Improved current density and magnetization reconstruction through vector magnetic field measurements

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 gives rise to the field and, under some conditions, into the equivalent 2D magnetization. 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 magnetization reconstruction) the different possible reconstruction pathways are analyzed and their performances compared. In particular, we find that the simultaneous measurement of both in-plane components (Bx and By) 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., Bz). On the other hand, for magnetization reconstruction, a single measurement of the out-of-plane field (Bz) is generally the best choice, regardless of the magnetization direction. We verify these findings experimentally using nitrogen-vacancy-center magnetometry in the case of a 2D current density and a 2D magnet with perpendicular magnetization.