1. Università Cattolica del Sacro Cuore
Magnetoelastic effects in permalloy nano-dots induced by laser-driven acoustic standing waves
Claudio Giannetti
Università Cattolica del Sacro Cuore
Dipartimento di Matematica e Fisica, Via Musei 41, Brescia, Italy.

2. 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, (2005).
Technological interest → Candidates to MRAM
R. Cowburn, J. Phys. D: Appl. Phys. 33, R1 (2000).

3. 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)

4. 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

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

6. 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)

7. 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

8. 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

9. 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)

10. 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, (2005)
Is it possible to excite the magnetic spectrum without magnetic pulses?
Magnetoelastic interaction
thermodynamic potential
piezomagnetism
magnetostriction

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

12. 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

13. 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

14. 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

15. 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

16. 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