Numerical Simulation Of Domain Wall Dynamics In Two-dimensional Magnets

In recent years, the dynamics of domain wall has been a focus of theoretical and experimental studies. Especially, understanding the domain-wall dynamics in nano-scale magnetic materials is regarded as one of the key to realize future spintronic devices. Therefore, the purpose of this dissertation is to study the dynamics of domain wall in low-dimensional and small-scale materials, such as thin films and nanowires. To capture the crucial feature of the domain wall in these systems, we introduce lattice models with microscopic structures and interactions. Based on the Monte Carlo method and numerical solution of the Hamiltonian equations, we investigate the critical phenomenon, the scaling behavior and the universality class of the domain wall. With the short-time dynamic approach, we also reveal the nonequilibrium scaling form and determine critical exponents during the dynamics processes.In Chapter1, we show that due to the limitations of Landau-Lifshitz-Gilbert equation and the Edwards-Wilkinson equation in describing the low-dimensional small-scale domain-wall dynam-ics, one need to build lattice models based on microscopic structures and interactions. We also introduce the concept of the short-time dynamics and how to use it as a research approach in s-tudying the critical phenomenon. We give a brief review of the studies on domain wall dynamics in disordered media, especially, the topics we concerned in the following chapters. In the end, we manifest our motivation and the main contents discussed in this dissertation.In Chapter2, we simulate the critical domain-wall dynamics of model B with Monte Carlo methods, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, dynamic scaling forms are revealed. Due to the existence of the quasi-random walkers, the short-time regime is separated by a time scale ts, at which the quasi-random walkers reach a "homogeneous" state. To explore the scaling form in the t<ts regime, we consider the average moving distance lr(t) of the quasi-random walkers as an additional spatial scale for the dynamics of model B. Both the scaling forms of the magnetization and the Binder cumulant are confirmed with new exponents λ and η related to lr(t). We also study the dynamic scaling forms of the mag- netization and the Binder cumulant in the regime of ts<t. Both the magnetization and the Binder cumulant show intrinsic dependence on the lattice size L. The new exponents which govern the L-dependence of the magnetization and the Binder cumulant are measured to be a and p, respectively. In addition, we also study the ageing phenomenon in the dynamics of model B. By adding lr(t’) as an additional spatial scale, we proposed a general scaling form of the autocorrealtion function A(t. t’). Based on the Monte Carlo methods, the general scaling form are revealed.In Chapter3, with Monte Carlo simulations, we study the creep motion and the zero-field relaxation of a domain wall in the two-dimensional random-field Ising model. We observe the nonlinear field-velocity relation, and determine the creep exponent μ. To further investigate the universality class of the creep motion, we also measure the roughness exponent ζ and energy barrier exponent Ψ from the zero-field relaxation process. We find that all the exponents depend on the strength of disorder, which may be induced by microscopic structures of the domain wall.In Chapter4, based on the Hamiltonian equation of motion of the04theory with quenched dis-order, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.