Sensitivity of the Power Spectra of Thermal Magnetization Fluctuations in Low Barrier Nanomagnets Proposed for Stochastic Computing to In-Plane Barrier Height Variations and Structural Defects

Abstract

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.