Diapositiva 1

1
Elastic, thermodynamic and magnetic properties of
nano-structured arrays impulsively excited by
femtosecond laser pulses
Claudio Giannetti c.giannetti_at_dmf.unicatt.it,
http//www.dmf.unicatt.it/elphos
Università Cattolica del Sacro Cuore Dipartimento
di Matematica e Fisica, Via Musei 41, Brescia,
Italy.
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Introduction
ARRAYS OF MAGNETIC DISKS

• Fundamental physics ? Vortex configuration
• T. Shinjo et al., Science 289, 930 (2000).
• Magnetic eigenmodes on permalloy squares
  and disks
• K. Perzlmaier et al., Phys. Rev. Lett. 94,
  057202 (2005).

• Technological interest ? Candidates to MRAM
• R. Cowburn, J. Phys. D Appl. Phys. 33, R1
  (2000).

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TIME-RESOLVED MEASUREMENTS OF THE DIFFRACTED
PATTERN
LIGHT SOURCE

• 800 nm
• t 120 fs
• 80 MHz

TiSapphire oscillator
G2?/D
EPUMP10 nJ/pulse fwhm60 µm
EPROBElt1 nJ/pulse fwhm40 µm
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.
Reflected intensity variation
Diffracted intensity variation
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TIME-RESOLVED DIFFRACTION AS A FUNCTION OF THE
ARRAY PERIODICITY
D201830 nm 2a990 10 nm h311 nm
D102050 nm 2a470 10 nm h212 nm
D81010 nm 2a380 20 nm h335 nm

• Oscillations in the diffracted signal triggered
  by the impulsive heating of the metallic
  nanoparticles.
• 2D SAWs or
• single modes of the dots

D6103 nm 2a320 10 nm h6020 nm
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2D Surface Acoustic Waves
SAW dispersion
Dispersion relation of the 2D SAW excited at the
center of the Brillouin zone. SURFACE WAVE
VELOCITIES VSAW4900 m/s _at_ Si(100) 5 VSAW5100
m/s _at_ Si(110) 5
The damping ?, due to energy radiation of SAWs to
bulk modes, is proportional to G4.
SAW damping
Initial transverse displacement uz0? h-1
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CHANGING THE DISK RADIUS
Constant periodicities and thicknesses
D1000 nm h50 nm
frequency shift
2a320 10 nm T207.60.1 ps
2a395 7 nm T212.40.1 ps
2a785 7 nm T218.90.1 ps
1st order perturbation theory predicts a
frequency-shift, due to the mechanical loading,
linear with the filling factor
rS reflection coeff.
??a2/D2 filling factor
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WAVELET ANALYSIS OF THE DIFFRACTED SIGNAL
? impulsive excitation
main period 220 ps
Convolution with the wavelet
Harmonic oscillator model, where the radial
displacement ur(t) depends on the temperature of
the disk.
C-Morlet wavelet
The solution, similarly to DECP, is given by
where ?2?02-?2 and ?1/?-?
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FREQUENCY ANALYSIS OF THE DIFFRACTED SIGNAL
time-domain dynamics
D10056 nm 2a7857 nm h512 nm
?SAW
?2
Si(110)
Detection of the diagonal collective mode
?2/?SAW1.3860.004 influence of the substrate
anisotropy (?35)
Si(100)
30
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WAVELET ANALYSIS OF THE DIFFRACTED SIGNAL
DATA
FIT with ?SAW 4.57 GHz and ?26.33 GHz
To reproduce the data we need to add a third
highly damped frequency ?38.5 GHz
(1-cos?t)-like excitation
sin?t-like excitation
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NUMERICAL CALCULATION OF EIGENMODES
Mode 1
Mode 2
4.19 GHz
3.78 GHz
Transverse mode
Longitudinal mode
1 µm
Symmetric mode ? Form-factor modulation at ?
Asymmetric mode ? Form-factor modulation at 2?
Mode 3
Mode 4
4.52 GHz
5.80 GHz
Asymmetric mode ? Form-factor modulation at 2?
Asymmetric mode ? Form-factor modulation at 2?
Periodic conditions on displacement, strain and
stress
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EIGENMODES DEPENDENCE ON THE DISK RADIUS
The highly damped ?3 frequency is close to the
double of the asymmetric mode 2 frequency at the
bottom of the band-gap
ELASTIC-mismatch INTERACTION opening of a gap
at zone center
Single disk modes
Possible opening of a gap ? TWO-DIMENSIONAL
SURFACE PHONONIC CRYSTAL in the GHz
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TIME-RESOLVED MAGNETO-OPTICAL KERR EFFECT
Static hysteresis cycle
MAGNETIZATION RECOVERY DYNAMICS
M
?
?
Polarization rotation induced by the interaction
with M

• is the rotation
• is the ellipticity
• ? ?, ? ? M

in press on Phys. Rev. Lett.
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• 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

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Acknowledgements

• Group leader
• Fulvio Parmigiani
• Thermodynamics
• F. Banfi and B. Revaz (University of Genève)
• Samples
• P. Vavassori (Università di Ferrara)
• V. Metlushko (University of Illinois)
• Ultrafast optics group (Università Cattolica,
  campus di Brescia)
• Gabriele Ferrini, Matteo Montagnese, Federico
  Cilento
• TR-MOKE
• Alberto Comin (LBL)