modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici
DESCRIPTION
Vito Puliafito Magnetism Research Group Università di Messina, Italy. Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici. XXVI Riunione Annuale dei Ricercatori di Elettrotecnica , ET 2010 9-11 Giugno 2010, Napoli. Unità di Messina. ww2.unime.it/ mrg. - PowerPoint PPT PresentationTRANSCRIPT
Modulazione non Modulazione non lineare lineare
di ampiezza e di ampiezza e frequenza frequenza
in nano-oscillatori in nano-oscillatori spintronicispintronici
Vito PuliafitoVito PuliafitoMagnetism Research Magnetism Research
GroupGroup
Università di Messina, Università di Messina, ItalyItaly
XXVI Riunione Annuale dei Ricercatori di Elettrotecnica, ET XXVI Riunione Annuale dei Ricercatori di Elettrotecnica, ET
20102010
9-11 Giugno 2010, Napoli9-11 Giugno 2010, Napoli
Unità di Messina
ComponentiComponentio Bruno Azzerbonio Alessia Bramantio Andrea Calistoo Giancarlo Consoloo Giovanni Finocchioo Alessandro
Prattellao Vito Puliafito
Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici
Vito Puliafito - ET 2010, Napoli, 11/06/2010
Principali tematiche di ricercaPrincipali tematiche di ricercao Modellizzazione materiali
magneticio Micromagnetismoo Spintronicao Elaborazione di segnali
biomedicali
Principali collaborazioni:Principali collaborazioni:o Unità ET di Perugia, prof.
Cardellio Università di Perugia, prof.
Carlottio Università di Ferrara, prof.
Nizzoli
o Università di Salamanca, Spagnao Università di Cornell, Ithaca, Usao Università di Oakland,
Rochester, Usao Royal Institute of Technology,
Svezia
ww2.unime.it/mrg
Outline
Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici
Vito Puliafito - ET 2010, Napoli, 11/06/2010
Introduction on analog modulation processes
Motivation of the present study Mathematical models of modulation Numerical analysis of spintronic nano-
oscillators Comparison between analytical,
numerical and experimental results Conclusions
Analog modulation processes
Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici
Vito Puliafito - ET 2010, Napoli, 11/06/2010
Carrier wave
Message signal (modulating)
Parameters of the carrier wave modified by the modulating signal:
- frequency (FM)
- amplitude (AM)
- phase (PM)
LFM
t
0
cos , cos 2π ,c i c is t A m t A f m d
cos 2c cc t A f tcarrier
output signal
cos 2m mm t A f tmodulating
,i cf m t f km t instantaneous frequency
cos 2π sin 2π mc cs t f t f tA
2
Jc n c m c m
AS f f f nf f f nf
frequency spectrum
m
m
kA
f
central frequency = fc symmetric sidebands sidebands number = ∞
dc aci t I i t 8.5 mAdcI
40 MHzmf cos 2πac m mi A f t
10,075 GHzcf
Motivation of the study[Pufall et al., APL 86,
082506, 2005]
shift of the central frequency
asymmetric sidebands
the Spin-Transfer Oscillator (STO)
works as a NFM modulator
central frequency shift
asymmetric sidebands
NFM
t
0
cos , cos 2π ,c i c is t A m t A f m d
output signal
instantaneous frequency 0
,v
hi h
h
f m t k m t
0 ck f
1
cos sinv
Ic c h h m
h
s t tA k h t
12
I vI hcc c h h m
h
f f k A
1
1,...,
1 1
2 h
p
vc
hh
p v
v vI Ic m h c m h
h h
AS f
f f f h f f f h
J
NFMComparison between NFM model Comparison between NFM model
and experiments [Pufall et al., and experiments [Pufall et al.,
APL 2005]APL 2005]
NFM model reproduces the central
frequency shift,
but notnot the different amplitudes of
sidebands.
Reason of the disagreementAdditive amplitude modulation effects are NOT INCLUDED.
There are theoretical, experimental and numerical evidences of amplitude modulation.
[Pufall et al., APL 2005][Pufall et al., APL 2005][Slavin and Kabos, IEEE Trans. Magn. 41, 2005][Slavin and Kabos, IEEE Trans. Magn. 41, 2005]
2k k kN B
frequency amplitude
0
,u
kc k
k
A m t m t
0 1
1,...,
1 1
1 1
1
4
i
j
u v
k k ik i
j v
v vI Ic i m c i m
i i
v vI Ic i m c i m
i i
S f
f f i k f f f i k f
f f i k f f f i k f
J
0
,v
hi h
h
f m t k m t
0 ck f
t
0
, cos , , cos 2π ,c i c is t A m t m t A m t f m d
output signal
instantaneous frequency
instantaneous amplitude
quantitatively
different asymmetric
sidebands
NFAM
LLGS equation of motion:
eff c0 0
If r R
t M t M
M M
H M M M M p
Numerical Integration method:- Finite-difference approach- Fifth-order Runge-Kutta scheme
Device: -Extended Point-Contact (800nm x 800nm x 5nm)
Parameters: -External field Hext=800mT directed at 80°80° w.r.t. the plane-Ms (FL) = 0.7 T (FL dynamics only); -A = 1.4×10-11 J/m-Rc = 20nm;-Spin-torque efficiency: 0.25-Cell size: 4nm-a = 0.01-uniform current density distribution-Abrupt Absorbing Boundary Conditions
Effective Field:-Magnetostatic, Exchange, Zeeman-NO Oersted-NO Anisotropy-No Thermal
Numerical study: framework
[V. Puliafito et al., IEEE Trans. Magn. 45, n.11, 2009]
STEP 1: CHOOSE the SETUPSTEP 1: CHOOSE the SETUPIn the free running condition i(t) = Idc
(NO modulation), choose a bias point and the operating range.
STEP 2: FITSTEP 2: FITFind the best polynomial fit of the functions f(I) and A(I) (or P(I)) and extract the values of amplitude (k) and frequency (kh) sensitivity coefficients. STEP 3: MODULATIONSTEP 3: MODULATION
Apply the modulating signal:i(t) = Idc + iac (t) = Idc + Am sin (2fmt).
STEP 4: USE NFAM MODEL STEP 4: USE NFAM MODEL Predict the composition of the Fourier Spectrum of the modulated signal by means of the analytical formula.
Analisys procedure
comparing the numerical results with the analytical models:
the shift of central frequency
12
I vI hcc c h h m
h
f f k A
for both NFM and NFAManalytical models:
Analysis #1: varying Am
comparing the experimental results with the analytical models:
the shift of central frequency
Analysis #1: varying Am
[Muduli et al., PRB 81, 140408(R), 2010]
I Il c m c mS f f lf S f f lf l is sideband order
comparing the numerical results with the analytical models:
the asymmetric sidebands
FULL AGREEMENT WITH THE NFAM MODEL
Analysis #1: varying Am
comparing the experimental results with the analytical models:
the asymmetric sidebands
Analysis #1: varying Am
[Muduli et al., PRB 81, 140408(R), 2010]
Analysis #2: varying fm
All the results presented so far are valid if .
When the frequency of the modulating signal is increased above this value, the modulation process vanishes (no sidebands are observed) as frequency pulling or injection locking phenomena are observed instead.
0.9 Im cf f
250 MHzmf 15 GHzmf
A “pure” NAM modulatorWe showed that it is not possible to build a pure frequency spintronic modulator, since there are amplitude modulation effects that we cannot disregard.
Let’s see if it is possible to have a pure amplitude spintronic modulator.
There is a critical angle, referred to as “linear angle”, at which the frequency tunability coefficient
is equal to zero.
[G.Consolo et al., PRB 78, 2008]
Here, the frequency is kept constant with the applied current and only the amplitude changes.
f I
[G. Consolo and V. Puliafito, IEEE Trans. Magn. 46, n.6, 2010]
0
,u
kc k
k
A m t m t
,i cf m t f
t
0
, cos , , cos 2π ,c i c is t A m t m t A m t f m d
output signal
instantaneous frequency
instantaneous amplitude
0
1
4
+
u
kk
c m c m
c m c m
S f
f f kf f f kf
f f kf f f kf
central frequency = fc
symmetric sidebands
number of sidebands = 2*u 1
uj
k j m jj
a A
NAM
polynomial order u
Analysis #3: a pure NAM
Analysis with no modulation
(dc current)
Analysis withmodulation
(dc+ac current)
Numeric results agree with the analytical model:at the “linear” angle configuration, the STO works as a pure NAM!
Conclusions
Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici
Vito Puliafito - ET 2010, Napoli, 11/06/2010
We developed a general analytical model for a nonlinear combined frequency-amplitude modulation process
It has been tested on a point-contact structure:
it generally works as a nonlinear modulator of both frequency and amplitude (in the range fm<0.9fc
I)
in the “linear angle” configuration, it works as a nonlinear modulator of the sole amplitude
GRAZIEGRAZIE
PERPER
L’ATTENZIONEL’ATTENZIONE
Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici
Vito Puliafito - ET 2010, Napoli, 11/06/2010
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