Nanoscale Magnetic Stray Field Estimation with Non-Ideal Reference Sample by Quantitative Magnetic Force Microscopy

Magnetic force microscopy (MFM) has the ability to provide quantitative information of the magnetic stray fields close to the surface of a sample with nano-scale resolution. A common approach to quantitative MFM is the Tip Transfer Function (TTF) method, which generates a parameter-free description of the scanning magnetic probe tip, which is then used to estimate the magnetic field. However, it requires a well grown and patterned calibration sample, which is not commercially available. On the other hand, magnetic hard drives, one of the most commonly used reference samples, have vaguely defined spatial profiles that hinders TTF generation. We overcome this challenge by using advanced optimization methods to obtain desired parameters from the hard drive while keeping the TTF parameter-free. The computed phase information (utilizing different error functions) is compared with experimentally obtained phase data of hard drive samples until the difference converges and relevant parameters are obtained. We further verify the method by patterning a ~170 nm Iron (Fe) thin film grown on a magnesium oxide (MgO) substrate and applying the TTF. Our preliminary stray field estimation values on a structure with a critical dimension of ~145 nm resemble simulation results within two orders of magnitude. While further development is in progress, the results provide a promising approach for easier access to quantitative magnetic properties at nanoscale that will aid in building pathways to more precise on-chip magnetic field control.