Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici

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



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



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


[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


comparing the experimental results with the analytical models:

the asymmetric sidebands


[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



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



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Modulazione non lineare di ampiezza e frequenza in nano-oscillatori spintronici

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