università cattolica del sacro cuore

From microphotonics to nanophononics October 16th-28th Cargèse, France

Elastic, thermodynamic and magnetic properties of nano-structured arrays impulsively excited by

femtosecond laser pulses

Università Cattolica del Sacro CuoreDipartimento di Matematica e Fisica, Via Musei 41, Brescia, Italy.

Claudio [email protected],

http://www.dmf.unicatt.it/elphos


ARRAYS OF MAGNETIC DISKS

Introduction

•Fundamental physics → Vortex configurationT. Shinjo et al., Science 289, 930 (2000).

Magnetic eigenmodes on permalloy squares and disksK. Perzlmaier et al., Phys. Rev. Lett. 94, 057202 (2005).

•Technological interest → Candidates to MRAMR. Cowburn, J. Phys. D: Appl. Phys. 33, R1 (2000).

1m

Fe20Ni80


DIFFRACTION FROM ARRAYS OF 3D CONFINED METALLIC

NANO-PARTICLES

This technique strongly increases the sensitivity to the periodicity of the system, allowing to follow the mechanical and thermodynamic relaxation dynamics of the system with high accuracy.

TIME-RESOLVED MEASUREMENTS OF THE DIFFRACTED PATTERN

a

tata

aRRDR

aRR

I

I

SiPySi

SiPy

refl

refl )(28.0)(

)(

)(222

a

ta

a

taRR

GaJ

GaJG

I

ISiPy

D

D )(5.2

)()(

)(

)(2

1

0

1

1

1st order d iffraction

AFM im age

PEM

10 s

pum p beam

crossedpolarizers

probe beam

UNIT CELL2a

D=4az

r0Zdh

= 800 nm =120 fs80 MHz

Ti:Sapphireoscillator

LIGHT SOURCE

EPUMP≈10 nJ/pulse fwhm≈60 µmEPROBE<1 nJ/pulse fwhm≈40 µm

Reflected intensity variation

Diffracted intensity variation

G=2/D


2.5

2.0

1.5

1.0

0.5

I1D

/I 1D

x 1

0-5

3000200010000delay (ps)

1/=950±30 ps

2=134.8±0.1 ps

2.5

2.0

1.5

1.0

0.5

I1D

/I 1D x

10

-5

1/=1690±60 ps

2=175±0.1 ps

2.5

2.0

1.5

1.0

0.5

I1D

/I 1D x

10

-5

1/=3980±300 ps

2=211.2±0.1 ps

2.5

2.0

1.5

1.0

0.5

I1D

/I 1D

x 1

0-5

1/=17000±5500 ps

2=409.4±0.3 ps

D=2018±30 nm2a=990 ±10 nmh=31±1 nm

D=1020±50 nm2a=470 ±10 nmh=21±2 nm

D=810±10 nm2a=380 ±20 nmh=33±5 nm

D=610±3 nm2a=320 ±10 nmh=60±20 nm

TIME-RESOLVED DIFFRACTION AS A FUNCTION OF THE ARRAY PERIODICITY

2x delay line

piezomotors

QPDs

Feedback system for pump-probe alignment control during the long-range

experiment (delay >1 m)

Oscillations in the diffracted signal triggered by the impulsive heating of the metallic nanoparticles.

2D SAWs or single modes of the dots


2000

1600

1200

800

arra

y pe

riod

(nm

)

400350300250200150oscillation period (ps)

vSAW=4850±75 m/s

107

108

109

1010

a2· (µ

m4·p

s)

5 6 7 8 91000

2 3 4 5

array period (nm)

1

10

100

1000

(n

s)

n=4

n=2.5 2

4

2220

41

a

D

ahu

D

z

Dispersion relation of the 2D SAW excited at the center of the Brillouin zone.

SURFACE WAVE VELOCITIESVSAW=4900 m/s @ Si(100) [5]VSAW=5100 m/s @ Si(110) [5]

The damping , due to energy radiation of SAWs to bulk modes, is proportional to G4.

SAW damping

SAW dispersion

Initial transverse displacement uz0 h-1

2D Surface Acoustic Waves

qvSAW

-/D /D


CHANGING THE DISK RADIUS3.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

I 1

D/I 1

D x

10-5

300025002000150010005000delay (ps)

frequency shift 2a=320 ±10 nm

T=207.6±0.1 ps

D=1000 nm; h=50 nmConstant periodicities and thicknesses

1st order perturbation theory predicts a frequency-shift, due to the mechanical loading, linear with the filling factor:

D

hrs

SAW

SAW v

v

rS: reflection coeff.

-1.6

-1.2

-0.8

-0.4

0.0

V

/V)·

D/h

0.50.40.30.20.1

filling factor

Failure of the 1st order perturbative approach at large filling factors

=a2/D2 filling factor

h

D

SAW

SAW

v

v

2a=395 ±7 nm

T=212.4±0.1 ps

2a=785 ±7 nm

T=218.9±0.1 ps


400

300

200

100

0

pe

riod

(p

s)

3000200010000delay (ps)

2.0

1.5

1.0

0.5

0.0

I 1

D/I 1

D x

10-5

3000200010000delay (ps)

400

300

200

100

0

pe

riod

(p

s)

3000200010000delay (ps)

Harmonic oscillator model, where the radial displacement ur(t) depends on the temperature of the disk.

)(2)]()([)( 020 tutututu rrrr

)sincos()( / teteetu tttr

/0 )( tr etu

The solution, similarly to DECP, is given by:

where 2=02-2 and =1/-

WAVELET ANALYSIS OF THE DIFFRACTED SIGNAL

''

)'(),( dts

tttxtsW

202

1

4

1

)( ees i

Convolution with the wavelet

C-Morlet wavelet

main period≈ 220 ps

← impulsive excitation


2.0

1.5

1.0

0.5

0.0

I 1

D/I 1

D x

10

-5

300025002000150010005000delay (ps)

Fo

uri

er

Tra

nsf

orm

(a

rb.

un

its)

1612840SAW frequency (GHz)

time-domain dynamics

FREQUENCY ANALYSIS OF THE DIFFRACTED SIGNAL

G1

G2

SAW

2

D=1005±6 nm2a=785±7 nmh=51±2 nm

Si(110)

Si(100)

X

M

(533)

(531) (311)

X-ray diffraction

Detection of the diagonal collective mode: 2/SAW=1.386±0.004

influence of the substrate anisotropy (θ=35°)

30°


2.0

1.5

1.0

0.5

0.0

I1D

/I1D

x 1

0-5

3000200010000delay (ps)

400

300

200

100

0

pe

riod

(p

s)

400

300

200

100

0

pe

riod

(p

s)

3000200010000delay (ps)

400

300

200

100

0

pe

riod

(p

s)

3000200010000delay (ps)

WAVELET ANALYSIS OF THE DIFFRACTED SIGNAL

DATA

FIT with SAW =4.57 GHz and 2=6.33 GHz

To reproduce the data we need to add a third highly damped frequency 3≈8.5 GHz

(1-cost)-like excitation

sint-like excitation


Periodic conditions on displacement, strain and stress

Mode 1

Mode 3

Mode 2

Mode 4

1 µm

4.19 GHz 3.78 GHz

4.52 GHz 5.80 GHz

Symmetric mode Form-factor modulation at

Asymmetric mode Form-factor modulation at 2



NUMERICAL CALCULATION OF EIGENMODES

Transverse mode

Longitudinal mode


0.5

1.5

2.5

3.5

4.5

5.5

6.5

0 100 200 300 400 500

disk radius (nm)

freq

uen

cy (

GH

z)

mode 1mode 2

mode 3

data

EIGENMODES DEPENDENCE ON THE DISK RADIUS

Single disk modes

Possible opening of a gap TWO-DIMENSIONAL SURFACE PHONONIC CRYSTAL in the GHz

The highly damped 3

frequency is close to the double of the asymmetric mode 2 frequency at the bottom of the band-gap

q-/D /D

ELASTIC-mismatch INTERACTION:

opening of a gap at zone center


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

M/M

x 1

0-4

5002500delay (ps)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

M/M

x 10-3

M/M single-domain vortex-state

12

8

4

0R/R

x 1

0-4

5004003002001000delay (ps)

10

0

-10

M/M

x 10-5

R/R

M/M single-domain vortex-state

0.6

0.4

0.2

0.0

-0.2

-0.4

Elli

ptic

ity v

aria

tion

x 10

-3

6004002000-200-400Field (Oe)

TIME-RESOLVED MAGNETO-OPTICAL KERR EFFECT

M

Polarization rotation induced by the interaction with M

E

is the rotation is the ellipticity→ , M

MAGNETIZATION RECOVERY DYNAMICS

-100 0 100Applied magnetic field (mT)

Static hysteresis cycle

in press on Phys. Rev. Lett.


FUTURE

• Brillouin scattering measurements to evidence the opening of the gap in the 2D surface phononic crystal

•Decoupling the thermodynamic and mechanical contributions (double pump experiment) CALORIMETRY of NANOPARTICLES

•Resonant excitation of magnetic eigenmodes of the system

•Applications to sub-wavelength optics


Acknowledgements

•Group leaderFulvio Parmigiani

•Thermodynamics F. Banfi and B. Revaz (University of Genève)

•SamplesP. Vavassori (Università di Ferrara) V. Metlushko (University of Illinois)

•Ultrafast optics group (Università Cattolica, campus di Brescia)Gabriele Ferrini, Matteo Montagnese, Federico Cilento

•TR-MOKEAlberto Comin (LBL)

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