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Fractal Dimension Behaviour of Maze Domain Pattern in Ferrite-Garnet Films During Magnetisation Reversal

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Experimental results of the study of magnetic bismuth-containing ferrite-garnet films grown on substrates from gadolinium-gallium garnet are analysed using specialised software. Based on the analysis of the transformation of the domain structure, the major loops of magnetic hysteresis for defective and defect-free areas of the films were obtained using the optical magnetometry method. A comparative analysis of the behaviour of the fractal dimension of the domain structure \(D_{L} (H)\) corresponding to these sites during remagnetisation along the major loop of hysteresis is conducted. The behaviour of the dependence \(D_{L} (H)\) corresponding to different branches of the hysteresis loop is shown to have a dome-like character. The relationship between the magnetic state (demagnetised state, partially magnetised in the external field) and the value of the fractal dimension of the domain structure for films of this type is established on the basis of the obtained results.

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This work is dedicated to the memory of R. M. Grechishkin (1941–2020).


The research was carried out with the financial support of the Ministry of Education and Science of the Russian Federation as part of the state task in the field of scientific activity (project no. 0817–2020-0007).

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A. D. Zigert performed numerical calculations and wrote the draft of the paper; G. G. Dunaeva and E. M. Semenova performed the experimental investigations; A. I. Ivanova formulated conceptualisation and validation rules, A. Yu. Karpenkov performed formal analysis and data curation; N. Yu. Sdobnyakov designed the work, as well as reviewed and edited the paper. All authors participated in the data analysis and manuscript revision.

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Correspondence to Nickolay Yu. Sdobnyakov.

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Zigert, A.D., Dunaeva, G.G., Semenova, E.M. et al. Fractal Dimension Behaviour of Maze Domain Pattern in Ferrite-Garnet Films During Magnetisation Reversal. J Supercond Nov Magn 35, 2187–2193 (2022).

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