Nanomagnets with small in-plane shape anisotropy energy barriers on the order of the thermal energy have unstable magnetization that fluctuates randomly in time. They have recently emerged as promising hardware platforms for stochastic computing and machine learning because the random magnetization states can be harnessed for probabilistic bits. Here, we have studied how the statistics of the magnetization fluctuations (e.g., the power spectral density) is affected by (i) moderate variations in the barrier height of the nanomagnet (caused by small size variations) and (ii) the presence of structural defects — both localized and delocalized — in order to assess how robust the stochastic computing platform based on Low Barrier Nanomagnets (LBM) is. We found that the power spectral density is relatively insensitive to moderate barrier height change and also relatively insensitive to the presence of small localized defects. However, extended (delocalized) defects, such as thickness variations over a significant fraction of the nanomagnet, affect the power spectral density very noticeably. That means extended defects can significantly alter the fluctuation rate of the magnetization in low barrier nanomagnets. Since the fluctuation rate is crucial for stochastic computing applications, this has very serious implications for the latter. Thickness variations are difficult to avoid in real nanomagnets with in-plane anisotropy since they must be thin to keep the barrier height small and the substrate on which they are fabricated may have surface roughness comparable to the nanomagnet thickness. This raises questions about the viability of stochastic computing with low barrier nanomagnets possessing in-plane anisotropy. Our results establish that small variations in the shape (causing small variations in the barrier height), or small localized defects, are relatively innocuous and tolerable but extended defects are not. The latter must be avoided for stochastic computing applications.

中文翻译：

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用于随机计算的低势垒纳米磁体中热磁化波动的功率谱对面内势垒高度变化和结构缺陷的敏感性

具有热能量级的小的面内形状各向异性能垒的纳米磁体具有随时间随机波动的不稳定磁化。它们最近已成为用于随机计算和机器学习的有前途的硬件平台，因为随机磁化状态可以用于概率位。在这里，我们研究了磁化波动的统计数据（例如，功率谱密度）如何受（i）纳米磁体势垒高度的适度变化（由小尺寸变化引起）和（ii）结构的存在影响。为了评估基于低势垒纳米磁体 (LBM) 的随机计算平台的鲁棒性，缺陷（局部和非局部）。我们发现功率谱密度对适度的势垒高度变化相对不敏感，并且对小的局部缺陷的存在也相对不敏感。然而，扩展（离域）缺陷，例如纳米磁体大部分的厚度变化，会非常显着地影响功率谱密度。这意味着扩展缺陷可以显着改变低势垒纳米磁体中磁化强度的波动率。由于波动率对于随机计算应用至关重要，这对后者具有非常严重的影响。在具有面内各向异性的实际纳米磁体中，很难避免厚度变化，因为它们必须很薄以保持势垒高度较小，并且制造它们的基板可能具有与纳米磁体厚度相当的表面粗糙度。这引发了对具有面内各向异性的低势垒纳米磁体进行随机计算的可行性的质疑。我们的结果表明，形状的微小变化（导致势垒高度的微小变化）或小的局部缺陷相对无害且可以容忍，但扩展缺陷则不然。对于随机计算应用程序，必须避免后者。