Determination of Intrinsic Magnetic Response from Local Measurements of   Fringing Fields
  Micron-sized Hall bars and micro-SQUIDs are now used routinely to measure the local static and dynamic magnetic response with micron-scale spatial resolution. While this provides a powerful new tool, determining the intrinsic magnetization presents new challenges, as it requires correcting for demagnetization fields that vary widely with position on a sample. In this paper we develop a method to correct for the demagnetization effect at local points of a rectangular prism shaped sample using a finite element analysis of Maxwell's equation applied to local Hall sensor measurements calibrated by bulk measurements of the magnetization. This method can be generalized to other geometric shapes to analyze data obtained with local magnetic probes. 
Bo Wen, Andrew J. Millis, Enric Pardo, Pradeep Subedi, Andrew D. Kent,   Yosi Yeshurun, Myriam P. Sarachik
cond-mat.mes-hall