Magnetic Logic Devices have the advantage of non-volatility, radiation hardness, scalability down to the sub-10nm range, and three-dimensional (3D) integration capability. Despite these advantages, magnetic applications for information processing remain limited. The main stumbling block is the high energy required to switch information states in spin-based devices. Recently, the spin transfer torque (STT) effect has been introduced as a promising solution. STT based magnetic tunneling junctions (MTJs), use a spin polarized electric current to switch magnetic states. They are theorized to bring the switching energy down substantially. However, the switching current density remains in the order of 1 MA/cm2 in current STT-MTJ devices, with the smallest device reported to date around 10nm. This current density remains inadequately high for enabling a wide range of information processing applications. For this technology to be competitive in the near future it is critical to show that it could be favorably scaled into the sub-10-nm range. This is an intriguing size range that currently remains unexplored. Nanomagnetic devices may display promising characteristics that can make them superior to their semiconductor counterparts. Below 10nm the spin physics from the vii surface become dominate versus those due to volume. The goal is to understand the size dependence versus the switching current.

The first part of this thesis is an experimental study of the spin-dependent transport in magnetic point contacts. Nano-contacts are produced micromechanically, by bringing a sharpened non-magnetic (N) tip into contact with a ferromagnetic (F) film. The magnetic and magneto-transport properties of such N/F nanocontacts are studied using transport spectroscopy, spanning the ballistic, diffusive, and thermal transport regimes. Single N/F interfaces can exhibit current driven magnetic excitations, which are often manifest as peaks in the differential resistance of a point contact defining the N/F interface. Our experiments show that such surface magnetization excitations, and thus the single-interface spin torques, are observed for diffusive and thermal transport regimes where the conduction electrons experience strong scattering near the N/F interface, and are absent for purely ballistic contacts. We conclude that the single-interface spin torque effect is due to impurity scattering at N/F interfaces. Single N/F interfaces can also exhibit hysteretic conductivity, which is qualitatively similar to the spin-valve effect found in F/N/F trilayers. Based on our measurements of N/F point contacts in the size range of 1-30 nm, we propose two mechanisms of the observed hysteresis. The first mechanism relies on a non-uniform spin distribution near the contact core and is magnetoelastic in origin. This interpretation is in good agreement with some of our experiments on larger point contacts as well as with a numerical micromagnetic model we have developed, where a stress-induced anisotropy creates a non-uniform, domain-wall-like spin distribution in the contact core. The second mechanism we propose is a surface effect which relies on a difference between the surface and interior spins in the ferromagnet in terms of their exchange and anisotropy properties. The surface spin-valve mechanism is in good agreement with the hysteretic magnetoresistance observed for our smallest contacts (~1 nm) and for contacts to nanometer thin ferromagnetic films. This interpretation means that the surface magnetization can be reduced and weakly coupled to the interior spins in the ferromagnet. We find that this surface spin layer can be affected by both external fields and the spin torque of a transport current. The surface magnetization can even form nano-sized spin vorticies at the interface. The nature of the magnetic excitations induced by by nominally unpolarized currents through single N/F interfaces was probed directly using microwave irradiation. We observed two characteristic high-frequency effects: a resonant stimulation of spin-wave modes by microwaves, and a rectification of off-resonant microwave currents by spin-wave nonlinearities in the point contact conductance. These experiments demonstrate that the effects observed are spin-dynamic in nature. In the second part of the thesis we study the spin-dynamics in spin-flop tunnel junctions used in toggle magnetic random access memory. Current pulses in the range of 100 ps used to excite the magnetic moments of the two coupled Py free layers into an oscillatory state, in both the antiparallel and scissor states of the cell. These oscillations are detected directly by measuring the junction resistance in real time with a 6 GHz measurement bandwidth. The junctions had the shape of an ellipse, with lateral size ranging from 350x420 to 400x560 nm. The optical and acoustical precession modes of the the spin-flop trilayer are observed in experiment, as expected from single-domain model. The experimental spectra contain additional features, which are explained using numerical micromagnetic simulations, as originating from magnetic state transitions between different magnetization states with non-uniform spin distributions. / QC 20100818

This thesis consists of three distinct components: (1) a test of Slocnzewski's theory of spin-transfer torque using the Boltzmann equation, (2) a comparison of macrospin models of spin-transfer dynamics in spin valves with experimental data, and (3) a study of spin-transfer torque in continuously variable magnetization. Slonczewski developed a simple circuit theory for spin-transfer torque in spin valves with thin spacer layer. We developed a numerical method to calculate the spin-transfer torque in a spin valve using Boltzmann equation. In almost all realistic cases, the circuit theory predictions agree well with the Boltzmann equation results. To gain a better understanding of experimental results for spin valve systems, current-induced magnetization dynamics for a spin valve are studied using a single-domain approximation and a generalized Landau-Lifshitz-Gilbert equation. Many features of the experiment were reproduced by the simulations. However, there are two significant discrepancies: the current dependence of the magnetization precession frequency, and the presence and/or absence of a microwave quiet magnetic phase with a distinct magnetoresistance signature. Spin-transfer effects in systems with continuously varying magnetization also have attracted much attention. One key question is under what condition is the spin current adiabatic, i.e., aligned to the local magnetization. Both quantum and semi-classical calculations of the spin current and spin-transfer torque are done in a free-electron Stoner model. The calculation shows that, in the adiabatic limit, the spin current aligns to the local magnetization while the spin density does not. The reason is found in an effective field produced by the gradient of the magnetization in the wall. Non-adiabatic effects arise for short domain walls, but their magnitude decreases exponentially as the wall width increases.

This thesis investigates the recently developed technique of spin-torque-driven ferromagentic resonance (ST-FMR). Contrary to conventional FMR techniques where the magnetodynamics are excited by torques on the magentic moments produced by microwave fields, ST-FMR uses the spin-transfer torque acting on a nanomagnet. Here we present two experiments which exploit ST-FMR in the standard AFM/FM/NM/FM exchange-biased spin valve (EBSV) structures, where the ferromagnetic (FM) layers are separated by a nonmagnetic (NM) spacer, and one ferromagnet is pinned with an antiferromagnetic (AFM) layer. In our experiments microwave currents are applied to a mechanical point contact between a sharpened Cu tip and a SV (IrMn/Py/Cu/Py) multilayer film. While most ST-FMR experiments require noncollinear orientation of FM-layer magnetizations, we studied ST-FMR in SVs above saturation, where the two FM layers have parallel magnetizations. The resulting magnetodynamics are detected electrically by a small rectified dc voltage, which appears across the structure during resonance. Studies of the resonance frequencies, amplitudes, line widths, and line shapes as a function of microwave power, microwave frequency, dc current and magentic field are presented. The results are analyzed in terms of ST-FMR and rectification based on GMR. However the origin of the observed voltage cannot be fully explained by the resistance changes which come from the giant magnetoresistance (GMR) effect of the spin valve. To investigate other sources of rectified dc voltages at resonance we have performed the second set of measurements with lithographically patterned pairs of (Py/Cu/Co/IrMn)-SV microstripes. These measurements also revealed a resonance in the rectified voltage at FMR frequencies, and showed additional structures which might be related to spin wave excitations. The observations can be tentatively attributed to additional rectification effects due to anisotropic magnetoresistance (AMR). The line pair structure allows us to use different measurement geometries to investigate the magnetodynamics in the SV. In this experiment FMR can either be excited by spin transfer or by a rf magnetic field created by the microwave current, depending on the used geometry. Qualitative studies of the FMR dependencies and characteristics are presented for different measurement geometries. / text

The manufacturing of nanocontact-based spin-torque oscillators (NC-STOs)has opened the door for spintronic devices to play a part as active microwaveelements. The NC-STO has the capability of converting a direct current intoa microwave signal, and vice versa, by utilizing the spin transfer torque (STT)in ferromagnetic multilayer systems. However, the high-frequency operation ofNC-STOs typically requires high magnetic fields and the microwave power theygenerate is rather limited. As a result, NC-STOs are not yet commercially used,and they require improvements in both material systems and device geometriesbefore they can find actual use in microwave applications. In order to improve and advance this technology, NC-STOs are requiredwith both different nanocontact (NC) sizes and geometries, and using differ- ent stacks of magnetic materials. This dissertation presents experimental in- vestigations into the manufacturing of such devices using different fabrication techniques and a number of different magnetic material stacks. Currently, the fabrication of NC-STOs is limited to advanced laboratories, because NC fabri- cation requires high-resolution lithography tools. In the present work, we have developed an alternative method of fabrication, which does not require such tools and has the capability of fabricating NC-STOs having one to hundreds of NCs in a variety of sizes, possibly  down to 20 nm. Devices fabricated with this method have shown mutual synchronization of three parallel-connected NCs, and pairwise synchronization in devices with four and five NCs. Furthermore, the present work demonstrates low-field operation (down to0.02 Tesla) of NC-STOs at a record high frequency of 12 GHz. This wasachieved by implementing multilayers with a perpendicular magnetic anisotropy(PMA) material in the free layer of the NC-STO. In addition, the fabricateddevices revealed an unexpected dynamic regime under large external appliedfield (above 0.4 Tesla). The new dynamic regime was found to be due to anentirely novel nanomagnetic dynamic object â a so-called magnetic droplet soliton,predicted theoretically in 1977 but not experimentally observed until now.Detailed experiments and micromagnetic simulations show that the droplet hasvery rich dynamics. Finally,  spin-torque-induced  transverse spin wave instabilities have beenstudied.  A NC-STO with  a material stack consisting of a single ferromag- netic metal sandwiched between two non-ferromagnetic metals was fabricated. Prior to this work, evidence of spin wave instabilities was reported as resis- tance switching in nanopillar- and mechanical point contact based STOs. In the present  work, the fabricated NC-STOs showed actual microwave  signals up to 3 GHz under zero applied field with strong current hysteresis. All  the fabricated NC-STOs open up new means of studying STT in different environ- ments, in order to resolve their current drawbacks for industrial applications. / <p>QC 20130527</p>

A ideia de transferência de spin, como forma de controle da magnetização, foi introduzida independentemente por Slonczewski e por Berger em 1996. Desde então, esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memorias magnéticas não voláteis e em osciladores de alta frequência. Devido _a complexidade do problema, a grande maioria das pesquisas teóricas sobre o assunto _e baseada em resultados numéricos. Porém, esses métodos podem dificultar a visualização das influências individuais dos diferentes termos envolvidos. Para isso, seria melhor a utilização de métodos analíticos, o que nos motiva a buscar por esses resultados. Nesse trabalho, apresentamos uma revisão sobre a teoria básica do efeito de transferência de spin e da dinâmica da magnetização. São revistas as principais equações que descrevem o comportamento da magnetização, as equações de Landau-Lifshitz e de Landau-Lifshitz-Gilbert, e comparadas suas componentes quando da inclusão do termo de transferência, analisando a melhor forma de incluir esse termo. É destacada a contribuição dada pelo termo de transferência na frequência de precessão da magnetização, que aparece ao se utilizar a equação de Landau-Lifshitz-Gilbert. Após essa revisão dos conceitos base, são buscadas soluções analíticas para a dinâmica da magnetização da camada livre de um sistema nanopilar em tricamada. Quatro casos são analisados: primeiro um sistema sem anisotropias e sem a inclusão do campo de Oersted, no segundo caso é incluído um termo de anisotropia e no terceiro novamente um sistema sem anisotropias, mas com a inclusão do campo de Oersted. Todas essas análises são feitas em uma aproximação de macrospin. Por último, uma aproximação de microspin com campo de Oersted. Nos três primeiros casos, é possível obter resultados analíticos e simular os resultados. São estimados o tempo de reversão e a frequência de precessão estável. / The idea of spin transfer as a way to control magnetization was introduced independently by Slonczewski and Berger in 1996. Since then, this e ect has been the subject of numerous studies, especially for potential applications in nonvolatile magnetic memories and high-frequency oscillators. Due to the complexity of the problem, the vast majority of theoretical research on this subject is based on numerical results. However, these methods might not display the in uences of individual terms involved. For this, it would be better to use analytical methods, which motivates us to search for these results. In this paper, we review the basic theory of spin transfer e ect and of magnetization dynamics. We review the main equations that describe the behavior of magnetization, the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations, and compare its components when inserting the spin torque term, analyzing the best way to include this term. The contribution of spin transfer on magnetization precession frequency, which appears when using the Landau-Lifshitz- Gilbert equation, is emphasized. After this review of basic concepts, analytical solutions for magnetization dynamics of the free layer in a tri-layer nanopillar are searched. Four cases are analyzed: rst a system without anisotropy and without the inclusion of the Oersted eld, in the second case an anisotropy term is considered and in the third case, again a system without anisotropy, but with the inclusion of Oersted eld. All these analisys are done in a macrospin approximation. Finally, a microspin approach including Oersted eld. In the rst three cases, it is possible to obtain analytical results and simulate these results. Reversal time and stable precession frequency values are estimated.

A ideia de transferência de spin, como forma de controle da magnetização, foi introduzida independentemente por Slonczewski e por Berger em 1996. Desde então, esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memorias magnéticas não voláteis e em osciladores de alta frequência. Devido _a complexidade do problema, a grande maioria das pesquisas teóricas sobre o assunto _e baseada em resultados numéricos. Porém, esses métodos podem dificultar a visualização das influências individuais dos diferentes termos envolvidos. Para isso, seria melhor a utilização de métodos analíticos, o que nos motiva a buscar por esses resultados. Nesse trabalho, apresentamos uma revisão sobre a teoria básica do efeito de transferência de spin e da dinâmica da magnetização. São revistas as principais equações que descrevem o comportamento da magnetização, as equações de Landau-Lifshitz e de Landau-Lifshitz-Gilbert, e comparadas suas componentes quando da inclusão do termo de transferência, analisando a melhor forma de incluir esse termo. É destacada a contribuição dada pelo termo de transferência na frequência de precessão da magnetização, que aparece ao se utilizar a equação de Landau-Lifshitz-Gilbert. Após essa revisão dos conceitos base, são buscadas soluções analíticas para a dinâmica da magnetização da camada livre de um sistema nanopilar em tricamada. Quatro casos são analisados: primeiro um sistema sem anisotropias e sem a inclusão do campo de Oersted, no segundo caso é incluído um termo de anisotropia e no terceiro novamente um sistema sem anisotropias, mas com a inclusão do campo de Oersted. Todas essas análises são feitas em uma aproximação de macrospin. Por último, uma aproximação de microspin com campo de Oersted. Nos três primeiros casos, é possível obter resultados analíticos e simular os resultados. São estimados o tempo de reversão e a frequência de precessão estável. / The idea of spin transfer as a way to control magnetization was introduced independently by Slonczewski and Berger in 1996. Since then, this e ect has been the subject of numerous studies, especially for potential applications in nonvolatile magnetic memories and high-frequency oscillators. Due to the complexity of the problem, the vast majority of theoretical research on this subject is based on numerical results. However, these methods might not display the in uences of individual terms involved. For this, it would be better to use analytical methods, which motivates us to search for these results. In this paper, we review the basic theory of spin transfer e ect and of magnetization dynamics. We review the main equations that describe the behavior of magnetization, the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations, and compare its components when inserting the spin torque term, analyzing the best way to include this term. The contribution of spin transfer on magnetization precession frequency, which appears when using the Landau-Lifshitz- Gilbert equation, is emphasized. After this review of basic concepts, analytical solutions for magnetization dynamics of the free layer in a tri-layer nanopillar are searched. Four cases are analyzed: rst a system without anisotropy and without the inclusion of the Oersted eld, in the second case an anisotropy term is considered and in the third case, again a system without anisotropy, but with the inclusion of Oersted eld. All these analisys are done in a macrospin approximation. Finally, a microspin approach including Oersted eld. In the rst three cases, it is possible to obtain analytical results and simulate these results. Reversal time and stable precession frequency values are estimated.

Le but de cette thèse est double: tester un solveur micromagnétique utilisant les éléments finis (feeLLGood), et étudier la dynamique d'aimantation pilotée par transfert de spin dans le but de comprendre des mesures expérimentales de plusieurs composants spintroniques. Deux schémas temporels implémentés dans le code ont été testés et comparés à d'autres solveurs, en particulier un code différences finies (ST_GL-FFT). Les comparaisons entre les résultats de simulations ont confimé la validité de feeLLGood, et ont montrés des artefacts numériques dans les simulations différences finies. D'autres pars, les simulations numériques ont permis des analyses approfondies de trois types de dispositifs spintroniques. (1) Des sauts en fréquences ont été étudiés dans l'oscillateur à transfert de spin planaire. Grâce à des techniques de cartographies spectrales , les sauts ont été attribués à l'excitation de modes non-linéaires. (2) Le diagramme d'état d'un oscillateur à transfert de spin composé d'un polariseur perpendiculaire et d'une couche libre planaire a été exploré, mettant en évidence plusieurs modes d'oscillation dépendant de l'état initial. De plus, le désaccord entre les simulations effectuées en différences finies et en éléments finis a montré l'effet d'un bord crennelé. (3) La commutation précessionelle induite par couple de transfert de spin a été simulée pour comprendre l'influence du champ de fuite du polariseur sur la probabilité de renversement. Un bon accord avec les mesures expérimentales sur STT-MRAM a été obtenu . / The goal of this PhD thesis has been two-fold: test a Finite Element micromagnetic solver (feeLLGood), and study spin-transfer-driven magnetisation dynamics to understand experimental measurements of several spintronic devices. Two time schemes implemented in the code have been benchmarked against other solvers, in particular against a Finite Difference code (ST_GL-FFT). Comparisons of the simulation results confirmed the accuracy of feeLLGood and showed artefacts in Finite Difference simulations. On the other hand, numerical simulations have allowed in-depth analyses of three types of spintronic device. (1) Frequency jumps have been studied in a planar Spin Torque Oscillator. Thanks to spectral mapping techniques, the jumps were shown to be linked to the excitation of non-linear modes. (2) The state diagram of a perpendicular-polariser/planar-free-layer Spin Torque Oscillator has been explored, showing various oscillation modes depending on the initial state. Moreover, discrepancy between Finite Difference and Finite Element simulations showed the effect of a staircase-like edge. (3) Precessional switching induced by spin transfer torque has been simulated to understand the influence of the polariser's stray field on the switching probability. A good agreement with experimental measurements of STT-MRAM has been found.

Depuis une quinzaine d’années, de nombreuses solutions différentes ont été proposés afin de modifier l’aimantations de matériaux sans aucun champ magnétique extérieur appliqué. La manipulation d’aimantation à moindre coût énergétique, de préférence à des échelles de temps ultracourtes, est devenu un enjeu fondamental avec des implications pour les technologies d’enregistrement magnétique et de nouvelles sortes de stockage. Sur ce chemin, le type d’interaction découverte par Stanciu et al. ouvre la voie à l’utilisation de la lumière comme moyen d’exciter et de sonder directement les matériaux magnétiques. La description des théories et modèles existants dans ce domaine permet de nous rendre attentif sur les différents paramètres impliqués par l’interaction des lasers ultrarapides et matériaux magnétiques. L’entrelacement spécifique des impulsions de chaleur et de moment angulaire propre aux lasers ultrarapides est mise en avant afin de discuter de leur rôle dans les phénomènes observés. Le délai des interactions responsables de l’état final de l’aimantation est abordé et notamment la manière dont celle-ci ont un impact sur la façon dont le système se stabilise après une excitation laser. En outre, nous nous sommes intéressés à la relation entre les paramètres matériels et l’état final de l’aimantation obtenue avec un laser ultrarapide. Grâce aux nombreuses classes de matériaux magnétiques existantes les paramètres magnétiques peuvent être ajustés dans une grande gamme de valeurs et de manière entièrement contrôlés. Notre installation d’imagerie magnétique est alors capable de sonder les caractéristiques optiques et la stabilité des domaines après l’excitation. Nous avons finalement démontré que le retournement optique dépendent de l’hélicité peut être observée non seulement dans un grand nombre de couches minces d’alliages de terre rare-métaux de transition (RE-TM) mais aussi dans une variété beaucoup plus large de matériaux, y compris les multicouches et hétérostructures de RE-TM. Nous montrons en outre que les hétérostructures ferrimagnétiques dépourvues de terres rares présentent également un retournement optique. Nous avons en plus développé le contrôle optique de multicouches ferromagnétiques dont des films granulaires actuellement explorés pour l’enregistrement magnétique ultra-haute densité de demain. Notre découverte montre que la manipulation de l’aimantation dans des matériaux magnétiques est un phénomène beaucoup plus général que précédemment suspecté et peut avoir un impact majeur sur l’enregistrement magnétique et le stockage de l’information grâce à l’intégration nouvelle de ce type de contrôle optique dans des bits ferromagnétiques / The possibilities of modifying magnetization without applied magnetic fields have attracted growing attention over the past fifteen years. The low-power manipulation of magnetization, preferably at ultrashort timescales, has become a fundamental challenge with implications for future magnetic information memory and storage technologies. In particular the interplay of laser and magnetism recently discovered by Stanciu et al. opens up new way for light to be used as an excitation and a probe of magnetic materials. A description of the current models and frameworks developed in the field requires a careful look at the different parameters involved through the interaction of ultrafast lasers and magnetic materials. The specific and complex interplay between heat and angular momentum transfer is highlighted in order to discuss the role of each of them in the phenomena observed. The timescales of the different interactions responsible for the final state of magnetization are presented and will impact the way the system recovery after a laser excitation. Besides we were interested in exploring the relation between the material parameters such as anisotropy, ordering temperature and exchange coupling on the final state of magnetization obtained with a laser. Indeed thanks to the many different magnetism classes existing the magnetic parameters can be tuned widely and in a controlled manner. Our imaging setup then is able to probe the optical characteristics and domain stability after the laser excitation. We finally demonstrated that all-optical helicity-dependent switching (AO-HDS) can be observed not only in selected rare earth-transition metal (RE-TM) alloy films but also in a much broader variety of materials, including RE-TM alloys, multilayers and heterostructures. We further show that RE-free Co-Ir-based synthetic ferrimagnetic heterostructures designed to mimic the magnetic properties of RE-TM alloys also exhibit AO-HDS. We further developed the optical control of ferromagnetic materials ranging from magnetic thin films to multilayers and even granular films being explored for ultra-high-density magnetic recording. Our finding shows that optical control of magnetic materials is a much more general phenomenon than previously assumed and may have a major impact on data memory and storage industries through the integration of optical control of ferromagnetic bits

A ideia de transferência de spin, como forma de controle da magnetização, foi introduzida independentemente por Slonczewski e por Berger em 1996. Desde então, esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memorias magnéticas não voláteis e em osciladores de alta frequência. Devido _a complexidade do problema, a grande maioria das pesquisas teóricas sobre o assunto _e baseada em resultados numéricos. Porém, esses métodos podem dificultar a visualização das influências individuais dos diferentes termos envolvidos. Para isso, seria melhor a utilização de métodos analíticos, o que nos motiva a buscar por esses resultados. Nesse trabalho, apresentamos uma revisão sobre a teoria básica do efeito de transferência de spin e da dinâmica da magnetização. São revistas as principais equações que descrevem o comportamento da magnetização, as equações de Landau-Lifshitz e de Landau-Lifshitz-Gilbert, e comparadas suas componentes quando da inclusão do termo de transferência, analisando a melhor forma de incluir esse termo. É destacada a contribuição dada pelo termo de transferência na frequência de precessão da magnetização, que aparece ao se utilizar a equação de Landau-Lifshitz-Gilbert. Após essa revisão dos conceitos base, são buscadas soluções analíticas para a dinâmica da magnetização da camada livre de um sistema nanopilar em tricamada. Quatro casos são analisados: primeiro um sistema sem anisotropias e sem a inclusão do campo de Oersted, no segundo caso é incluído um termo de anisotropia e no terceiro novamente um sistema sem anisotropias, mas com a inclusão do campo de Oersted. Todas essas análises são feitas em uma aproximação de macrospin. Por último, uma aproximação de microspin com campo de Oersted. Nos três primeiros casos, é possível obter resultados analíticos e simular os resultados. São estimados o tempo de reversão e a frequência de precessão estável. / The idea of spin transfer as a way to control magnetization was introduced independently by Slonczewski and Berger in 1996. Since then, this e ect has been the subject of numerous studies, especially for potential applications in nonvolatile magnetic memories and high-frequency oscillators. Due to the complexity of the problem, the vast majority of theoretical research on this subject is based on numerical results. However, these methods might not display the in uences of individual terms involved. For this, it would be better to use analytical methods, which motivates us to search for these results. In this paper, we review the basic theory of spin transfer e ect and of magnetization dynamics. We review the main equations that describe the behavior of magnetization, the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations, and compare its components when inserting the spin torque term, analyzing the best way to include this term. The contribution of spin transfer on magnetization precession frequency, which appears when using the Landau-Lifshitz- Gilbert equation, is emphasized. After this review of basic concepts, analytical solutions for magnetization dynamics of the free layer in a tri-layer nanopillar are searched. Four cases are analyzed: rst a system without anisotropy and without the inclusion of the Oersted eld, in the second case an anisotropy term is considered and in the third case, again a system without anisotropy, but with the inclusion of Oersted eld. All these analisys are done in a macrospin approximation. Finally, a microspin approach including Oersted eld. In the rst three cases, it is possible to obtain analytical results and simulate these results. Reversal time and stable precession frequency values are estimated.