Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials. Founded at 2009


Complexity analysis of magnetic domain structure of high- and low-anisotropic compounds bulk samples

A.I. Sinkevich, S.D. Smetannikova

Tver State University

DOI: 10.26456/pcascnn/2025.17.161

Original article

Abstract: For uniaxial crystals bulk samples with known structural and magnetic characteristics, it is possible to predict the magnetic domain structure configuration and its elements geometrical parameters. However, this estimation only provides information about the final structure on the basal plane, while the formation features are not considered. In this study, we present a complexity analysis of the domain structure of high- and low-anisotropic compounds, based on its stray field investigation, as well as within the framework of fractal geometry methods. The conducted analysis allowed us to estimate the domain structure complication level through the formation process from bulk domains to the basal plane surface structure. Additionally, based on the scanning probe microscope tips signal spatial distribution, the stray field fractal analysis was carried out. As a result of the obtained data comparison for high- and low-anisotropic compounds, it was shown that the objects with qualitatively different domain structure configurations, but similar formation patterns, have close structure complexity parameter values. At the same time, objects with a simplified structure and a reduced additional domain number have lower values for the structure complexity parameter.

Keywords: magnetic domain structure, magnetic force microscopy, stray fields, fractal dimension

  • Artem I. Sinkevich – Senior Lecturer, Condensed Matter Physic Department, Tver State University
  • Sofia D. Smetannikova – 2nd year student, Faculty of Physics and Technology, Tver State University

For citation:

Sinkevich A.I., Smetannikova S.D. Analiz kompleksnosti magnitnoj domennoj struktury obemnykh obraztsov vysoko- i nizkoanizotropnykh soedinenij [Complexity analysis of magnetic domain structure of high- and low-anisotropic compounds bulk samples], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 161-171. DOI: 10.26456/pcascnn/2025.17.161.

Full article (in Russian): download PDF file

References:

1. Hubert A., Schäfer R. Magnetic domains: the analysis of magnetic microstructures. Berlin, Springer Science & Business Media Publ., 2008, 686 p. DOI: 10.1007/978-3-540-85054-0.
2. Coey M., Parkin S. Handbook of magnetism and magnetic materials, Cham, Springer Publ., 2021, 1713 p. DOI: 10.1007/978-3-030-63210-6.
3. Kittel C. Theory of the structure of ferromagnetic domains in films and small particles, Physical Review, 1946, vol. 70, issue 11-12, pp. 965-971. DOI: 10.1103/PhysRev.70.965.
4. Teodorescu C.M. Kittel’s model for ferromagnetic domains, revised and completed, including the derivation of the magnetic hysteresis, Results in Physics, 2023, vol. 46, art. no. 106287, 17 p. DOI: j.rinp.2023.106287.
5. Bodenberger R., Hubert A. Zur Bestimmung der Blochwandenergie von einachsigen Ferromagneten, Physica Status Solidi (a), 1977, vol. 44, issue 1, pp. K7-K11. DOI: 10.1002/pssa.2210440146.
6. Buschow K.H.J. New permanent magnet materials, Materials Science Reports, 1986, vol. 1, issue 1, pp. 1-63. DOI: 10.1016/0920-2307(86)90003-4.
7. Sinkevich A.I., Smetannikova S.D., Semenova E.M. et al. Domain structure of Y2(FexCo1-x)17 compounds and their hydrides: qualitative and quantitative analysis, Crystallography Reports, 2024, vol. 69, suppl. 1, pp. S52-S60. DOI: 10.1134/S1063774525600048.
8. Kazakova O., Puttock R., Barton C. et al. Frontiers of magnetic force microscopy, Journal of Applied Physics, 2019, vol. 125, issue 6, pp. 060901-1-060901-28. DOI: 10.1063/1.5050712.
9. Bi C., Fishbein K., Bouhrara M., Spencer R.G. Stabilization of parameter estimates from multiexponential decay through extension into higher dimensions, Scientific Reports, 2022, vol. 12, art. no. 5773, 16 p. DOI: 10.1038/s41598-022-08638-7.
10. Han B.S., Li D., Zheng D.J., Zhou Y. Fractal study of magnetic domain patterns, Physical Review B, 2002, vol. 66, issue 1, art. no. 014433, 5 p. DOI: 10.1103/PhysRevB.66.014433.
11. Kim D.H., Cho Y.C., Choe S.B., Shin S.C. Correlation between fractal dimension and reversal behavior of magnetic domain in Co/Pd nanomultilayers, Applied Physics Letters, 2003, vol. 82, issue 21, pp. 3698-3700. DOI: 10.1063/1.1578185.
12. Kim D.H., Cho Y.C., Choe S.B., Shin S.C. Fractal analysis of time‐resolved magnetic domain patterns in Co/Pd multilayer with varying number of repeats, Physica Status Solidi (b), 2004, vol. 241, issue 7, pp. 1669-1672. DOI: 10.1002/pssb.200304608.
13. Xing Y., Sun Q., Zhu M., Bai J., Wang Q. Correlation between anisotropic fractal dimension of fracture surface and coercivity for Nd-Fe-B permanent magnets, Journal of Materials Research and Technology, 2021, vol. 15, pp. 745-753. DOI: 10.1016/j.jmrt.2021.08.073.
14. Lee K.S., Kim D.H., Choe S.B. Fractal dimension of magnetic domain walls in CoFe/Pt multilayers, Journal of Magnetics, 2010, vol. 15, issue 3, pp. 99-102. DOI: 10.4283/JMAG.2010.15.3.099.
15. Guseva A.M., Sinkevich A.I., Smetannikova S.D. et al Analiz parametrov domennoj struktury monokristallov RFe11Ti (R = Y, Gd, Ho, Er) po dannym magnitno-silovoj mikroskopii [Analysis of domain structure parameters of RFe11Ti (R = Y, Gd, Ho, Er) single crystals based on magnetic force microscopy data], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2024, issue 16, pp. 85-95. DOI: 10.26456/pcascnn/2024.16.085. (In Russian).
16. Zigert A.D., Dunaeva G.G., Sdobnyakov N.Yu. Fraktal'nyj analiz labirintnoj domennoj struktury ferrit-granatovykh plenok v protsesse peremagnichivaniya [Fractal analysis of the maze-like domain structure of ferrite-garnet films in the process of magnetization], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2021, issue 13, pp. 134-145. DOI: 10.26456/pcascnn/2021.13.134. (In Russian).
17. Semenova E.M., Ivanov D.V., Lyakhova M.B. et al. Fractal geometry of the nano- and magnetic domain structures of Sm-Co-Cu-Fe ferromagnetic alloy in a high coercive state, Bulletin of the Russian Academy of Sciences: Physics, 2021, vol. 85, issue 9, pp. 955-958. DOI: 10.3103/S1062873821090252.
18. Semenova E.M., Lyakhova M.B., Kuznetsova Yu.V. et al. A comparative analysis of magnetic properties and microstructure of high coercivity Sm(CoCuFe)5 quasi-binary alloys in the framework of fractal geometry, Journal of Physics: Conference Series, 2020, vol. 1658, art. no. 012050, 6 p. DOI: 10.1088/1742-6596/1658/1/012050.
19. Mikheev S.A., Semenova E.M., Pastushenkov Yu.G. et al. Fractal properties of the Nd100-xFex alloys surface in the fractal thermodynamics model, Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques, 2024, vol. 18, issue 2, pp. 354-360. DOI: 10.1134/S1027451024020113.
20. Zigert A.D., Kuz’min N.B., Sdobnyakov N.Yu. et al. Fractal analysis of magneto-optical visualization of the remagnetization of a permanent magnet in a pulsed field, Bulletin of the Russian Academy of Sciences: Physics, 2023, vol. 87, issue 10, pp. 1421-1424. DOI: 10.3103/S1062873823703422.
21. Otsu N. A threshold selection method from gray-level histograms, IEEE Transactions on Systems, Man, and Cybernetics, 1979, vol. 9, issue 1, pp. 62-66. DOI: 10.1109/TSMC.1979.4310076
22. Li J., Du Q., Sun C. An improved box-counting method for image fractal dimension estimation, Pattern Recognition, 2009, vol. 42, issue 11, pp. 2460-2469. DOI: 10.1016/j.patcog.2009.03.001.

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