

( ) tm

eEtxx ωωω

ω sinsin 220

00 −

== ( )

lit damplitude depends on ω amplitude

0x0ω ω

°0phase

damped oscillator

°−180

Sum of the two waves:

Δz incoming + outgoing

amplitude

( ) EE i0 phase( ) tEzE ωsin0 0== phase

Phase of the light after transmission

( ) ⎟⎞

⎜⎛ ztEE i( ) ⎟

⎠⎜⎝

tEzE ωsin0

zΔextra time because of n:czn Δ

− )1(

⎞⎛ Δ

( ) ⎟⎠⎞

⎜⎝⎛ Δ

−−−=czn

cztEzE )1(sin0 ω

phase delay:czn Δ

− )1(ω

zz = 0

( ) tEE i0 thus if a phase delay occurs( ) tEzE ωsin0 0== thus if a phase delay occurs,this is equivalent to the refractive index

Absorption en refractive index

multiple resonances:

amplitude = absorption

phase = refractive index

2 20/ 2 1Ne Ne ω ωγ −0

2 2 2 20 0 0 0 0

12 ( ) ( / 2) 4 ( ) ( / 2)e e

nc m m

γαε ω ω γ ε ω ω ω γ

= − =− + − +

t f d i

γ accounts for damping

Kramers-Kronig relations

εεε i+= ( )∞21 εεε i+=

iknn +=~ ( ) ( )duu

u∫∞

−−

πωωε

iknn +=

( ) ( ) duu

∫∞

221 kn −=ε

( ) ( ) duu

uu∫ −

1 ωε

πωε

nk22 =ε

real and imaginary parts are not independent!

Dispersion of glass

Optical constants of metals

Ni AuNi Au

Interaction of light with magnetic solids How does magnetic field (magnetization) modify dielectric tensor?dielectric tensor?

00xx⎥⎤

⎢⎡ε

y EDrr

0εε=

0000 nyy

=⎥⎥⎥

⎦⎢⎢⎢

εεx H=0if isotropic00 zz ⎥⎦⎢⎣ ε

if isotropic

⎥⎥⎤

⎢⎢⎡

= ??????

εM or H

H≠0Er

⎥⎥⎦⎢

⎢⎣

=??????εH≠0E

How does magnetic field modify conductivity?g y y

⎥⎤

⎢⎡ xxσ 00

E j H=0

x ⎥⎥⎥

⎦⎢⎢⎢

σσσ00

00 Ejrr

E j Hy

FL=e[V×H] Lorentz force

⎦⎣ zz

FL e[V H] Lorentz force

jEy → jxEx → jy

j H ⎥⎤

⎢⎡ xyxx σσ

E ⎥⎥⎥

⎦⎢⎢⎢

σσσσ00

Onsager principle:symmetry of kinetic coefficientssymmetry of kinetic coefficients

⎥⎤

⎢⎡ xyxx εε 0

⎥⎤

⎢⎡ xxε 00

⎥⎥⎥

⎦⎢⎢⎢

εεεε00

0⎥⎥⎥

⎦⎢⎢⎢

εεε00

00H=0 H≠0

XfW ∂∂fSXjiij SS =

t ∂=

∂jiji fSX =

X - responseIf S is a function of magnetic field

S (H) S (H) S ( H)f - stimulusW - energy

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

∂∂

∂ Onsager principleis applicable to ε

εij(H)=-εji(H)=εji(-H)jiji ED ε=

in non-absorbing media εij=εji*

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

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

Faraday effect – 1

⎞⎛

Isotropic medium in a magnetic field:

⎟⎟⎟⎞

⎜⎜⎜⎛ −

iiεεεε

ˆzxy M∝ε

⎟⎟

⎠⎜⎜

⎝ + zz

εε 0

00 2zzz M∝ε

= Eryxin EjEiE

zHH =inEr outE

x ???=outEr

Ei 0 ⎞⎛⎞⎛

To find the eigenvalues of the problem:

xy rrr2

ˆ =⎟⎟⎟⎞

⎜⎜⎜⎛

⎟⎟⎟⎞

⎜⎜⎜⎛ −

== εεεε

ε ⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −

εεεε

0 000 ⎟⎠

⎜⎝

⎟⎠

⎜⎝ ε ⎠⎝⎠⎝⎠⎝ yyxy 0

−−−

niin xy

εεεε ⇒ 0

εε xyn ±=

0 ni xy εε

ε xyn ±≅ 43 1010~ −− −xyε

yx iEE ±= ⎟⎟⎞

⎜⎜⎛1

⎟⎟⎞

⎜⎜⎛ 1eigenmodes and, oryx iEE ± ⎟⎟

⎠⎜⎜⎝ i ⎟⎟

⎠⎜⎜⎝− i

g and, or

1 ε xy

yx iEE ±=Two circularly polarized waves

ith diff t f ti i di0

εε xyn ±≅±

with different refractive indices:

−E +E outEr

−E +E lFα

2 επlFaraday rotation:

λπα xy

M. Faraday, On the magnetization of light and the illumination of magneticlines of force, Phil. Trans. R. Soc. Lond. 136, 104 (1846).

f f ( )

Kerr effect: various geometries

θθ θ θθ

o0>>θo0≈θ o0>>θ

polar longitudinal transverse

Magnetic linear birefringence

rrlight propagates along x axis, so that

zyin EkEjErrr

⎟⎞

⎜⎜⎛ −

iiεεεε

ˆ y⎟⎟

⎠⎜⎜

⎝ +=

xyiεε

εεε

2zzεε +0,0εEigenvalues 2Mzz ∝ε

Eigenmodes zy EErr

orbits light wavespins orbits light wavespins

exchange + spin-orbit

What could be measured?

B i l PRL 76 4250 (1996)-3 0 3

-0.3'down'

Beaurepaire et al, PRL 76, 4250 (1996).3 0 3Field (kOe)

dynamicshysteresis

Electromagnetic wave equation and source term

∂ 222 2P∂

rr 22 Q̂MP ∂∂∂

=∇⋅−∂∂ 22

2 2tPS

∂∂

∇−∂

∂×∇+

∂∂

ωω EEd )1(1Φ

( )),1(),1(),1( ωωωωωω χχχ EEHEEE dmd ∇++−=Φωωχ EEd ),1(

−=Φ( )or

,...1 ωωω γβα EHE +∇+++×

ωω χ EP d ),1(

=Φ∂

−=Er or

),1(),1(),1(... ωωωω χχχ EHEP qmd +∇++= χE∂ ...),2(),2(),2( ωωωωωω χχχ EEHEEE qmd ∇+++

electric dipole approximationmagnetic dipole electric quadrupole

magnetic dipole electric quadrupole

Harmonic oscillator

U(x) (L)

Linear response

U(x) P(L)

x E21)( xkxU =

kxdUF )(1)( xkxU

Fel ==)(

EFx edtdm el =+2

2)()()()( ωωχω jij

Li EP =

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.

Nonlinear oscillatorAnharmonism )()( NLL PPP +=

P(NL)U(x)

2ω + DC

1)( xkxkxU +=ω

)()()2()2()( ωωωχωNL EEP =2

21 32)( xkxkdx

xdUFel +==)()()0()0()( ωωχ kjijk

NLi EEP =

)()()2()2( ωωωχω kjijki EEP =

Nonlinear polarization and symmetry

( ) ...)2()1( +⋅+⋅∝ ωωω χχω EEEP (electric dipoleapproximation)

tie ω tititi eee ωωω 2=⋅ second-harmonic generation

tititi eee 0⋅− =⋅ ωωoptical rectification

inversion symmetry:

( )( ) ωωχω EEP ⋅∝ )2(2−1 −1−1 1 11

( ) 02 ≡ωP( )except at surface/interface

Magnetization-sensitive SHG

( ) )()(2 ωωω χ kjijki EEP = ( ) )()()()( ωωχχ kjm

ijk EE±=crystallographic

±magnetic

space inversion:

, HMrr

polarvector

axialvector time reversal:vector vector time reversal:

i dR.R. Birss, Symmetry and Magnetism (North-Holland, Amsterdam, 1966). A. Kirilyuk and Th. Rasing,

J. Opt. Soc. Am. B 22, 148 (2005)

Example: surface/interface sensitivity

ultrathin Co/Cu(001) films

Fe(110) surface

C (001)

Co (x ML)

total mag

Cu(001)

a gnetizatio

t on (arb. u

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)

General phenomenology

...:: )3()2()1( +++⋅∝ EEEEEEPrrrrrrr

χχχ χχχ

( )[ ]3)( mmmmemmeenlrrrrrrrrr

( )[ ]3)( ,::: HEoHHHEEEP emmeemeeenlrrrrrrrrr

+++∝ χχχ

( )[ ]3)( ,::: HEoHHHEEEM mmmmemmeenl +++∝ χχχ

( )[ ]3)( ,:::ˆ HEoHHHEEEQ qmmqemqeenlrrrrrrrr

+++∝ χχχ ( )[ ],Q χχχSource term:

sum- and differencefrequency generation,including SHG andincluding SHG andoptical rectification

E i t l k hExperimental know-how: time-resolved pump-probe setuptime resolved pump probe setup

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 fsPulse 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 oof 16 fs pulse obtained with external

group velocity dispersion compensation

you have some choice!Andrei Kirilyuk, Targoviste – August 2011 Radboud University Nijmegen38

you have some choice!

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

time base pump

adjustabledelaydelay

Stroboscopic magneto-optical pump-probe measurements

Ti:Sapphire1 KHz

100 fs 805 nm100 fs, 805 nm

delay τ

Delay line0 1 μm = 0 7 fs

delay τ

Polarization change ( )

r 0.1 μm = 0.7 fsof the probe beam is detected

( )τM∝

Optical pump-probe measurements of FMR

before pump pulse arrives after pump has arrived

external field

saniexteff HHHH

rrrr++=

Pump pulseaffected by the laser

All-optical magnetic resonance in antiferromagnets

175 K, 433 GHz (x6)

ZδM155 K, 406 GHz (x6)

135 K, 372 GHz (x3)

115 K, 327 GHz (x3)

95 K, 271 GHz (x3)

0 25 50 750.0

Pulse fluence (mJ/cm2)0.4

) 450 20 50 80 110 140 170Amp

Temperature (K)

kσ+ quasi-FM

75 K, 211 GHz

60 K, 175 GHz0.3

300Znc

50 K, 159 GHz

4 0 K 153 GH z

δM S2

quasi-AFMmode

4 0 K, 153 GH z

30 K, 151 GHz

1 8 K 151 GH

0.1150

25 50 75 100 125 150 175

Ykσ+X

1 8 K, 151 GH z

0 50 100 150 200 250 300

0.025 50 75 100 125 150 175

Temperature (K)

Time delay (ps)

Effects of the laser pulse: classification

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

Thermal laser-induced effects ultrafast phase transitionsexcitation and study

of spin waveslaser-induced collapse of magnetization

ex1 TS ×

A1 HS ×

A2 HS ×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)

, , ( )

II. Nonthermal photo-magnetic effects:based on photon absorption

Photo-magnetic effects: modification of anisotropy

polarization-dependentpolarization-dependenteffect => nonthermal!

Hansteen et al., PRL 95, 047402 (2005);Phys. Rev. B 73, 014421 (2006).

Circular polarization, photon spin, and absorption

1S1+=zS 21

1−=zS

−=zS

1 h t / it 20000 K ΔTvery fast and easy?

~0.01 phot/site max

1 photon / site = 20000 K ΔT

ff 10 4p

≤0.01 efficiencyeffect ≤ 10-4

II. Nonthermal photo-magnetic effects:based on photon absorption

III N th l t ti ff tIII. Nonthermal opto-magnetic effects:do not require absorption

Extended introduction in laser-induced dynamics

everything you ever wanted to know abouteverything you ever wanted to know aboutlaser-induced magnetization dynamics...

Thermodynamics of magneto-optics

( ) ( )ωωεε *0 EE=Φ

( ) ( ) ( ) ( )EEH ∂−=

Φ∂−=

εωωε *010 σ+( ) ( ) ( ) ( )M

H∂∂

ωωμμ 00 0

0σ−σ

⎞⎛

δH+ δH−

( )⎟⎟⎟⎞

⎜⎜⎜⎛+

−= 0

0ˆ Mi

εααε

Inverse Faraday effect

δH δH( )⎟⎠⎜⎝ + 200 MOzzε

( ) ( ) ( )[ ]ωωαε *00 EEHrrr

×=( ) ( ) ( )[ ]μ0 Pitaevskii, Sov. Phys. JETP 12, 1008 (1961).

van der Ziel Phys. Rev. Lett. 15, 190 (1965).

Faraday effectInverse

F d t ti2 απθ Ml

=Faraday rotation:0ελ

θF =no absorption required!

( ) ( ) ( )[ ]ωωαε *00 EEHrrr

×=no angular momentum transfer!

( ) ( ) ( )[ ]μ0

−E +EinEr

−E +E l outEr

++= =Fα

Effect for opposite pulse helicities

it works!!!

i l t t 100 fequivalent to a 100 fsmagnetic field pulse ofsome 0.5–1 Tesla!

[ ]ε( ) ( ) ( )[ ]ωωαμε *

00 EEHrrr

1001.0~ −IFEH Tesla

Hansteen et al., PRL 95, 047402 (2005);Phys. Rev. B 73, 014421 (2006).

y , ( )

Works everywhere! (almost)

σ−σ+

0.1δM− 0.5

0 25 50 750.0

DyFeOT = 95 K

3σ−Fara

0.00 25 50 75

Pulse fluence (mJ/cm2)

T = 95 Kσ0 15 30 45 60

Time delay (ps) ( ) ( ) ( )[ ]ωωαε *00 EEHrrr

×=Time delay (ps) ( ) ( ) ( )[ ]ωωαμ0

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

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 photonsis conservedhω2 hω2

hω1 h(ω1−Ω) Process can be fastτ ~ 1 / ω ~ 1 fs

L=0 hΩ

light helicity (= angular momentum) is also conserved!

Manipulating pulse frequencies picture courtesy Th.Baumert

Amplitudes and phasesof 320 componentsof 320 components

Opto-magnetic effect with “shaped” pulse

ΩAFMR

ΩAFMRAFMR

Higher frequency component? A. Reid et al., Phys. Rev. Lett. 105, 107402 (2010).

Hi h fHigh 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).

p , y ( )

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

“d”–sites

ferrimagneticferrimagneticorder

“a”–sites

different local environment!

Exchange Resonance

Shouldn’t be able to see it.

Neither OM nor MO necessarily correlate with M.

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 Nijmegen62

locally driven spin dynamics!

Transient magneto-optical response

Transient complex (Kerr or Faraday) rotation

( ) ( ) ( ) ( )tMtFtGt +=θ~

( ) ( ) ( ) ( )tMFtFMtGtT Δ+Δ+Δ=Δ 00~θPump-induced change

( ) ( )tMFGt 00~

+=θ( )( )

GGFtF ≡

If, by some chance , then ( ) ( )00( ) 0GtG ≡

( ) ( ) ( )

, y , then

( ) ( ) ( )000 MtMtt Δ

( ) ( ) ( )tMtt ΔΔΔ εθ ( ) ( ) ( )000 MtMtt Δ

system out of equilibriumsystem out of equilibrium

Optical effects?

nonmagnetic

magneticmagnetic

Messages to take home

not everything you measure is magnetization

t ti ff t l d t l hopto-magnetic effects lead to real change of M during the pulse

it is a challenge to show whether there is an other nonthermal mechanism to do this!any other nonthermal mechanism to do this!

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