Nanoscale physics
Hausdorff analysis of magnetic flux front penetration into NbTi and the pinning structure transformation as a result of magneto-thermal effect
V. F. Rusakov1, O. I. Kuchuk2, I. Abaloszewa3, O. M. Chumak2,3         V. V. Chabanenko2, O. Abaloszew3, A. Nabiałek3, and R. Puz´niak3

1Vasyl’ Stus Donetsk National University, MOE, Ul. 600 Richcha 21, Vinnytsia, 21021 Ukraine. 
E-mail: v.rusakov@donnu.edu.ua
2O. Galkin Donetsk Institute for Physics and Engineering, National Academy of Science, Pr. Nauki 46, Kyiv, 03028 Ukraine.
3Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland.

The Hausdorff dimension has experienced application in the characterization and comparison of highly rough structures. It is famous that the concept of Hausdorff dimension is applied as well to magnetic flux front (induction of the magnetic field) analysis in superconductors [1]. In this report, MO registration of the magnetic flux penetration was used in the NbTi superconductor for visualization of the mechano-thermal effect on the pinning structure as key element of high critical current density. The disc shape sample was cut from a rod of NbTi after extrusion. The structure of the boundary between the Meissner and critical states was studied during external magnetic field penetration into alloy a) after the extrusion and b) after the heat treatment stages. Based on the analysis of the correlation function, it was found that: the fractal Housdorff dimension of flux front amounts to about 1.5; the fractal dimension increases a) with increasing external magnetic field and b) in fixed external magnetic field with increasing level of induction. The heat treatment stage leads to significant changes of fractal Housdorff dimension of flux front and the value of critical current density. The obtained values of roughness exponent α lie in the range of 0.435–0.480. A system with a roughness value α˂0.5 is described by a model of dynamic stochastic disorder [2], which is characteristic of the fractal nature of the structure of the magnetic flux front in a superconductor [1]. 

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2. M. Kardar, G. Parisi, Y.-C. Zhang. Dynamic scaling of growing interfaces // Phys. Rev. Let. -1986.- 56.-P. 889-892.