Università Cattolica del Sacro Cuore Magnetoelastic effects in permalloy nano-dots induced by laser-driven acoustic standing waves 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.

ARRAYS OF MAGNETIC DISKS Introduction 1m Fe20Ni80 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).

THERMODYNAMICS AT NANOSCALE Introduction THERMODYNAMICS AT NANOSCALE Cylindrical disks, in thermal contact with the substrate, are suitable to study the mechanical properties and the dynamical heat exchange at the solid interface. Py disk Si substrate Fundamental physics → limits of classical thermodynamics C. Bustamante et al., Physics Today 58, 43 (2005) Technological problems → measuring without perturbing the nano-system T.S. Tighe et al., Appl. Phys. Lett. 70, 20 (1997)

DIFFRACTION Diffraction by ordered arrays → S/N<10-6 → S/N<10-5 The contribution from the periodic structure is decoupled from the substrate contribution modulation 50 kHz 1/f noise reduction pump probe Ti:Sapphire oscillator = 800 nm t =120 fs 76 MHz → S/N<10-6 time-resolved reflectivity and time-resolved MOKE → S/N<10-5

TIME-RESOLVED REFLECTIVITY Standing waves induced by lattice heating TIME-RESOLVED REFLECTIVITY The laser-induced non-adiabatic heating triggers radial acoustic standing waves Oscillations in the transient reflectivity on the diffraction pattern ~10 ps 170 ps 2a=400 nm ~245 J/cm2 The background at negative delays is related to the mean heating of the sample

Standing waves induced by lattice heating Si substrate Py disk Impulsive heating striggers acoustic longitudinal standing waves electron-phonon coupling electronic specific heat excitation intensity ELASTIC OSCILLATION OF CYLINDRICAL FUSES G.D. Mahan et al., J. Appl. Phys. Lett. 70, 20 (1997)

Mechanical properties Frequency dependance on the dot size SIMPLE COMPRESSION MODEL: Oscillation period 1080 nm 600 nm 500 nm 400 nm Young modulus 300 nm Radial displacement z q ur r L.D. Landau and E.M. Lifshitz, Theory of Elasticity

Thermodynamics at nanoscale We use an harmonic oscillator model, where the radial displacement ur(t) depends on the temperature of the disk. Heat exchange with the substrate 2a=300 nm The solution is given by: where 2=02-2 and =1/- We are able to estimate the relaxation time between the nano-sized system and the substrate.  damping → dephasing between disks oscillations  relaxation → heat exchange between the disk and the substrate

THERMAL DECOUPLING: ACCESSING CRTherm Thermodynamics at nanoscale THERMAL DECOUPLING: ACCESSING CRTherm a0 l Si substrate Py disk Isothermal nanodisk in contact with Si substrate through intrinsic thermal resistance RTherm: Nanodisk isothermal on ps to ns time scale provided Biot number true in our case RTherm10-8 Km2/W kel=91 W/Km Bi~0.03 From the measured  we are able to obtain the specific heat of a mesoscopic physical system: Measured specific heat Specific heat of a Ni thin film Cs ~ 3106 J/(m3K) Cs ~ 2.2106 J/(m3K)

Magneto-optical Kerr microscopy The excitation modes of the vortex state phase can be studied by TR-Kerr microscopy Magnetic field pulse dynamics of the excited magnetization vortex H Ultrafast SC switch K. Perzlmaier et al., Phys. Rev. Lett. 94, 057202 (2005) Is it possible to excite the magnetic spectrum without magnetic pulses? Magnetoelastic interaction thermodynamic potential piezomagnetism magnetostriction

KERR ELLIPTICITY Kerr hysteresis cycles The hysteresis cycle can be reproduced via micromagnetic simulation software OOMMF vortex configuration single-domain Vortex expulsion

LASER INDUCED VARIATION of KERR ELLIPTICITY Dynamical hysteresis cycles LASER INDUCED VARIATION of KERR ELLIPTICITY Ellipticity variation non-magnetic contribution Subtracting measurements taken at opposite values of the external magnetic field, eliminates non-magnetic contributions Kerr ellipticity at fixed delay The S/N ratio is increased by adding the difference of all the points in the cycle Magnetization is averaged over different magnetic configurations: only qualitative information single-domain vortex configuration

OSCILLATION in the AVERAGED MAGNETIZATION Dynamical magnetoelastic coupling OSCILLATION in the AVERAGED MAGNETIZATION We measure transient hysteresis cycles as a function of the delay between the pump and probe pulses Averaged magnetization as a function of the pump-probe delay 510-5 After subtraction of the background, a small oscillation of the magnetization averaged over the cycle is evidenced Improving of the experimental resolution to discriminate magnetoelastic coupling in the different magnetic configurations

PHYSICS TIME-SCALE time delay Conclusions PHYSICS TIME-SCALE time delay ps ns 10 ns Pump excitation photon-e- e--phonon Isothermal nanodisk @ 50 oC Nanodisk-substrate coupling through interface resistance RTherm gives R/R decay: access to CRTherm R/R oscillations: access to elastic properties and coupling to the magnetization Steady-state : access to RTherm (in process) coupling nanodisk heating

Future Improving of the experimental resolution to discriminate magnetoelastic coupling in the different magnetic configurations Different Fe-Ni composition to investigate the coupling between elastic and spin modes Study of the shape of the transient hysteresis cycles to investigate the photon-electron interaction Mechanical and thermodynamical properties of nanometric systems across a phase transition

Acknowledgements Group leader Fulvio Parmigiani TR-MOKE Alberto Comin (LBL) Samples P. Vavassori (Università di Ferrara) V. Metlushko (University of Illinois) Thermodynamics F. Banfi and B. Revaz (University of Genève) Ultrafast optics group (Università Cattolica, campus di Brescia) Gabriele Ferrini, Stefania Pagliara, Emanuele Pedersoli, Gianluca Galimberti