Micromagnetic Simulation Of Domain Wall Dynamics In Magnetic Materials

In recent years,the domain-wall dynamics of magnetic materials is widely investigated in both experiments and theories,due to the potential applications in data storage and logic devices.How to control the domain-wall motion is a major focus of attention.There have been theoretical efforts with the quenched Edwards-Wilkinson(QEW)equation and the Monte Carlo simulation,to understand the depinning phase transition of the domain-wall motion.The QEW equation is a simple phenomenological model,where the domain wall is supposed to be described by a single-valued elastic string,and detailed microscopic structures and interactions of the materials are not concerned.The single-valued elastic string hardly captures the complex structure of the domain wall,for example,the overhangs and islands.The Monte Carlo method provides also only an artificial dynamics of the domain wall,typically for the Ising-like model.Both the QEW equation and the Ising model with the Monte Carlo method can not describe the orientations of the magnetic domains,the vortex structure,the spin-wave propagation,and the interactions of the spin wave with the domain-wall motion etc.The Landau-Lifshitz-Gilbert(LLG)equation is fundamental in the theoretical study of micromagnetics,and very important in understanding dynamical properties of magnetic materials,such as the domain-wall motion.In magnetic nanowires,the domain wall will propagate under the driving field and the spin wave will be generated.Driven by an external field,the Walker breakdown will occur in the domain-wall propagation.When the driving field is below the Walker breakdown threshold,the domain wall exhibits the stable Walker propagation,while above the threshold presents the retro-grade breathing mode.In the magnetic materials,the spin-transfer torque can effectively drive a domain wall to propagate along the wires.The propagation speed is sensitive to the microwave frequency.Therefore,a spin transfer torque can be motivated by the local alternating field to ma-nipulate the magnetic domain wall in nanowires,it is significant for application.The magnetic skyrmion has emerged as an active research topic in the recent decade,as it is a stable topolog-ical soliton anticipated to be a fundamental component in future magnetic data storage.In fact,the domain wall in nanowires is equivalent to the structure of the radial direction of skyrmion.It has been theoretically suggested that the skyrmion can be created and remain stable in magnetic nanodisks with the Dzyaloshinskii-Moriya interaction(DMI).And there are different topological number skyrmion under different conditions.In both experiments and theories,the skyrmionium which topological number equals 0 has been proved.In the first chapter,we introduce the genera-tion and the properties of skyrmionium.The depinning transition induced by defects in magnetic materials are widely investigated in both experiments and theories.There are various defects can induce the domain wall pinning such as notches,vacancies and quenched disorder.For the domain wall pinning induced by notches in a strip and quenched disorder in nanowires,for example,the depinning phase transition have been investigated,which looks like first-order one or crossover,presumably due to the relatively simple pinning mechanism.However,for the domain wall pinning induced by disorder such as random fields in thin film,the depinning phase transition is typically of second order,and the experiments clearly indicate the existence of such a dynamic transition in magnetic thin films.In our work,for the first time,based on LLG equation and the dynamic scaling form,numerical methods have been developed to detect the transition point and measure both the static and dynamic critical exponents.The results are compared with those of the QEW equation and Monte Carlo(MC)simulation of the Ising model.