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Elastic, thermodynamic and magnetic properties of nano-structured arrays impulsively excited by femtosecond lase r pulses. Claudio Giannetti [email protected] , http://www.dmf.unicatt.it/elphos. Università Cattolica del Sacro Cuore - PowerPoint PPT Presentation
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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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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°
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
Asymmetric mode Form-factor modulation at 2
Asymmetric mode Form-factor modulation at 2
NUMERICAL CALCULATION OF EIGENMODES
Transverse mode
Longitudinal mode
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
-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.
From microphotonics to nanophononics October 16th-28th Cargèse, France
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
From microphotonics to nanophononics October 16th-28th Cargèse, France
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)