From magnetoFrom magneto-optics to ultrafast manipulation of …magnetism.eu/esm/2011/slides/kirilyuk-slides1.pdf · 2017-06-20 · From magnetoFrom magneto-optics to ultrafast manipulation

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”?

1 km

Transmission through water

UVX rayw

ave IR

1 km

X-ray

Radio Mic

row1 m

1 mm

1 µm

1 km 1 m 1 mm 1 µm 1 nm

visiblespectrum

wavelength


spectrum

Optics

1.5–3.2 eV

EDrr

0ε̂ε= EPrr

0ˆεχ=rrr

or

)(0

trkieEE ω−=rrrr PED

rrr+= 0ε χε ˆ1ˆ +=

2


2n=ε

Anisotropic media

⎟⎞

⎜⎛ xzxyxx εεε

⎟⎟⎟

⎠⎜⎜⎜

⎝

= yzyyyx εεεε̂

Er

⎟⎠

⎜⎝ zzzyzx εεε

Er

yE

⎞⎛ 00if H = 0

xE

⎟⎟⎞

⎜⎜⎛

=xx

εε

ε 0000

ˆ⎟⎟

⎠⎜⎜

⎝ zz

yy

εεε00

00

i.e. one could chose such a coordinate system


Driven oscillator model

tE ωsin0

0ω0

Fxdt

xdm =⎟⎟⎠

⎞⎜⎜⎝

⎛+ 2

02

2

ωdt ⎠⎝

teEF ωsin0=

tEexxd ωω sin22

=+ tEm

xdt

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

ω

0x0ω ω

0ωω

°0phase

damped oscillator

°−180

p


Sum of the two waves:

Δz incoming + outgoing

amplitude

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


Phase of the light after transmission

Δz

( ) ⎟⎞

⎜⎛ ztEE i( ) ⎟

⎠⎜⎝

−=c

tEzE ωsin0

zΔextra time because of n:czn Δ

− )1(

⎞⎛ Δ

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∫∞

−−

= 221

212

ωε

πωωε

iknn +=

( ) ( ) duu

u

∫∞

2

0

2 ε

ωπ

221 kn −=ε

k2

( ) ( ) duu

uu∫ −

=0

222

1 ωε

πωε

nk22 =ε

real and imaginary parts are not independent!


Dispersion of glass

ω

λλ


Optical constants of metals

Ni AuNi Au


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

rr

00xx⎥⎤

⎢⎡ε

y EDrr

0εε=

2

0000 nyy

xx

=⎥⎥⎥

⎦⎢⎢⎢

⎣

=ε

εεx H=0if isotropic00 zz ⎥⎦⎢⎣ ε

z

if isotropic

⎥⎥⎤

⎢⎢⎡

= ??????

εM or H

H≠0Er

⎥⎥⎦⎢

⎢⎣

=??????εH≠0E


How does magnetic field modify conductivity?g y y

H 0y

⎥⎤

⎢⎡ xxσ 00

E j H=0

x ⎥⎥⎥

⎦⎢⎢⎢

⎣

=

zz

yy

xx

σσσ00

00 Ejrr

σ=

E j Hy

x

FL=e[V×H] Lorentz force

⎦⎣ zz

x

FL e[V H] Lorentz force

HE

jEy → jxEx → jy

j H ⎥⎤

⎢⎡ xyxx σσ

00

E ⎥⎥⎥

⎦⎢⎢⎢

⎣

=

zz

yyyx

σσσσ00

0


Onsager principle:symmetry of kinetic coefficientssymmetry of kinetic coefficients

⎥⎤

⎢⎡ xyxx εε 0

⎥⎤

⎢⎡ xxε 00

⎥⎥⎥

⎦⎢⎢⎢

⎣

=

zz

yyyx

εεεε00

0⎥⎥⎥

⎦⎢⎢⎢

⎣

=

zz

yy

εεε00

00H=0 H≠0

XfW ∂∂fSXjiij SS =

tf

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)

tDE

tW

∂∂

=∂

∂ 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:

⎟⎟⎟⎞

⎜⎜⎜⎛ −

= xy

xy

iiεεεε

ε 0

0

00

ˆzxy M∝ε

⎟⎟

⎠⎜⎜

⎝ + zz

xy

εε 0

0

00 2zzz M∝ε

HHrr

= Eryxin EjEiE

rrr+=

zHH =inEr outE

x ???=outEr

yz



Ei 0 ⎞⎛⎞⎛

To find the eigenvalues of the problem:

EnEE

ii

ED y

x

xy

xy rrr2

0

0

00

ˆ =⎟⎟⎟⎞

⎜⎜⎜⎛

⎟⎟⎟⎞

⎜⎜⎜⎛ −

== εεεε

ε ⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −

y

x

y

x

xy

xy

EE

nEE

ii 2

0

0

εεεε

0 000 ⎟⎠

⎜⎝

⎟⎠

⎜⎝ ε ⎠⎝⎠⎝⎠⎝ yyxy 0

02

20 =

−−−

niin xy

εεεε ⇒ 0

2

1 ε

εε xyn ±=

0 ni xy εε

00 2

1εε

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

0 21

εε xyn ±≅±

with different refractive indices:

r

−E +E outEr

inEr

−E +E lFα

=++=F

2 επlFaraday rotation:

0

2εε

λπα xy

Fl

=

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

MrM

r

Mr

Hr

o0>>θo0≈θ o0>>θ

polar longitudinal transverse


Magnetic linear birefringence

rrlight propagates along x axis, so that

zyin EkEjErrr

+=zH

xy⎟

⎟⎞

⎜⎜⎛ −

=xy

iiεεεε

ε0

00

ˆ y⎟⎟

⎠⎜⎜

⎝ +=

zz

xyiεε

εεε

0

0

000

2zzεε +0,0εEigenvalues 2Mzz ∝ε

Eigenmodes zy EErr

,


orbits light wavespins orbits light wavespins

exchange + spin-orbit


What could be measured?

0.3

(deg

)

'up'

0.0

tizat

ion"

(

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

-0.3'down'

"Mag

net

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

dynamicshysteresis


dynamicshysteresis







Electromagnetic wave equation and source term

E rrr

∂ 222 2P∂

rr 22 Q̂MP ∂∂∂

rrr

SEctE

=∇⋅−∂∂ 22

2 2tPS

∂∂

=r

22 tQ

tM

tPS

∂∂

∇−∂

∂×∇+

∂∂

=

ωω EEd )1(1Φ

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

or2

−=Φ( )or

,...1 ωωω γβα EHE +∇+++×

ωω χ EP d ),1(

or

=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

kxdx

Fel ==)(

2

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

Ex

ω3

22

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

ijkcr

ijk EE±=crystallographic

±magnetic

space inversion:

g

PErr

, HMrr

,p

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

t

Fe(110) surface

C (001)

Co (x ML)

ast (

%)

total mag

Cu(001)

tic c

ontr

a gnetizatio

G m

agne

t on (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)


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

probe


Stroboscopic magneto-optical pump-probe measurements

Ti:Sapphire1 KHz

100 fs 805 nm100 fs, 805 nm

delay τ

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)

1.0

units

)

0.7

1

un.)

ZδM155 K, 406 GHz (x6)

135 K, 372 GHz (x3)

0.5

Am

plitu

de(a

rb.u

0 5

0.6

0.01

0.1

plitu

des

(arb

.u

Z

YX

δM

115 K, 327 GHz (x3)

95 K, 271 GHz (x3)

0 25 50 750.0

A

Pulse fluence (mJ/cm2)0.4

0.5

(deg

) 450 20 50 80 110 140 170Amp

Temperature (K)

YX

kσ+ quasi-FM

mode

z)

75 K, 211 GHz

60 K, 175 GHz0.3

yro

tatio

n

300Znc

y (G

Hz

,

50 K, 159 GHz

4 0 K 153 GH z

0.2

Fara

day

δM S2

Y

Z

k

S1

quasi-AFMmode

Freq

uen

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

Tex

ex1 TS ×

S1

Tex

Tex

S2

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

=zS

1−=zS

121

−=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

EEM

H∂∂

ωωμμ 00 0

0σ−σ

⎞⎛

δH+ δH−

( )⎟⎟⎟⎞

⎜⎜⎜⎛+

−= 0

0ˆ Mi

Mi

yy

xx

εααε

ε

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

Hr


H

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 *

0

00 EEHrrr

×=

1001.0~ −IFEH Tesla

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


y , ( )

Works everywhere! (almost)

+1.0

σ+

(deg

.)

σ−σ+

0.2

b. u

nits

)

σ

tatio

n (

δM+

0.1δM− 0.5

plitu

de (a

r

day

rot

0 25 50 750.0

Amp

DyFeOT = 95 K

3σ−Fara

d

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

0 EEH

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( )( )

0

GGFtF ≡

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

( ) ( ) ( )

, y , then

( ) ( ) ( )000 MtMtt Δ

=Δ

=Δ

εε

θθ

and


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

=Δ

=Δ

εε

θθ

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!


Documents

From magnetoFrom magneto-optics to ultrafast manipulation of …magnetism.eu/esm/2011/slides/kirilyuk-slides1.pdf · 2017-06-20 · From magnetoFrom magneto-optics to ultrafast manipulation