We study current-induced domain wall dynamics in a thin ferromagnetic nanowire. We derive the effective equations of domain wall motion, which depend on the wire geometry and material parameters. We describe the procedure to determine these parameters by all-electric measurements of the time-dependent voltage induced by the domain wall motion. We provide an analytical expression for the time variation of this voltage. Furthermore, we show that the measurement of the proposed effects is within reach with current experimental techniques. We also show that a certain resonant time-dependent current moving a domain wall can significantly reduce the Joule heating in the wire, and thus it can lead to a novel proposal for the most energy efficient memory devices. We discuss how Gilbert damping, non-adiabatic spin transfer torque, and the presence of Dzyaloshinskii-Moriya interaction can effect this power optimization. Furthermore, we propose a new nanodot magnetic device. We derive a specific time-dependent current that is needed to switch the magnetization of the nanodot the most efficiently.

The domain wall dynamics is used in many spintronic devices based on the uniaxial ferromagnetic wires to transport and store information. Therefore, the domain wall velocity is one of the main parameters that determine the operation speed of these devices. Recently, a big attention is being paid to amorphous glass-coated microwires due to the very high domain wall velocities that reach up to 20 km/s. In this work, the fast domain wall propagation in amorphous glass-coated microwires was found in the presence of two main factors: (i) relatively low magnetic anisotropy, (ii) complex geometry of magnetic anisotropies given by internal distribution of mechanical stresses. The domain wall dynamics was examined in amorphous glass-coated microwires of reduced diameter down to 1 μm. It was shown, that the domain wall dynamics in these wires is the same as in wires of bigger diameter. It proves that the high domain wall velocities in microwires are not the effect of microwire diameter value. The direct observation of the surface domain wall structure by use of MOKE microscope confirmed that the domain wall is inclined relatively to the main axis. A new method for magneto-optical observation of the samples with cylindrical geometry was proposed. The inclined structure of the domain wall was found to be partially responsible for the high apparent domain wall velocity measured by the Sixtus-Tonks method in microwires.

La dynamique des paroi de domaine est utilisée dans de nombreux dispositifs de spintronique basés sur des micro et nanofils magnétiques pour la transmission et le stockage de l'information. La vitesse de la paroi de domaine est donc un des paramètres qui déterminent la vitesse de fonctionnement de ces dispositifs. Actuellement, un accent considérable est mis sur la compréhension de l'origine des grandes vitesses parois de domaines dans les microfils, qui peuvent atteindre 20 km/s. Dans ce travail, des fortes vitesses de parois ont été trouvées en présence de deux principaux facteurs: (i) une valeur relativement faible de l'anisotropie magnétique, et (ii) une distribution complexe de l'anisotropie magnétique due aux contraintes internes. En outre, la dynamique d'une paroi de domaine a été étudiée pour les échantillons à diamètre réduit, jusqu'à 1 μm. Il a été démontré que la dynamique d'une paroi de domaine est la même que dans les échantillons plus épais, ce qui confirme que les vitesses élevées ne sont pas seulement liées à la taille des microfils. L'observation directe de la structure de surface des parois de domaines par microscopie MOKE confirmé la forme de la paroi de domaine inclinée par rapport à l'axe du fil. Une nouvelle méthode a été proposée pour effectuer des observations sur des échantillons cylindriques. La structure inclinée de la paroi de domaine est jugée en partie responsable des valeurs élevées de vitesse apparente des parois de domaines mesurées par la méthode Sixte-Tonks dans ces microfils. / The domain wall dynamics is used in many spintronic devices based on the uniaxial ferromagnetic wires to transport and store information. Therefore, the domain wall velocity is one of the main parameters that determine the operation speed of these devices. Recently, a big attention is being paid to amorphous glass-coated microwires due to the very high domain wall velocities that reach up to 20 km/s. In this work, the fast domain wall propagation in amorphous glass-coated microwires was found in the presence of two main factors: (i) relatively low magnetic anisotropy, (ii) complex geometry of magnetic anisotropies given by internal distribution of mechanical stresses. The domain wall dynamics was examined in amorphous glass-coated microwires of reduced diameter down to 1 μm. It was shown, that the domain wall dynamics in these wires is the same as in wires of bigger diameter. It proves that the high domain wall velocities in microwires are not the effect of microwire diameter value. The direct observation of the surface domain wall structure by use of MOKE microscope confirmed that the domain wall is inclined relatively to the main axis. A new method for magneto-optical observation of the samples with cylindrical geometry was proposed. The inclined structure of the domain wall was found to be partially responsible for the high apparent domain wall velocity measured by the Sixtus-Tonks method in microwires. / Dynamika doménovej steny sa používa v mnohých spintronických zariadeniach na báze tenkých magnetických drôtoch na prenos a uchovávanie informácie. Rýchlosť doménovej steny je preto jedným z parametrov, ktoré určujú operačnú rýchlosť týchto zariadení. V súčasnosti je kladený značný dôraz na pochopenie pôvodu veľkých rýchlostí doménovej steny v mikrodrôtoch, kde rýchlosti dosahujú až 20 km/s. Veľké rýchlosti doménovej steny v mikrodrôtoch boli v tejto práci nájdené v prítomnosti dvoch faktorov: (i) relatívne nízka hodnota magnetickej anizotropie a (ii) zložitá distribúcia magnetických anizotropií daných vnútornými pnutiami. Navyše, dynamika doménovej steny bola študovaná aj na vzorkách s redukovaným priemerom až do 1 μm. Bolo ukázané, že dynamika doménovej steny je v týchto drôtoch rovnaká ako je tomu v hrubších vzorkách, čo potvrdzuje, že vysoké rýchlosti nie sú len efektom rozmeru amorfných, sklom potiahnutých mikrodrôtoch. Priame pozorovania povrchovej štruktúry doménovej steny pomocou MOKE mikroskopu potvrdili naklonený tvar doménovej steny vzhľadom na os drôtu. Bola navrhnutá nová metóda na vykonávanie magneto-optických pozorovaní valcových vzoriek. Naklonený tvar doménovej steny bol nájdený ako jeden z faktorov umožňujúcich zdanlivo veľké rýchlosti doménovej steny meraných Sixtusovou-Tonkosvou metódou na mikrodrôtoch.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Amorphous glass-coated microwires are materials with soft magnetic properties suitable for various technological applications, mainly magnetic sensors. One of the outstanding properties of microwires with positive magnetostriction is the magnetic bi-stability, that means, the inversion of the magnetization is done by one magnetic domain wall displacement along the wire. In this work it was developed a system to determine the domain wall speed in microwires and studied its dynamic. Particularly, were studied the relation between domain wall speed, magnetic field and magnetoelastic anisotropy in Fe77;5Si7;5B15 microwires. It has been verified that the main source of domain wall damping is the eddy-currents and spin relaxation, both with a strong relation with the magnetoelastic energy. The magnetoelastic energy is changed by the axial applied stress which, by its time, modifies the damping mechanisms. It was also verified that the domain wall damping present different behavior at low (mainly eddy-currents) and high applied stress (spin relaxation). / Microfios amorfos recobertos por vidro são materiais com propriedades magnéticas macias adequadas para várias aplicações tecnológicas, especialmente sensores magnéticos. Uma das propriedades interessantes dos microfios com magnetostricção positiva é a biestabilidade magnética, cuja inversão da magnetização se dá pela propagação de uma parede de domínio ao longo do material. Nesse trabalho foi desenvolvido um sistema para a determinação da velocidade de uma parede de domínio em microfios e estudada a dinâmica dessa parede. Em particular, foram estudadas as relações entre velocidade da parede de domínio, campo magnético e anisotropia magnetoelástica em microfios amorfos com composição nominal de Fe77;5Si7;5B15. Verificouse que os principais mecanismos de amortecimento das paredes de domínio têm origem nas microcorrentes de Foucault (eddy-currents) e na relaxação de spins, ambas com forte dependência da energia magnetoelástica. A energia magnetoelástica varia com a aplicação de uma tensão axial ao fio influenciando os mecanismos de amortecimento. Verificou-se também que a variação do amortecimento efetivo das paredes de domínio com a tensão tem comportamentos distintos a baixas (eddy-currents) e altas tensões aplicadas (relaxação de spin).

The static and dynamic properties of spin distributions within domain walls(DWs) confined by Permalloy nanowire conduits are investigated by numerical simulations and high-speed magneto-optic polarimetry. Phase boundaries and critical points associated with DW spin distributions of various topologies are accurately determined using high-performance computing resources. Field-driven mobility curves that characterize DW propagation velocities in 20 nm thick nanowires are calculated with increasing the width of nanowires. Beyond the simple one-dimensional solution, the simulations reveal the four distinct dynamic modes. Oscillations of the field-driven DW velocity in Permalloy nanowires are observed above the Walker breakdown condition using high-speed magneto-optic polarimetry. A one-dimensional analytical model and numerical simulations of DW motion and spin dynamics are used to interpret the experimental data. Velocity oscillations are shown to be much more sensitive to properties of the DW guide structure (which also affect DW mobility) than the DW spin precessional frequency, which is a local property of the material. Transverse bias field effects on field-driven DW velocity are studied experimentally and numerically. DW velocities and spin configurations are determined as functions of longitudinal drive field, transverse bias field, and nanowire width. For a nanowire that supports vortex wall structures, factor of ten enhancements of the DW velocity are observed above the critical longitudinal drive-field (that marks the onset of oscillatory DW motion) when a transverse bias field is applied. The bias-field enhancement of DW velocity is explained by numerical simulations of the spin distribution and dynamics within a propagating DW that reveal dynamic stabilization of coupled vortex structures and suppression of oscillatory motion in the nanowire conduit resulting in uniform DW motion at high speed. Current-driven and current-assisted field-driven domain wall dynamics in ferromagnetic nanowires have thermal effects resulting from Joule heating, which make difficult to separate the spin-torque effects on DW displacements. To understand the thermal effects on DW dynamics, the temperature dependence of field-driven DW velocity is explored using high-bandwidth scanning Kerr polarimetry. Walker critical fields are decreased with increasing temperature and temperature-induced dynamic mode changes are observed. The results show that Joule heating effects are playing an important role in current-driven/current-assisted field-driven DW dynamics. / text

Dans les dispositifs actuels de sauvegarde de données, les bits d'informations sont stockées sous la forme de paroi de domaines dans une couche mince, voire des media "patternés". Le support reste donc 2D. De nos jours, la densité de stockage tend vers une valeur maximale qu'il est difficile de dépasser pour des raisons fondamentales et technologiques. Ainsi, récemment des efforts ont été réalisés pour développer des dispositifs 3D qui allient la polyvalence de la mémoire RAM solide avec un coût comparable à celui des disques durs actuels.Un nouveau concept théorique particulièrement intéressant pour une mémoire magnétique en 3D a été proposé en 2004 par S. Parkin et al.. Cette mémoire de type registre à décalage est constituée d'un réseau de nanofils magnétiques verticaux avec une section transversale cylindrique ou bien rectangulaire. Dans ce nouveau type de mémoire, les bits sont codés sous forme d'une série de parois de domaine. Cette dernière peut être déplacée vers une tête de lecture intégrée par des impulsions de courant polarisé en spin de quelques nanosecondes.Les parois de domaines magnétiques dans des nanofils cylindriques ont suscité l'intérêt de la communauté scientifique en raison de leur application possible dans un dispositif fonctionnel ainsi qu'en raison de nouvelles propriétés intéressantes qui résultent du confinement géométrique des parois. A ce jour, seules quelques études expérimentales sur de telles parois de domaines existent. Elles ont mis en évidence la difficulté de maîtriser la propagation de parois dues à des forts effets de piégeage. Jusqu'à présent, l'origine microscopique de ce piégeage n'a été que partiellement comprise. On s'attend à ce qu’indépendamment de la qualité géométrique du fil, la microstructure du matériau puisse jouer un rôle non négligeable.Dans le cadre du projet européen FP7 m3D, l'objectif de mon travail de thèse a été d'étudier la propagation des parois de domaine dans des nanofils cylindriques avec des modulations de diamètre. L'énergie de ces parois de domaine augmentant avec le diamètre du fil, on s'attend à ce que des excroissances (ou des constrictions) agissent comme des barrières d'énergie artificielles (respectivement puits). Par conséquent, une propagation de paroi de domaine contrôlée via la géométrie du fil semble possible.La première partie de mon travail concerne l'optimisation des matériaux. Des fils d'un alliage de NiCo (diamètre de 100-200nm et longueur de plusieurs dizaines de micromètres) avec deux géométries distinctes ont été fabriqués par électrodéposition en collaboration avec le groupe du Prof. J. Bachmann à l' Université d'Erlangen. Pour chaque géométrie, j'ai exploré l'effet de la composition de l'alliage ainsi que d'un recuit sur la microstructure du matériau. Par la suite, la propagation des parois de domaine dans des nanofils individuels a été étudiée sous l'influence d'un champ magnétique quasi-statique ou d'une impulsion de champ magnétique avec une durée d'impulsion de l'ordre de la nanoseconde. Dans la dernière partie de ma thèse, j'ai effectué des simulations micromagnétiques complémentaires pour étudier l'effet de la géométrie des modulations sur le piégeage de ces parois de domaine magnétiques. / In all current data storage devices, the information bits are stored in form of domain walls in a thin film or in patterned media on a two-dimensional surface . Within the next decade, further increase of the storage density in these devices is expected to come to a halt due to several fundamental and technological issues. Thus there have recently been efforts to develop three-dimensional devices combining the versatility of solid state RAM with the cost efficiency of common hard disk drives.A particularly interesting theoretical concept for a three-dimensional magnetic memory has been proposed in 2004 by S. Parkin et al. . Their racetrack memory consists of a vertical array of magnetic nanowires with either cylindrical or rectangular cross section. The bits are encoded in a series of up to 100 domain walls per wire. Using nanosecond spin polarized current pulses these walls are shifted past an integrated read head.Magnetic domain walls in cylindrical nanowires have raised the interest of the scientific community due to their possible application in a functional device as well as due to exciting new properties which arise from the geometric confinement. Up to date, only a few pioneering experimental studies on such domain walls exist. They indicate strong pinning effects preventing a deterministic domain wall propagation. So far the microscopic origin of this pinning has only partially been understood. It is expected however that beside the wire geometry the material microstructure may play a considerable role.Situated within the framework of the European FP 7 project m3D, the objective of my work has been to investigate the domain wall propagation in cylindrical nanowires with diameter modulations by means of magnetic force microscopy and micromagnetic simulation. As the domain wall energy increases with the wire diameter, protrusions (resp. notches) are expected to act as an artificial energy barrier (resp. well). Consequently, a deterministic domain wall propagation controlled via the wire geometry seems possible.A first part of my work concerns material optimization. For this, NiCo alloy wires (100-200nm diameter and multiple tens of micrometers in length) with two distinct geometries have been fabricated by template assisted electrodeposition (Chemist collaborators at Univ. Erlangen, Prof. J.Bachmann). I have then explored the impact of the alloy composition as well as of possible post-fabrication annealing on the material microstructure. Subsequently, domain wall propagation in individual nanowires has been investigated under the influence of either a quasistatic magnetic field or a nanosecond magnetic field pulse. In addition I have performed complementary micromagnetic simulations to study the effect of the modulation geometry on the domain wall pinning.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, we have measured the domain wall velocity in the low field regime and studied the domain wall dynamics in Joule-annealed amorphous glass-covered microwires with positive magnetostriction. Such microwires are known to present magnetic bi-stability when axially magnetized. In order to measure of the single domain wall dynamics under different conditions, an electrical current was applied to the wire simultaneously to the mechanical stress and driving magnetic field. We have observed that the applied stress decreases the domain wall mobility. When the dc current is applied to the sample, an increase or a decrease is observed on the axial domain wall mobility, depending on the current direction. When we have treated the orthogonal motion of the domain wall, the current influence is not detected. On the other hand, it was verified a modification on the domain wall length. It was also observed a change in the domain wall shape from conical to parabolic one. These results are explained in terms of the change in the magnetic energy promoted by the additional Oersted field which, by its time, modifies the length and shape of the conical domain wall, in such a way that the orthogonal domain wall velocity is not changed by the applied current. / Nesse trabalho, foi medida a velocidade de paredes de domínios em regime de baixos campos e estudada a dinâmica dessas paredes em microfios amorfos recobertos por vidros com magnetostricção positiva tratados via efeito Joule. Tais microfios são conhecidos por apresentar biestabilidade magnética quando axialmente magnetizados. A fim avaliar a dinâmica de uma única parede de domínio sob diferentes condições, corrente elétrica DC foi aplicada simultaneamente a tensões mecânicas e campo magnético externo. Foi verificado que quando uma tensão mecânica externa é aplicada, a mobilidade da parede de domínio diminui. Já quando a corrente foi aplicada na amostra, um aumento ou decréscimo da mobilidade axial da parede foi observado, dependendo do sentido da corrente aplicada. Quando foi tratado da velocidade ortogonal da parede de domínio, não foi observada influência da corrente. Por outro lado, foi verificado uma modificação no comprimento da parede de domínios. Além disto, foi observado uma mudança na forma da parede de domínio, passando de um formato cônico para parabólico. Os resultados são explicados em termos da mudança na energia magnética promovida pelo campo de Oersted, gerado pela corrente aplicada, que por sua vez modifica o comprimento e a forma da parede de domínio sem que a velocidade ortogonal da parede de domínio seja alterada pela corrente aplicada.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Barkhausen noise (BN) corresponds to the voltage pulses induced in a sensing coil wound around a ferromagnetic material submitted to a variable magnetic field. It is related to the irregular motion of the domain walls (DWs) in a disordered magnetic material. Due to its stochastic character, most of the studies aim to explain the BN statistical properties. The statistical functions are, in general, well described by a power-law behavior with cutoff, whose exponents and cutoffs can be compared with the predictions obtained with theoretical models. Interestingly, statistical properties seem to be independent of microscopic and macroscopic details but controlled by a few general properties, as the system dimensionality and range of the relevant interactions governing the DWs dynamics. For bulk materials, there is a well established and consistent interpretation for the BN statistical properties, including the distributions of jump sizes and durations, average size vs. duration and power spectrum, which are related to the exponents t, a, 1=(snz) and J, respectively. In this case, the results clearly indicate that bulk samples present an essentially three-dimensional magnetic behavior and the exponents can be grouped in two distinct universality classes, according the range of interactions governing the DWs dynamics. For ferromagnetic films, the statistical properties are not so well studied due to experimental and theoretical difficulties and most of the experimental results reported so far make use of magneto-optical techniques, which restrict the analysis to the distributions of sizes. In all cases, the reported exponents for films are smaller than that obtained for bulk samples, indicating a possible two-dimensional magnetic behavior. Due to the insufficient amount of experimental data, the structural character and film thickness influence on the exponents was not observed and a complete comprehension of the DWs dynamics in films is still lacking. In this work, we report BN experimental results obtained with the classical inductive method in policrystalline and amorphous ferromagnetic films with thickness in the range 10 - 1000 nm. We investigate the BN statistical properties in order to understand the effects of the interplay between the system dimensionality and the range of the relevant interactions governing the DWs and magnetization dynamics. In particular, we perform an extended statistical analysis which includes the distributions of jump sizes and durations, average size vs. duration curve, power spectrum and the average shape of the Barkhausen jump, reported for the first time for films. The results show evidence of a three to two-dimensional crossover in the DWs dynamics as the film thickness is decreased. Also, the effect of the range of interactions governing the DWs dynamics in this range of thickness is observed, indicating the same two distinct universality classes observed for bulk materials. Through these results, we provide experimental evidence to the validity of different three and two-dimensional heoretical models for DWs dynamics. / O ruído Barkhausen (BN) corresponde aos pulsos de tensão detectados por uma bobina sensora enrolada em torno de um material ferromagnético, quando submetido a um campo magnético variável. O ruído é produzido por mudanças súbitas da magnetização, principalmente devido ao movimento irregular das paredes de domínio (DWs) em um meio magnético desordenado. Devido ao seu caráter estocástico, grande parte dos estudos visa explicar as propriedades estatísticas do ruído. As funções estatísticas são, em geral, bem descritas por leis de potência com cutoff , cujos expoentes e valores de cutoff podem ser comparados com valores obtidos teoricamente. Como ponto interessante, as propriedades estatísticas parecem ser independentes dos detalhes microscópicos e macroscópicos, sendo dependentes de apenas algumas propriedades gerais, como a dimensionalidade do sistema e o alcance das interações que governam a dinâmica de DWs. Para materiais bulk , há uma interpretação robusta e bem estabelecida para as propriedades estatísticas do ruído, incluindo as distribuições de área e duração dos saltos, área média do salto vs. duração e espectro de potência, que estão relacionados com os expoentes t, a, 1=(snz) e J, respectivamente. Neste caso, os resultados claramente indicam que amostras bulk apresentam um comportamento magnético essencialmente tri-dimensional e que os expoentes podem ser agrupados em duas classes de universalidade distintas, de acordo com o alcance das interações que governam a dinâmica de DWs. Para filmes ferromagnéticos, as propriedades estatísticas não são tão bem estudadas devido a dificuldades teóricas e experimentais e devido ao fato de que a maioria dos resultados experimentais publicados até o momento, obtidos através de técnicas magneto-ópticas, restringem a análise apenas à distribuição de área dos saltos. Em todos os casos, os expoentes obtidos para filmes são menores do que os obtidos para amostras bulk , indicando um possível comportamento magnético bi-dimensional. No entanto, devido à insuficiente quantidade de dados experimentais, a influência da espessura do filme e do caráter estrutural sobre os expoentes ainda não foi observada e uma compreensão completa da dinâmica de DWs em filmes ainda não foi obtida. Neste trabalho, são apresentados resultados experimentais de BN obtidos, através do tradicional método indutivo, em filmes ferromagnéticos policristalinos e amorfos, com espessuras no intervalo de 10 - 1000 nm. Neste caso, as propriedades estatísticas do ruído são investigadas com o objetivo de compreender os efeitos da dimensionalidade do sistema e do alcance das interações sobre os expoentes e sobre a dinâmica de DWs em filmes. Em particular, foi realizada uma vasta e sistemática análise estatística, envolvendo distribuições de amplitude, área e duração dos saltos, área média do salto vs. duração, espectro de potência e a forma média do salto Barkhausen, pela primeira vez obtida para filmes. Os resultados mostram evidências experimentais de um crossover dimensional da dinâmica de DWs à medida que a espessura do filmes é reduzida. Também, o efeito do alcance das interações sobre a dinâmica de DWs em filmes é observado, indicando a existência das mesmas duas classes de universalidade observadas para materiais bulk . Deste modo, os expoentes medidos fornecem evidências experimentais para a validade de diferentes modelos tri e bi-dimensionais para a dinâmica de DWs.