Finite Element Formalism for Micromagnetism

The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several possibilities to solve the complex Landau-Lifschitz-Gilbert equations numerically. Our method is based on a Galerkin-type finite element approach. We start with the dynamic Landau-Lifschitz-Gilbert equations, the associated boundary condition and the constraint on the magnetization norm. We derive the weak form required by the finite element method. This weak form is afterwards integrated on the domain of calculus. We compared the results obtained with our finite element approach with the ones obtained by a finite difference method. The results being in very good agreement, we can state that our approach is well adapted for 2D micromagnetic systems.Comment: Proceedings of conference EMF200

Chirality-induced asymmetric magnetic nucleation in Pt/Co/AlOx ultrathin microstructures

The nucleation of reversed magnetic domains in Pt/Co/AlO$_{x}$ microstructures with perpendicular anisotropy was studied experimentally in the presence of an in-plane magnetic field. For large enough in-plane field, nucleation was observed preferentially at an edge of the sample normal to this field. The position at which nucleation takes place was observed to depend in a chiral way on the initial magnetization and applied field directions. An explanation of these results is proposed, based on the existence of a sizable Dzyaloshinskii-Moriya interaction in this sample. Another consequence of this interaction is that the energy of domain walls can become negative for in-plane fields smaller than the effective anisotropy field.Comment: Published version, Physical Review Letters 113, 047203 (2014

Optical Switching in Tb/Co-Multilayer Based Nanoscale Magnetic Tunnel Junctions

Magnetic tunnel junctions (MTJs) are elementary units of magnetic memory devices. For high-speed and low-power data storage and processing applications, fast reversal by an ultrashort laser pulse is extremely important. We demonstrate optical switching of Tb/Comultilayer-based nanoscale MTJs by combining optical writing and electrical read-out methods. A 90 fs-long laser pulse switches the magnetization of the storage layer (SL). The change in magnetoresistance between the SL and a reference layer (RL) is probed electrically across the tunnel barrier. Single-shot switching is demonstrated by varying the cell diameter from 300 nm to 20 nm. The anisotropy, magnetostatic coupling, and switching probability exhibit cell-size dependence. By suitable association of laser fluence and magnetic field, successive commutation between high-resistance and low-resistance states is achieved. The switching dynamics in a continuous film is probed with the magneto-optical Kerr effect technique. Our experimental findings provide strong support for the growing interest in ultrafast spintronic devices.Comment: total pages 22, Total figure

Developpement d'un code de calcul micromagnetique 2D et 3D: Application a des systemes reels de types films, plots et fils

Hugues Dreysse, Martha Pardavi-Horvath, Andre Thiaville, Jean-Christophe Toussaint, Ursula EbelsThe magnetic behavior of lateral confined ferromagnetic systems is of great interest both from a fundamental and a technological point of view. The understanding of the effects induced by reducing the system sizes requires a combined experimental and theoretical study. The aim of this work is to develop specific numerical tools for the investigation of ferromagnetic systems based on micromagnetic modelling. A finites differences method is used for the evaluation of the energies and the fields describing the magnetic configuration of the system. The minimization procedure of the free energy includes the time integration of the Landau-Lifshitz-Gilbert equation. The improvement of the numerical precision, the enhancement of the stability of the integration scheme and the validation of the codes developed against standard problems as well as against experimental results, has been a permanent effort throughout this work. The flexibility of such a numerical approach allows us to investigate bi- and tri-dimensional, periodic and non-periodic systems. In particular, the details of the magnetization configuration of domain walls in Co thin films with in-plane or out-of-plane magnetocrystalline anisotropy have been obtained and analyzed as a function of the thickness of the film and the externally applied field. The 3D simulation studies of the cylindrical Co dots have established the limits of stability of different magnetic configurations depending on the dot sizes and the material parameters. Special attention has been given to the evolution of the vortex state and its stability under a perpendicular applied field. The tri-dimensional features of the domain walls in epitaxial Co wires with magnetocrystalline anisotropy parallel or perpendicular to the wire axis have been confirmed.Le comportement des systèmes magnétiques submicroniques suscite un vif intérêt, motivé par le progrès continu des techniques de nano-fabrication et entretenu par une multitude d'applications potentielles (mémoires non-volatiles). La compréhension des effets induits par le confinement de la taille latérale des systèmes magnétiques combine le micromagnétisme expérimental et numérique. L'objectif de ce travail est de développer des outils numériques appropriés à l'étude du magnétisme des structures de dimensions réduites, en utilisant la modélisation micromagnétique. L'approximation des différences finies est utilisée pour l'évaluation des énergies et des champs internes qui décrivent l'état du système. L'algorithme de la minimisation de l'énergie libre repose sur l'intégration temporelle de l'équation de Landau-Lifshitz-Gilbert. L'amélioration de l'approche numérique (la précision du calcul, la stabilité du schéma d'intégration) ainsi que sa validation à travers des problèmes test et des résultats expérimentaux représentent les premières étapes de nos travaux. Cette approche numérique flexible nous a permis d'étudier des systèmes bi- et tri-dimensionnels, périodiques et non-périodiques. Ainsi, les détails de la structure interne des parois de domaines dans des couches minces de Co à anisotropie magnétocristalline uniaxiale planaire ou perpendiculaire ont été obtenus et analysés en fonction de l'épaisseur de la couche et du champ externe appliqué. L'étude menée sur les plots cylindriques de Co nous a permis d'établir les limites de stabilité des différents états magnétiques en fonction de la taille latérale et des paramètres de matériau. Notamment l'état de type vortex, favorisé par la symétrie circulaire de l'objet, a été analysé pour un champ appliqué perpendiculairement au plan du plot. Le caractère tridimensionnel des parois de domaines dans des nanofils de Co épitaxiés à anisotropie magnétocristalline parallèle ou perpendiculaire à l'axe du fil a été mis en évidence

Developpement d'un code de calcul micromagnétique 2D et 3D (Application à des systèmes réels de types films, plots et fils)

Le comportement des systèmes magnétiques submicroniques suscite un vif intérêt, motivé par le progrès continu des techniques de nano-fabrication et entretenu par une multitude d'applications potentielles (mémoires non-volatiles). La compréhension des effets induits par le confinement de la taille latérale des systèmes magnétiques combine le micromagnétisme expérimental et numérique. L'objectif de ce travail est de développer des outils numériques appropriés à l'étude du magnétisme des structures de dimensions réduites, en utilisant la modélisation micromagnétique. L'approximation des différences finies est utilisée pour l'évaluation des énergies et des champs internes qui décrivent l'état du système. L'algorithme de la minimisation de l'énergie libre repose sur l'intégration temporelle de l'équation de Landau-Lifshitz-Gilbert. L'amélioration de l'approche numérique (la précision du calcul, la stabilité du schéma d'intégration) ainsi que sa validation à travers des problèmes test et des résultats expérimentaux représentent les premières étapes de nos travaux. Cette approche numérique flexible nous a permis d'étudier des systèmes bi- et tri-dimensionnels, périodiques et non-périodiques. Ainsi, les détails de la structure interne des parois de domaines dans des couches minces de Co à anisotropie magnétocristalline uniaxiale planaire ou perpendiculaire ont été obtenus et analysés en fonction de l'épaisseur de la couche et du champ externe appliqué. L'étude menée sur les plots cylindriques de Co nous a permis d'établir les limites de stabilité des différents états magnétiques en fonction de la taille latérale et des paramètres de matériau. Notamment l'état de type vortex, favorisé par la symétrie circulaire de l'objet, a été analysé pour un champ appliqué perpendiculairement au plan du plot. Le caractère tridimensionnel des parois de domaines dans des nanofils de Co épitaxiés à anisotropie magnétocristalline parallèle ou perpendiculaire à l'axe du fil a été mis en évidence.The magnetic behavior of lateral confined ferromagnetic systems is of great interest both from a fundamental and a technological point of view. The understanding of the effects induced by reducing the system sizes requires a combined experimental and theoretical study. The aim of this work is to develop specific numerical tools for the investigation of ferromagnetic systems based on micromagnetic modelling. A finites differences method is used for the evaluation of the energies and the fields describing the magnetic configuration of the system. The minimization procedure of the free energy includes the time integration of the Landau-Lifshitz-Gilbert equation. The improvement of the numerical precision, the enhancement of the stability of the integration scheme and the validation of the codes developed against standard problems as well as against experimental results, has been a permanent effort throughout this work. The flexibility of such a numerical approach allows us to investigate bi- and tri-dimensional, periodic and non-periodic systems. In particular, the details of the magnetization configuration of domain walls in Co thin films with in-plane or out-of-plane magnetocristallin anisotropy have been obtained and analyzed as a function of the thickness of the film and the externally applied field. The 3D simulation studies of the cylindrical Co dots have established the limits of stability of different magnetic configurations depending on the dot sizes and the material parameters. Special attention has been given to the evolution of the vortex state and its stability under a perpendicular applied field. The tri-dimensional features of the domain walls in epitaxial Co wires with magnetocristallin anisotropy parallel or perpendicular to the wire axis have been confirmed.STRASBOURG-Sc. et Techniques (674822102) / SudocSudocFranceF

Compact modeling of a magnetic tunnel junction based on spin orbit torque

International audienceHigh endurance, high speed, scalability, low voltage, and CMOS-compatibility are the ideal attributes of memories that any integrated circuit designer dreams about. Adding non-volatility to all these features makes the magnetic tunnel junctions (MTJs) an ultimate candidate to efficiently build a hybrid MTJ/CMOS technology. Two-terminal MTJs based on spin-transfer torque (STT) switching have been intensively investigated in literature with a variety of model proposals. Despite the attractive potential of the STT devices, the issue of the common writing/reading path decreases their reliability dramatically. A three-terminal MTJ based on the spin-orbit torque (SOT) approach represents a pioneering way to triumph over current two-terminal MTJs by separating the reading and the writing paths. In this paper, we introduce the first compact model, which describes the SOT-MTJ device based on recently fabricated samples. The model has been developed in Verilog-A language, implemented on Cadence Virtuoso platform and validated with Spectre simulator. For optimized simulation accuracy, many experimental parameters are included in this model. Simulations prove the capability of the model to be efficiently used to design hybrid MTJ/CMOS circuits. Innovative logic circuits based on the SOT-MTJ device, modeled in this paper, are already in progress

Non-linear mode interaction between spin torque driven and damped modes in spin torque nano-oscillators

International audienceThe influence of dynamic coupling in between magnetic layers of a standard spin torque nano-oscillator composed of a synthetic antiferromagnet (SyF) as a polarizer and an in-plane magnetized free layer has been investigated. Experiments on spin valve nanopillars reveal non-continuous features such as kinks in the frequency field dependence that cannot be explained without such interactions. Comparison of experiments to numerical macrospin simulations shows that this is due to non-linear interaction between the spin torque (STT) driven mode and a damped mode that is mediated via the third harmonics of the STT mode. It only occurs at large applied currents and thus at large excitation amplitudes of the STT mode. Under these conditions, a hybridized mode characterized by a strong reduction of the linewidth appears. The reduced linewidth can be explained by a reduction of the non-linear contribution to the linewidth via an enhanced effective damping. Interestingly, the effect depends also on the exchange interaction within the SyF. An enhancement of the current range of reduced linewidth by a factor of two and a reduction of the minimum linewidth by a factor of two are predicted from simulation when the exchange interaction strength is reduced by 30%. These results open directions to optimize the design and microwave performances of spin torque nano-oscillators taking advantage of the coupling mechanisms. (C) 2015 AIP Publishing LLC

Spin-orbit torque driven chiral magnetization reversal in ultrathin nanostructures

International audienceWe show that the spin-orbit torque induced magnetization switching in nanomagnets presenting Dzyaloshinskii-Moriya (DMI) interaction is governed by a chiral domain nucleation at the edges. The nucleation is induced by the DMI and the applied in-plane magnetic field followed by domain-wall propagation. Our micromagnetic simulations show that the dc switching current can be defined as the edge nucleation current, which decreases strongly with increasing amplitude of the DMI. This description allows us to build a simple analytical model to quantitatively predict the switching current. We find that domain nucleation occurs down to a lateral size of 25 nm, defined by the length scale of the DMI, beyond which the reversal mechanism approaches a macrospin behavior. The switching is deterministic and bipolar

Single-shot switching in Tb/Co-multilayer based nanoscale magnetic tunnel junctions

Magnetic tunnel junctions (MTJs) are elementary units of magnetic memory devices. For high-speed and low-power data storage and processing applications, fast reversal of the magnetization by an ultrashort laser pulse is extremely important. We demonstrate single-shot switching of Tb/Co-multilayer based nanoscale MTJs by combining the optical writing and the electrical read-out methods. A 90-fs-long laser pulse switches the magnetization of the storage layer (SL). The change in the tunneling magnetoresistance (TMR) between the SL and a reference layer (RL) is probed electrically across the oxide barrier. Single-shot switching is demonstrated by varying the cell diameter from 300 nm to 20 nm. The anisotropy, magnetostatic coupling, and switching probability exhibit cell-size dependence. By suitable association of laser fluence and magnetic field, successive commutation between high-resistance and low-resistance states is achieved. The nature of the magnetization reversal of both SL and RL in a continuous film is probed with a depth-resolved magneto-optical Kerr effect (MOKE) magnetometry. The ultrafast dynamics in the continuous full-MTJ stack is investigated with the time-resolved pump–probe technique. Our experimental findings provide strong support for the growing interest in ultrafast spintronic devices