magnetic nanostructures in modern technology_bab 1-3_cynthia sagta_3225111288

8/9/2019 Magnetic Nanostructures in Modern Technology_Bab 1-3_Cynthia Sagta_3225111288

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Magnetic Nanostructurein Modern Technology

Cynthia Sagita 3225

UNIVERSITAS NEGER

CHAPTER 1-CHAPT


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Spin-Polarized Current and Spin TrTorque in Magnetic Multilayer

JOHN

IBM Re


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1. Outline

1. Abstrack

2. Introduction

3. Two channel spin-polarized transport

4. Effective circuit for a non-collinear all-metallic pillar

5. Current-driven pseudo torque

6. Magnetoresistanece and current-driven torque of symmetric p

7. Dynamics of magnetization driven by current

8. Quantum tunneling theory

9. Currents and torque in magnetic tunnel junctions

10. Junction using MgO bariers


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1. Abstract

We expose the theory of quantized spin-polarized electronperpendicular to the plane of a magnetic multilayer with nomagnetization vectors. The dependence of resistance andriven torque on relative angle between 2 magnetic mommultilayer pillar are derived. Spacers of both metallic and tunnel-barrier types are considered. The classical Land

equation describes the dynamics of the magnetization cspintransfer torque.


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2. Introduction

In 1996, Luc Berger predicted that electric current flowing acrnormal metal spacer between two magnets could excite forwpropagating spin waves in one of them.1 In the same year, a bWKB model predicted that a steady current may create a spintorque which would excite magnetic precession in one of twoseperated single-domain magnets having dimensions of ordenm.2 If the sign of uniaxial anisotropy is negative, this precessremain steady, making conceivable an RF oscillator. If the anispositive, magnetic reversal may ultimately occur, in which casmagnetic memory is conceivable. Subsequent experiments suthese predictions and led to the vast array of new spin-transfephenomena under investigation today.


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3. Two channel spin polarized transport

SUPPRESSION OF TRANSVERSE POLARIZATION

Strong suppression of tcomponents in a ferrocredible the spin-chanelectron transport. Consisubmicron metallic pillanon-magnetic semi-infinof composition N shown

rotated 90so that the dis oriented vertically. Theleft (FL) and rightseparated by a very thinspacer. The cross-sectioparallel to the substratwith dimensions typically

The thickness of each sublayercomponent must be less

than the corresponding diffusion length. Sufficient suchconditions for the pillar of Fig. 1 are


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HALF-PILLAR RESISTORS

One may decompose each of the 4 half-pillarunit-area channel resistors RL and RR into terms inseries arising from 2-channel bulk resistivity ,from 2- channel unit-area interfacial resistance r,

and from an end-effect term occurring at the pillar-lead connection. Thus the half-pillar unit-arearesistances, with the subscripts R and L here elided,are


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4. Effective circuit for a non collinear all metallic p

SPIN POLARIZATION IN A ROTATED REFERENCE FRAME

The term spin accumulation, or spin-polarization density, in a normal mto the expectation value ofzfor a set of electrons occupying a unitcourse, its value depends on the quantization axis considered. How itin a spacer under coordinate-axis rotation is crucial to electron tnoncollinear magnetic multilayers.


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SPIN-DEPENDENT ELECTRON DISTRIBUTION


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FORMULAS FOR CONNECTING CHANNELS ACROSS A SPACER

the single spacer-mparameter required


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TORQUE MECHANISM

how the exchange-reaction torque created by scattpreferentially polarized electrons incident from a normal metferromagnet concentrates on the magnetization located

distance equal to 2 or 3 atomic layers of the interface.

Crucial is the conservation of spinwhich follows fromspin operators in th

hamiltonian for a so


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A GENERAL TORQUE RELATION

Spin-momentum conservation causes the corresponding effective vectosurfacetorque densities TL and TR (with l TL = 0 and r TR = 0) to satisfyequation

here

the coplanar orientations of TL(t) and TR(t) with the

moments ML and MR displayed in Fig. 6 are general. Their

scalar magnitudes are obtained by forming the scalarproducts of Eq. (25) alternatively withML andMR:


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5. Magnetoresistance and current driven torque of a symmet

THE MAGNETORESISTANCE


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TORQUES ON A SYMMETRIC TRILAYER

torque relation for either

with

and


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6. Dynamics of magnetization driven by current

The latter three functions are plotted in Fig. 10 for t

dimensionless current I . (Units for all physical

arbitrary.) The function g() employed is from an earcorresponds approximately to the Figure 10. symmet

= 0.4 in Fig. 9. Obvious conditions for the stability of

are d/dt= 0 (equilibrium) and d[d/dt]/d


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7. Quantum Tunneling Theory

INTERACTION PICTURE

Let satisfy the Schroedinger wave equation

for the one-particle hamiltonian

A general wave function may be expanded thus:


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TUNNELING RATE

To describe tunneling from

specialize to the case ofV ap

constant barrier height B withbarrier (Fig. 12)

The total potential of the s

VL(x) + V R(x). The basic app

Bardeen method is to n

orthogonality of to n(n =

the small wave-function obarrier


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8. Currents and torques in magnetic tunnel juncti

MAGNETO-CONDUCTION AND TORQUES

Fig. 13 (a), a stationary basis state |pferromagnetic electrode FLis assigned

and majority/minority spin = quan

satisfies (H + eV p,)|p, = 0, and dwithin the barrier, considered semi-inf

defining the basis states.

Fig. 13 (b) as shorted in each magn

and/or external-contact region

spin lattice relaxation due to sp

orbit coupling.


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GENESIS OF POLARIZATION FACTORS

Although MTJ relations depending on polarization factors are often used to interpret

experiments, their validity is theoretically justified only under a severe restriction: Th

barrier is so thick that only a single basis function on each side penetrates it.

consider the Schroedinger equation in two dimensions within the region of a

flat barrier of height B:

A solution is

the greater the y-momentum, the steeper the decay of .


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The torque on the right magnet is

the torque coefficient

the torque on the left magnet is


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9. Junctions using MgO barriers


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MAGNETO-CONDUCTANCE AND TORKANCE

ELASTIC TUNNELING


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ELASTIC TUNNELING

Compose each channel current density of elastic and inelastic

terms:

Define a tunnel-rate coefficient U, proportional to the mean-square matrix element fo

tunneling between the orbital states of spin channels (= ) and (= ).

Including all other factors in the conventional tunneling expression

for current except the state densities,, it may be written


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For finite V, we may integrate the transition rate of the golden rule with respect to V. Th

of the relation, the current density due to elastic tunneling at T = 0 K reduces to

the relative dependence of GPon V is much weaker than that of GAP . Thus, we take GPco

and assume, to first order in v,

Notice here that U+ is distinct from U+ because breaking of the selection rule forbiddi

k|| = 0 minority state in a magnetic electrode to 1in MgO is allowed only by disorder in

interface, or presence of a foreign interfacial layer.

INELASTIC TUNNELING


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INELASTIC TUNNELING

The following argument sketches the crux of a theory for the V-dependence

of inelastic tunneling current Iinel at T = 0K: For V > 0, write

In the case of a perfectly ordere

MTJ having a composition inFeCo)/MgO/(Fe, Co, FeCo), a

selection rule forbids mixing of t

waves at k||= 0, having little-gro

the MgO gap wave function hav

coefficient .

Then,

where we have neglected G altogether

OBSERVABLE SIGNATURES


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OBSERVABLE SIGNATURES

assume GPis constant and plot schematically GAPand dTR/dV in Fig. 16 for 5

special cases AE reflecting terms in these equations:

A: Symmetric reference case, with U+ U+ = ,1 = DL DR = 0: Here GAP has th

dependence on |V| due to inelastic scattering exemplified by the data in Fig. 14

B: Asymmetry of elastic tunneling: Let U+ > U+, which reflects the difference in de

disorder or dislocation density at the two F/I interfaces. GAPdoes not change. But no

makes a constant shift amounting to (U+ U+)+,0sin

C: Dependence of state density on energy: Let ,1 > 0. This does not change GAPbu

torkance a true linear dependence.


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D

:Asymmetry of distribution of inelastic tunneling centers:

Let DL > DR. This causes no cbut gives pseudo-linear dependence to torkance. Depending on the sign of DL DR, thewith |V| as shown, or falls.

E

:Combine tunnel m trix symmetry with dependence of on energy:

Let both U+ >> 0. This gives GAP a true linear bias. The torkance acquires a superposition of the effecand C, namely a shift and a tilt.


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SPIN-TRANSFER-DRIVEN MAGNETIZATION DYN

GIORG

Istituto Nazionale di Ricerca Metrologica,


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2. SPIN-TRANSFER-DRIVEN MAGNETIZATION DYN

Outline

1. Abstrack

2. Introduction

3. Equation for spin-transfer-driven magnetizaion dynamics

4. Magnetization dynamics and dynamical system theory

5. The role of thermal fluctuations

6. Uniaxial symmetry


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1. Abstrack

Analytical methods are discussed for the study of spin-trans

magnetization dynamics in nanomagnets. Particular emphasto the case of uniformly magnetized systems, which prerequisite before attempting any numerical computation ospin-transfer devices. The onset of current-induced oscillations of the magnetization is analyzed in the frame ofdynamical system theory and bifurcation theory. Method

description of the effect of thermal fluctuations by aLangevin or Fokker-Planck equations are also considered. Ithat for systems exhibiting uniaxial symmetry the analytical can be developed in considerable detail without introdapproximation.


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2. introduction

Electrons exert a torque of quantum-mechanical origin, know

transfer torque, when they flow across a ferromagnetic eleeffect is added to the magnetic torque that any electrtraversing a ferromagnetic element generates because of thfield surrounding the current. When the current density is slarge (of the order of 107108 A cm2) and the ferromagnetis sufficiently small (lateral dimensions of the order of a fe

nanometers), the spin-transfer torque exceeds the Oersted-fiand a wealth of spin-transfer-driven effects appearmagnetization dynamics of the ferromagnetic element. Thethe interpretation of these effects was laid in the 1990s by BSlonczewski (Berger, 1996; Slonczewski, 1996).


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3. Equation for spin transfer driven magnetization dynamics

The effect of spin transfer on magnetization dynamics can bquite independently of the details of the microscopic mresponsible for it, by adding an appropriate spin-transfer te

other magnetic torques present in the Landau-Lifshitz-Gilequation for the free-layer magnetization.

The effective field heff = gL/m, where gL (m; ha) is the nfree energy of the free layer, measured in units of0M2 s S

free-layer surface area). In the case where both shape aanisotropy have identical (ellipsoid-like) symmetry, the expressed as:

We previously mentioned that we are interested in situations


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We previously mentioned that we are interested in situationsand are quantities much smaller than unity. To the first or, becomes:

Where:


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4. Magnetization dynamics and dynamical system theory

The admissible types of response to the field and current:

Chaos is precluded

The only possible types of steady-state magnetization respoare:

Stationary modes associated with static solutions (fixed poi

Self-oscillations associated with periodic solutions (limit cyc


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5. The role of thermal fluctuations

The effect of thermal fluctuations on spin-transfer-driven magdynamics can be modeled by a method analogous to the one pby Brown for the study of thermally induced magnetization swsmall particles (Brown, 1963).


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6. Uniaxial symmetry

Uniaxial symmetry is realized when the anisotropy coefficientthat Dx = Dy = D and the external field is applied along the convenient to use spherical coordinates (, )to identify po

unit sphere: mx = sin cos , my = sin sin , mz = coexpressed in terms of (, ), both the system energy gpotential become functions of only. After dropping constant offsets, one finds:


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SPIN-TRANSFER-DRIVEN MAGNETIZATION DYN

GIORGIO

Istituto Nazionale di Ricerca Metrologica, T


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3.a. Outline

Outline

1. Abstrack

2. Introduction

3. Numerical Modeling

4. Modeling of the Thermal Effect


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1. Abstrack

In this chapter will be presented the numerical details ne

model the magnetization dynamics driven by a spin-polarize(SPC) of a ferromagnet in a confined system, spin valves, ortunnel junctions (MTJs).


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2. Introduction

A sufficiently large spin-polarized current (SPC) can apply a torque to

ferromagnet that is able to invert the magnetization of the ferromagnpersistent magnetic dynamics.1, 2 These behaviors have been exobserved in both spin valves (SVs)3 and magnetic tunnel junctions (Mdevices are composed of two ferromagnetic layers separated by a normthin insulator, respectively. One of the ferromagnetic layers (pinned orPL) is either thicker than the other (free layer, FL) or exchanged biaantiferromagnetic material.5, 6 The resistance of the device deperelative orientation of the magnetization of the ferromagnets; theresistance state when the magnetization of the two layers are align

state, PS) and a high resistance state when they are anti-aligned (antipAPS). This property is a key point in the design of magnetoresistive ranmemory (MRAM). A main application of a SPC is the possibility tomechanism for MRAM, in particular; from the technological point of vieshow promise as high-performance MRAM with respect to the SVs.


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Continue...

The FL is discretized considering cubic (or prismatic) cells (a

of discretization of a rectangular FL is shown in Fig. 1), the ensure enough precision in the solution according to thecriterion in micromagnetics which consist of using cell sizthan the exchange length of the material of the FL (e.g. 6 nmnm for Co) and big enough in order to define the magnetizat

nm).


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The numerical LLG

(LLGS) equation has to

each cell, its expression the following:

The numerical expression of the effectuniaxial magneto-crystalline aniso

computational cell11) is the following:

O i t ti t f th i


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One more interesting aspect of the micrpossibility to perform a study of thnonidealities of the shape of a sample wideal case. For example, Fig. 2 (botexample of a nonideal shape computed image, Fig. 2 (top) shows the shapsystematic study performed to determthe nonidealities of the shape of threversal reveals that the mechanism of iqualitatively depending on the nonidealities can either increase oswitching time


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4. Modeling of the Thermal Effect

The thermal field, Hth, is a random fluctuating 3D vector quan

given by:

where KB is the Boltzmann constant, Visthe volume of the computational cubiccell, t is the simulation time step, TS isthe true temperature of the sample, 16,18 and is a Gaussian stochasticprocess. The thermal field Hth satisfiesthe following statistical properties:

MICROMAGNETIC MODELING OF MAGNETIZATION DYNAMICS


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MICROMAGNETIC MODELING OF MAGNETIZATION DYNAMICS

BY SPIN-POLARIZED CURRENT: ANALYSIS OF NONCONFI

SYSTEMS

GIANCARLO CONSOLO,

Dipartimento di Fisica della Materia e Tecnolog

Faculty of Engineering, University of Messina,

LUIS LOPEZ

University of Salamanca, Departamento de Fi

de la Merced, 3700


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3.b. Outline

1. Abstrack

2. Introduction on nonconfined systems

3. Micromagnetic modelling of point-contact devices

4. Results


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1. Abstrack

We present a brief overview of the magnetization dynamics d

spin-polarized current in nonconfined ferromagnetic multilaa point-contact setup is used. The possibility to sustain oscillations in these systems could be employed in the current controlled microwave oscillators on nanometric attempt to reproduce the main experimental results by meamacrospin and micromagnetic models encounters many diffichave focused on the latter, summarizing the state-of-art anout the still unsolved methodological problems arising fromodeling.


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2. Introduction on nonconfined systems

It has been proved both experimentally1, 6, 9, 10 and theoretically

that the spin-transfer torque exerted by a spin polarized current (Smagnetic moment of a ferromagnet can produce persistent magnedynamics in the ferromagnet, which could be used for developingtechnological applications, such as oscillators and resonators.8 Difgeometries and materials have been proposed to explore this effereport we will focus on the point contact system where, differenclassical nanopillar structure (see the previous chapters by G. Fino

and M. Carpentieri et al. of this book), the current flows only throconfined region at the center of the structure, whereas the lateraldevice is about two orders of magnitude larger Such systems couldin current-controlled oscillators at RF frequency with very narrow (more than five times than in pillar devices).

3. Micromagnetic modeling of point contact devic


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The Model

Regarding the polarization function g(M(i, j, k), P,), which mostrength of the spin-transfer torque, we started from the exprderived by Slonczewski for a macrospin model7 which, in norterms, can be described as follows:

When considering this expression within a micromagnetic framework one could as

time and uniform in space value (g(m,p,) = c, u(m,p,) = 1) or, alternatively, allow fo

variation (g(m,p,) = u(m,p,), c=1).11 In our model, the efficiency value at time tis thcontact area of the efficiencies found evaluating locally at the previous computa

According to our simulations, these different interpretations of the efficiency fadifferences in both the trajectory of the average magnetization and the high harmonics

BOUNDARY CONDITIONS


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Another issue involves the choice of the boundary conditexchange field. As reported by Berkov et al.,5 the use oboundary conditions (PBC) does not represent the optimal sthree main reasons. First, PBC do not represent physical or properties. Second, an interference between waves is howedue to the waves traveling inwards coming from the neighimages. Third, in an implicit manner, the implementatioequivalent to the simulation of a matrix of point-contaapproach, NBCs have been implemented in the usual manner

where n is the direction normal to the boundaries.


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4. RESULTS

Results of simulations using a current I =8 mA and a constant

g(m, p, )=c=0.21 are shown in Fig. 1.


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The 3D trajectory followed by the avera

and a snapshot of the spatial magnetiza

are shown in Fig. 2. As reported in pr

magnetization in the FL precesses in a ne

around the direction of the external field.


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MICROMAGNETIC MODELLING OF MAGNETIZATION DYNAMICS DRIVEN

POLARIZED CURRENT: STABILITY DIAGRAMS AND ROLE OF THE NON S

EFFECTIVE FIELD CONTRIBUTIONS

MARIO CARPENTIERI, BRUNO

Dipartimento di Fisica della Materia e Tecnologie FisicFaculty of Engineering, Universit

Salita Sperone 31, 98166 M

Departamento de Fisica Aplicada, University of Salamanca, Plaza 37008 Sala


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3.c. Outline

1. Abstrack

2. Introduction of the magnetostatic coupling

3. Effect of the Classical Ampere Field

4. Analysis of Presistent Dynamics Processes


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1. Abstrack

The spin-polarized current can exert a torque on the magnetization and if it iscan induce reversal or even excite persistent dynamical regimes. Micromag

can be used to describe the general features of the magnetization dynamics coexistence of an applied field and a spin-polarized current. In particular, mcoupling (MC) between ferromagnets and also the classical Ampere field havinto account. A systematic study of the effect of these two contributions will The main results are that the MC always helps the switching from parallel statparallel state (APS) and, more precisely, the application of a current, which givswitching (PSAPS or vice versa), results in a faster process with MC thaDifferently, the role of the Ampere field depends on the physical and geometof the system under investigation and it has to be investigated in ea

simulations reveal a complex switching behaviour that involves highly inhmagnetization configurations with multiple domains. Lastly, in order to desbehaviour of the magnetization dynamics in these multilayer structures, sodynamical stability diagrams have been computed.


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2. Introduction of the magnetostatic cou

The theoretical demonstration by Slonczewski1, 2 that a spicurrent (SPC) flowing through a ferromagnetic conductor exerts aits magnetic moment opened new ways for manipulating madynamics. These experimental results are usually interpreted asseach magnetic layer is uniformly magnetized although some expclaimed that multiple domains and possibly domain wall motiinvolved.5, 8 This point is difficult to verify experimentally innanostructures, but it can be investigated by means of micmodelling.9, 10 The SPC is generating interest as an alternative to

the magnetic field for switching elements in Magnetic RandMemory (MRAM). The interaction between MC and Slonczewproduces more symmetric switching processes from PS to APversa, yielding approximately the same absolute values of criticashown by the experimental data.


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3. Influence of the magnetostatic couplin

Figure 1 (right panel) showabsolute value of theMCvespacer to the FL due to a PL o(c) nm of thickness, respecomponents of MC have zeroplay a crucial role in the magwill be shown by the micromprincipally due to the non-uthe structure. The non-unifchecked in Figure 1 (right panbetween the x componencomponents, respectively. Thdetains the greatest value (soy-axis has a smaller value along the z-axis has an interline). Naturally, in all cases,decrease with the distanparticular, the MC is able toPSAPS (see Fig. 2 left panother hand, the MC delays tfor short pulse of current, bthe critical current for the lon

4. Effect of the Classical Ampere Field


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The investigatedcircular multila(PL)/6 nm Cu/

with a radius oapplied an exand constant fieA/m) in order tthe magnetizatCo layer and negative currenA/cm2. In this c

field contributtrigger the swPSAPS transpassage occursaround 1 ns (panel, solid line

5. Analysis of Persistent Dynamics Processes


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The zone PS/APS is chanoisy oscillation of thebetween the stable PS andcharacteristic frequencies Fourier Transform (FFT) p

in this zone, neither ctelegraph noise were obright panel). Finally the reW presented characteriin the FFT (Fig. 4a right paself-oscillation of the magoscillations could be correspond to periodic soones found in uniformmodels,19 but the

computations show that, iare associated to a non-unoscillation involving the fodomains.

In order to check the effect o


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In order to check the effect othe magnetization dynamics shpanel) has been recomputed i(i) using a constant value of gP))(the maximum) and (ii) usP) = g(, P) constant including the angular depenany time t with the avermagnetization found at the pretime tt). The computed freshown in the right panel of observed how both the angdependence of the polarizatiothe presence of oscillatcharacteristic frequencies in Some of these modes, presecould be identified with

experimentally.8 This fact rmicromagnetic model incuniformities of MC, Ampere fiepolarization function can givoscillation modes without canisotropies or microstructure

magnetic nanostructures in modern technology_bab 1-3_cynthia sagta_3225111288

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