Nanoobjects microscopy

Quantification of magnetic force microscopy data: model approaches for reconstruction and quantitative characterization
 Efremov A.A., Lytvyn P.M., Prokopenko I.V. 
V. Lashkaryov Institute of Semiconductor Physics National Academy of Sciences of Ukraine, pr. Nauki 41, Kyiv-03028, Ukraine. E-mail: plyt@isp.kiev.ua 
Since the invention of magnetic-force microscopy (MFM), the problem of extracting quantitative data on a magnetic sample remains relevant. After the MFM measures the gradient of the magnetic force F’’z, which characterizes not the initial magnetization, MS(x,y,z), but only the second derivative of the stray field above the sample at the scan height d i.e. H’’z(x,y,d) [1,2]. Furthermore, even this value appears in the form of a convolution with the magnetic parameters of the magnetic probe tip Mtip(x’,y’,z’). 
A set of different model approaches was proposed earlier for estimating of MS by F’’z. Since the inverse problem F’’zMS is not solvable in general, a sample was constructed initially (based on some a priori information), and then a chain of computations MSH’’zF’’z, should be carried out while the results will not coincide with the experiment [2]. We propose an alternative approach, which differs from the known ones both by the method of calculation [1,2] and the method of using an a priori information. It also includes the use of some reference structures for calibration purposes. 
In the frame of the approach, practically oriented theoretical models have been developed and the scanning magnetic force simulator software has been created. They allow us to reconstruct the quantitative magnetization distribution of the studied objects basing on the experimental MFM data (magnetic force gradient maps).  Individual properties of nanoscale magnetic probes were taken into account as well. A spatial lateral resolution of magnetic maps reached the value of ~10 nm in a number of cases. Capabilities of the proposed quantitative approach are illustrated by the sets of simulation and experimental data collected over the test samples and the samples with unknown, arbitrary magnetic structure. 

1.	Grütter P., Mamin H.J., Rugar D. Magnetic Force Microscopy (MFM). //In Wiesendanger R., Güntherodt HJ. (eds) Scanning Tunneling Microscopy II. Springer Series in Surface Sciences.-1992.-28, Springer, Berlin, Heidelberg- P. 151-207
2.	Миронов В.Л. Основы сканирующей зондовой микроскопии, М.: Техносфера, - 2004. – C. 144.