Numerical Simulation Of Domain Wall Dynamics In An Ultra-thin Magnetic Film

Domain-wall dynamics is believed to be relative to many important physical phe-nomenons. In particular, the domain-wall motion in ferromagnetic or ferroelectric mate-rials is an important topic both on the theoretical and experimental sides. Under different types of driving fields, the domain-wall motion is complex and volatile, exhibiting a rich physical picture. From a pragmatic point of view, understanding the controlled movement of domain walls plays an important role in developing new classes of potential nonvolatile storage-class memories. From a purely theoretical point of view, it is also essential for understanding nonequilibrium dynamics in disordered media. In this dissertation, we fo-cus on the domain-wall dynamics in ultra-thin magnetic film with external magnetic field. Up to date, theoretical approaches to the domain-wall dynamics are typically based on the Edwards-Wilkinson equation with quenched disorder(QEW). However, some results in numerical simulation of QEW equation are incompatible with the experiments and a self-inconsistency is puzzling. In this thesis, with the Monte Carlo method, we systematically investigate the relaxation dynamics of domain-wall motion in the ultra-thin ferromagnetic or ferroelectric film with lattice models, such as two-dimensional Ising model and random-field Ising model. Based on the short-time dynamic scaling form, we accurately determine the transition field, static and dynamic exponents, and local and global roughness expo-nents. Chapter 2 and 3 are two focal points of our work.In Chapter 1, we first give a brief introduction to the definition of magnetic domain wall, the phenomenons of domain-wall motion, and the significance of identifying the domain-wall dynamics. The domain-wall dynamics in an ultra-thin magnetic film is our main research object, and short-time dynamics method is our main research approach. Subsequently, we show the motivation of our work:By building lattice models based on microscopic structures and interactions of the materials, instead of elastic string model (such as the QEW equation), we model domain-wall motion in ultra-thin magnetic film and investigate phase transitions with short-time dynamic method.In Chapter 2, we investigate the relaxation dynamics with a domain wall at the crit-ical temperature of ordered-disordered phase transition without the external driving field, using two dimensional Ising model as an example. The dynamic scaling behavior is care-fully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surface. For the do-main interface, new critical exponents characterizing the magnetization, Binder cumulant, height function, and roughness function are extracted. Subsequently, a universal law is rev-eled after investigating the critical dynamics behavior of domain wall in different models, consistent with analytical calculation.In Chapter 3, we study the relaxation dynamics of a domain wall in the two-dimensional random-field Ising model with a constant driving field. The short-time dynamics behavior of domain wall at the pinning-depinning transition is carefully examined, and the rough-ening process is observed. Based on the short-time dynamic scaling form, we accurately determine the transition field, static and dynamic exponents, and local and global roughness exponents. Comparing these exponents with those of the QEW equation, about 10%～30% difference is observed, indicating that the random field Ising model does not belong to the universality class of the QEW equation. It is believed that overhangs and islands lead to this difference. Subsequently, we examine the dynamics of overhangs and islands at the pinning-depinning transition carefully.In Chapter 4, Monte Carlo simulations of a two-dimensional, random-field Ising model with an ac driving field are used to study the relaxation-to-creep transition of domain-wall motion at low temperatures. The resultant complex susceptibilityχ(f-,T)=χ'-iχ" ex-hibits features in agreement with the experiments of ultrathin ferromagnetic and ferroelec-tric films:the semicircle and straight line in theχ'-χ" plot are Cole-Cole signatures of relaxation and creep states, respectively. The exponentβdescribing the creep motion is measured, and an intermediate state between the relaxation and creep states is identified.we observe that the frequency f1 characterizes the transition behavior of amplitude A(f,T), while f2 depicts that of phase shift function tanδ(f, T), i.e. the relaxation-to-creep transi-tion occurs in two stages, somewhat similar to the scenario of the two-dimensional melting.