Artificial spin ices are ideal frustrated model systems in which to explore or design emergent phenomena with unprecedented characterization of the constituent degrees of freedom. In square spin ice, violations of the ice rule are topological excitations essential to the kinetics of the system, providing an ideal test bed for studying the dynamics of such defects under varied quench rates. In this work we examine possible scenarios including the Kibble-Zurek mechanism and critical coarsening in colloidal square and hexagonal ice under quenches from a weakly interacting liquid state into a strongly interacting regime. As expected, for infinitely slow quenches, the system is free of defects such as monopoles, while for increasing quench rate, an increasing number of defects in the form of monopoles or grain boundaries remain in the sample. For square ice, we find regimes in which the defect population decreases as a power law with decreasing quench rate. A detailed scaling analysis shows that for a wide range of parameters, including quench rates that are accessible by experiments, the behavior is best described by critical coarsening rather than the Zurek-Kibble scenario if we assume that the equilibrium phase transition in this system is in the Ising universality class. The appearance of critical coarsening is likely due to the strong defect interactions in the colloidal ice system leading to relevant defect dynamics during the quench. For hexagonal ice we do not find evidence for a power-law decay in the defect density, which is consistent with the absence of an equilibrium phase transition in the hexagonal ice as well as a lack of critical coarsening.

中文翻译：

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人造胶体冰的猝灭动力学

人造旋转冰是理想的受挫模型系统，在其中探索或设计具有前所未有的组成自由度特征的新兴现象。在方形自旋冰中，违反冰规则是系统动力学必不可少的拓扑激励，这为研究在各种淬火速率下此类缺陷的动力学提供了理想的测试平台。在这项工作中，我们研究了可能的情况，包括Kibble-Zurek机理以及在从弱相互作用的液态转变为强相互作用状态的骤冷下胶体正方形和六角形冰中的临界变粗。正如预期的那样，对于无限缓慢的淬火，系统没有诸如单极之类的缺陷，而对于增加的淬灭速度，越来越多的单极或晶界形式的缺陷保留在样品中。对于方冰，我们发现其中缺陷数量随着幂率随淬灭速率降低而降低的状态。详细的缩放分析表明，对于各种参数（包括可通过实验获得的淬火速率），如果我们假设此系统中的平衡相变处于，则通过临界粗化而不是Zurek-Kibble方案可以最好地描述其行为。 Ising通用性类别。临界粗化的出现可能是由于胶态冰系统中强烈的缺陷相互作用，导致淬火期间相关的缺陷动态。对于六角形冰，我们找不到缺陷密度的幂律衰减的证据，这与六角形冰中没有平衡相变以及缺乏临界粗化相符。我们发现，随着淬灭速率的降低，缺陷种群以幂律的形式减少。详细的缩放分析表明，对于各种参数（包括可通过实验获得的淬火速率），如果我们假设此系统中的平衡相变处于，则通过临界粗化而不是Zurek-Kibble方案可以最好地描述其行为。 Ising通用性类别。临界粗化的出现可能是由于胶态冰系统中强烈的缺陷相互作用，导致淬火期间相关的缺陷动态。对于六角形冰，我们找不到缺陷密度的幂律衰减的证据，这与六角形冰中没有平衡相变以及缺乏临界粗化相符。我们发现，随着淬灭速率的降低，缺陷种群以幂律的形式减少。详细的缩放分析表明，对于各种参数（包括可通过实验获得的淬火速率），如果我们假设此系统中的平衡相变处于，则通过临界粗化而不是Zurek-Kibble方案可以最好地描述其行为。 Ising通用性类别。临界粗化的出现可能是由于胶态冰系统中强烈的缺陷相互作用，导致淬火期间相关的缺陷动态。对于六角形冰，我们找不到缺陷密度的幂律衰减的证据，这与六角形冰中没有平衡相变以及缺乏临界粗化相符。