Università Cattolica del Sacro Cuore

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

2. Fe20Ni80 1m Introduction ARRAYS OF MAGNETIC DISKS • Fundamental physics → Vortex configuration • T. Shinjo et al., Science289, 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).

3. h • TIME-RESOLVED MEASUREMENTS OF THE DIFFRACTED PATTERN LIGHT SOURCE • = 800 nm t =120 fs 80 MHz Ti:Sapphire oscillator G=2/D EPUMP≈10 nJ/pulse fwhm≈60 µm EPROBE<1 nJ/pulse fwhm≈40 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

4. QPDs piezomotors 2x delay line Feedback system for pump-probe alignment control during the long-range experiment(delay >1 m) TIME-RESOLVED DIFFRACTION AS A FUNCTION OF THE ARRAY PERIODICITY D=2018±30 nm 2a=990 ±10 nm h=31±1 nm D=1020±50 nm 2a=470 ±10 nm h=21±2 nm D=810±10 nm 2a=380 ±20 nm h=33±5 nm • Oscillations in the diffracted signal triggered by the impulsive heating of the metallic nanoparticles. • 2D SAWs or • single modes of the dots D=610±3 nm 2a=320 ±10 nm h=60±20 nm

5. vSAW q -/D /D 2D Surface Acoustic Waves SAW dispersion Dispersion relation of the 2D SAW excited at the center of the Brillouin zone. SURFACE WAVE VELOCITIES VSAW=4900 m/s @ Si(100) [5] VSAW=5100 m/s @ Si(110) [5] The damping , due to energy radiation of SAWs to bulkmodes, is proportional to G4. SAW damping Initial transverse displacement uz0h-1

6. Failure of the 1st order perturbative approach at large filling factors CHANGING THE DISK RADIUS Constant periodicities and thicknesses D=1000 nm; h=50 nm frequency shift 2a=320 ±10 nm T=207.6±0.1 ps 2a=395 ±7 nm T=212.4±0.1 ps 2a=785 ±7 nm T=218.9±0.1 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

7. 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/-

8. G2 G1 X-ray diffraction M (533) (531) (311)  X FREQUENCY ANALYSIS OF THE DIFFRACTED SIGNAL time-domain dynamics D=1005±6 nm 2a=785±7 nm h=51±2 nm SAW 2 Si(110) Detection of the diagonal collective mode: 2/SAW=1.386±0.004 influence of the substrate anisotropy (θ=35°) Si(100) 30°

9. 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-cost)-like excitation sint-like excitation

10. 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

11. /D -/D q 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

12. 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.

13. 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 ofNANOPARTICLES • Resonant excitation of magnetic eigenmodes of the system • Applications to sub-wavelength optics

14. 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)