Application of the Autocorrelation Function and Fractal Geometry Methods for Analysis of MFM Images

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Presented work is focused on the use of correlation methods for numerical analysis of magnetic stray field over the surface of materials. Obtained results extend our previous findings about application of the autocorrelation function and the fractal analysis for characterization of magnetic surfaces. Several domain images are recorded at various tip-sample gaps (i.e. the lift heights), and then their average widths were extrapolated down to the zero distance in order to estimate the width seen right on the surface. Apart from that, fractal parameters were derived from autocorrelation function, which turned out to be sensitive to the lift height, and might constitute universal measure (the critical lift height), above which the MFM signal became dominated by thermal noises and non-magnetic residual interactions.

[1] J.E. Lennard-Jones, On the Determination of Molecular Fields, Proc. R. Soc. Lond. A 106 (738), 463-477 (1924).

[2] L. Kong, S.Y. Chou, Quantification of magnetic force microscopy usingamicronscale current ring, Appl. Phys. Lett. 70 (15), 2043-2045 (1997).

[3] U. Hartmann, An elementary introduction to atomic force microscopy and related methods, PDFdocument from the Institute of Experimental Physics, Univ. of Saarbrücken (

[4] R. Proksch, K. Babcock, J. Clevelan d, Magnetic dissipation microscopy in ambient conditions, Appl. Phys. Lett. 74, 419-421 (1999).

[5] P. Grutter, Y. Liu, P. Le Blanc, U. Durig, Magnetic dissipation force microscopy, Appl. Phys. Lett. 71, 2, 279-281 (1997).

[6] E. Mainsah, J.A. Greenwood, D.G. Chetwynd, Metrology and Properties of Engineering Surfaces, Kluwer Academic Publishers (2001).

[7] K.J. Stout, P.J. Sullivan, W.P. Dong, E. Mainsah, N. Luo, T. Mathia, H. Zahouani, The development of methods for the characterisation of roughness in three dimensions, Publication no EUR15178ENof the Commission of the European Communities Dissemination of Scientific and Technical Knowledge Unit Directorate General Information Technologies and Industries and Telecommunications, University of Birmingham Edgbaston, Birmingham, B152 TT, 1993.

[8] M. Bramowicz, S. Kulesza, Amagnetic force microscopy study of magnetic domain structure in maraging steel, Solid State Phenomena - in press.

[9] J.C. Russ, Fractal Sufaces, Plenum Press, New York (1994).

[10] J.J. Wu, Analyses and simulation of anisotropic fractal surfaces, Chaos, Solitons and Fractals 13, 1791-1806 (2002).

Archives of Metallurgy and Materials

The Journal of Institute of Metallurgy and Materials Science and Commitee on Metallurgy of Polish Academy of Sciences

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