Direct reconstruction of two-dimensional currents in thin films from magnetic field measurements

TL;DR

This paper introduces a direct inversion method for reconstructing two-dimensional currents in thin films from magnetic field measurements, improving accuracy and boundary reconstruction without oversmoothing.

Contribution

A novel direct inversion technique that bypasses the traditional stream function approach, enhancing accuracy and boundary current reconstruction in thin film magnetic measurements.

Findings

Enhanced accuracy over a range of noise levels

Effective boundary current reconstruction

Numerical examples demonstrate method effectiveness

Abstract

Accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low dimensional materials and interfaces, of superconducting thin films and of electronic devices. Current distribution is usually derived from the measurement of the perpendicular component of the magnetic field above the surface of the sample, followed by numerical inversion of the Biot-Savart law. The inversion is commonly obtained by deriving the current stream function $g$, which is then differentiated in order to obtain the current distribution. However, this two-step procedure requires filtering at each step and, as a result, oversmoothes the solution. To avoid this oversmoothing we develop a direct procedure for inversion of the magnetic field that avoids use of the stream function. This approach provides enhanced accuracy of current reconstruction over a wide range of noise levels. We further introduce a reflection procedure that allows for the reconstruction of currents that cross the boundaries of the measurement window. The effectiveness of our approach is demonstrated by several numerical examples.