通过矢量磁场测量改进的电流密度和磁化强度重建
Improved current density and magnetisation reconstruction through vector magnetic field measurements
摘要：
杂散磁场包含了凝聚态系统的电磁性质的重要信息。对于二维（2D）系统，杂散场测量甚至可以完全确定源的数量。例如，杂散磁场的2D图可以被唯一地转换成产生该场的2D电流密度，并且在某些条件下转换成等效的2D磁化强度。然而，实现这些变换通常需要截断初始数据，并且涉及可能引入误差、伪影和放大噪声的奇点。在这里，我们调查的可能性，减轻这些问题，通过矢量测量。对于每种情况（电流重建和磁化重建）的不同可能的重建途径进行了分析，并比较其性能。特别是，我们发现，同时测量两个平面内的组件（$B_x$和$B_y$），使电流密度的接近理想的重建，没有奇异性或截断伪影，这构成了一个显着的改进，基于一个单一的组件（例如$B_z$）的重建。另一方面，对于磁化重构，无论磁化方向如何，面外场（$B_z$）的单次测量通常是最佳选择。我们验证了这些发现实验使用氮空位磁强计的情况下，一个二维的电流密度和一个二维磁铁与垂直磁化。
英文摘要：
Stray magnetic fields contain significant information about the electronic and magnetic properties of condensed matter systems. For two-dimensional (2D) systems, stray field measurements can even allow full determination of the source quantity. For instance, a 2D map of the stray magnetic field can be uniquely transformed into the 2D current density that gave rise to the field and, under some conditions, into the equivalent 2D magnetisation. However, implementing these transformations typically requires truncation of the initial data and involves singularities that may introduce errors, artefacts, and amplify noise. Here we investigate the possibility of mitigating these issues through vector measurements. For each scenario (current reconstruction and magnetisation reconstruction) the different possible reconstruction pathways are analysed and their performances compared. In particular, we find that the simultaneous measurement of both in-plane components ($B_x$ and $B_y$) enables near-ideal reconstruction of the current density, without singularity or truncation artefacts, which constitutes a significant improvement over reconstruction based on a single component (e.g. $B_z$). On the other hand, for magnetisation reconstruction, a single measurement of the out-of-plane field ($B_z$) is generally the best choice, regardless of the magnetisation direction. We verify these findings experimentally using nitrogen-vacancy magnetometry in the case of a 2D current density and a 2D magnet with perpendicular magnetisation.
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