【作者】 董瑞华；

【导师】 郑波；

【作者基本信息】 浙江大学 ， 理论物理， 2012， 博士

【摘要】 磁性材料中的畴壁动力学过程及其相关物理现象是近年来理论与实验研究的热点之特别是纳米尺度畴壁的动力学问题研究已成为实现新型磁电子器件的理论基础,因而受到广泛关注。本博士论文的主要目的是用数值模拟方法研究低维小尺度磁性材料中的畴壁动力学问题。为了抓住这类小尺度系统中畴壁运动的关键特性,我们引入带有微观结构和相互作用的格点模型,应用Monte Carlo和数值求解哈密顿方程等数值模拟方法,研究畴壁运动中的运动形态、相变现象、临界行为和普适类问题,并与相关实验结果进行比较,揭示新的物理现象。在第一章中,我们首先介绍Landau-Lifshitz-Gilbert方程和Edwards-Wilkinson方程在描述低维小尺度畴壁动力学时的局限性,并由此提出应该建立微观格点模型来描述这一尺度上的畴壁问题。我们还介绍了短时动力学概念及其在研究临界行为时的重要应用。接下来我们简单回顾无序介质中畴壁动力学的研究进展,特别是本博士论文中所关心的相关课题。在最后,我们给出本文的研究动机和目的,以及后面几章的主要研究内容。而在第二章中,我们以二维Ising模型为例,应用Monte Carlo方法,模拟序参数守恒模型(模型B)中畴壁在有序-无序相变温度下的动力学驰豫过程。我们在远离平衡态的宏观短时区域内研究系统的动力学标度行为,发现了模型B中动力学行为明显受到准随机粒子的影响,并且测量与之相关的新临界指数。当系统中的准随机粒子尚未达到均匀状态时,通过引入准随机粒子的空间扩散长度标度lr(t),我们揭示了磁化强度与Binder累积量满足的动力学标度行为,并测量与lr(t)相关的新指数γ和η。而当准随机粒子达到均匀状态后,标度函数中不再显含lr(t),我们发现此时磁化强度与Binder累积量表现出对格点大小L的内秉依赖,并测量了标度函数中与L相关的新指数σ和ρ。另一方面,我们在模型B老化现象的自关联函数中引入准随机粒子空间标度fr(t),由此提出一般化的标度函数假设,并用模拟数据支持了这一观点。在第三章中,引入带弱无序相互作用的微观格点模型,在有限但较低温度下研究二维系统中畴壁的蠕动行为和零场弛豫过程。应用Monte Carlo方法,我们模拟在外场驱动下二维随机场Ising模型中畴壁的蠕动行为,重点强调系统中无序强度对于蠕动行为的影响。我们发现微观格点模型能够描述蠕动行为,并在不同无序强度下都证实了速度-外场的非线性关系,测量相应的蠕动指数μ。进一步的,通过研究零场弛豫过程,测量粗糙指数ζ和能垒指数Ψ,我们发现格点模型中畴壁动力学相关指数依赖于系统的无序强度,这与QEW方程理论描述的弹性弦模型差异很大。我们认为导致这两者差异的原因是畴壁在传播过程中产生的悬凸等微观构型。通过分析系统在不同无序强度下所变现出的微观构型,我们讨论了畴壁微观构型对蠕动行为普适类的影响。在第四章中,我们通过构造含淬火无序的Ginzburg-Landau类型模型(Φ4理论),首次从多体的基本运动方程,即确定性的哈密顿运动方程出发,研究二维磁性系统中的畴壁钉扎相变现象。并且这一理论描述方法触及了统计物理和非平衡态统计物理的基本问题。应用短时动力学方法,我们仔细测定系统的钉扎相变点和相关的静态和动力学临界指数,这些结果表明哈密顿运动方程描述的钉扎相变现象属于新的普适类,与常见的等效随机运动方程和Monte Carlo动力学方法描述的普适类不同。特别是Φ4理论中静态指数β明显大于另外两种模型,而整体粗糙指数ζ又小于1。同时,我们测量得到的局域粗糙指数ζloc<1与实验中的结果可比较。更多还原

【Abstract】 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.更多还原