The interaction-energy landscapes (ELs) and magnetization dynamics of two-dimensional ensembles of dipole-coupled magnetic nanoparticles are theoretically investigated. Extended nanostructures are modeled by considering nonoverlapping nanoparticles (NPs) in a square unit cell with periodic boundary conditions. The local minima and connecting transition states of the EL are determined systematically for representative NP arrangements having different degrees of disorder. The topology of the ergodic networks of stationary points is analyzed from both local and energy perspectives by using kinetic networks and disconnectivity graphs. We show that increasing the degree of disorder not only increases, most significantly, the number of local minima and transition states but also changes the shape of the EL in a very profound way. While slightly disordered ensembles correspond to good structure seekers, which are funneled towards the global minima, strongly disordered systems show very rough landscapes with multiple low-energy local minima separated by relatively large energy barriers. The consequences of this transition on the long-time Markovian dynamics of the nanostructures are quantified by calculating the field-free magnetic relaxation after saturation and after quenching. The simulations indicate that the relaxation of weakly disordered systems follows a slightly stretched exponential law, with a single characteristic timescale for a wide range of temperatures. In contrast, strongly disordered systems show a much more complicated relaxation dynamics involving multiple timescales, slowing down and trapping, which is reminiscent of spin glasses.

中文翻译：

---

偶极子耦合磁性纳米粒子二维集合中能量态的无序诱导转变和磁化动力学

理论上研究了偶极耦合磁性纳米粒子二维团簇的相互作用能态（ELs）和磁化动力学。通过考虑具有周期性边界条件的方形晶胞中的非重叠纳米颗粒（NP），可以对扩展的纳米结构进行建模。对于具有不同无序度的代表性NP排列，系统地确定EL的局部最小值和连接过渡状态。通过使用动力学网络和不连续性图，从局部和能量角度分析了固定点的遍历网络的拓扑。我们表明，增加无序度不仅会最大程度地增加局部极小值和过渡态的数量，而且还会以非常深刻的方式改变EL的形状。稍微混乱的合奏对应于向全局最小值漏斗的良好结构搜寻器，而强烈混乱的系统则显示出非常粗糙的地形，其中多个低能量局部最小值被相对较大的能垒隔开。通过计算饱和后和淬灭后的无场磁弛豫，可以量化这种转变对纳米结构的长时间马尔可夫动力学的影响。仿真表明，弱无序系统的弛豫遵循略微扩展的指数定律，在很宽的温度范围内具有单个特征时标。相比之下，严重混乱的系统显示出复杂得多的松弛动力学，涉及多个时间尺度，放慢速度和陷井，这让人联想到旋转玻璃。