Abstract
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.
Similar content being viewed by others
Data Availability
The raw data required to reproduce these findings cannot be shared at this time as it also forms part of an ongoing study.
References
Hubert, A., Schaefer, R.: Magnetic domains: analysis of magnetic microstructures. Springer-Verlag, Berlin Heidelberg (1998)
Ivanova, A.I., Semenova, E.M., Dunaeva, G.G., et al.: Influence of defects on magnetic characteristics of ferrite-garnet films. Phys. Chem. Aspects Stud. Clusters, Nanostruct. Nanomater. (2020). https://doi.org/10.26456/pcascnn/2020.12.103
Scheunert, G., Heinonen, O., Hardeman, R., et al.: A review of high magnetic moment thin films for microscale and nanotechnology applications. Appl. Phys. Rev. (2016). https://doi.org/10.1063/1.4941311
Zvezdin, A.К, Kotov, V.A.: Modern magnetooptics and magnetooptical materials. Taylor & Francis Croup, New York (1997)
Kudasov, Yu.B., Logunov, M.V., Kozabaranov, R.V., et al.: Magnetooptic properties of bismuth-substituted ferrite–garnet films in strong pulsed magnetic fields. Phys. Solid State (2018). https://doi.org/10.1134/S106378341811015X
Iskhakov, R.S., Komogortsev, S.V.: Magnetic microstructure of amorphous, nanocrystalline, and nanophase ferromagnets. Phys. Met. Metallogr. (2011). https://doi.org/10.1134/S0031918X11070064
Herzer, G.: Magnetization process in nanocrystalline ferromagnets. Mater. Sci. Eng. A (1991). https://doi.org/10.1016/0921-5093(91)90003-6
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. Appl. Phys. Lett. (2003). https://doi.org/10.1063/1.1578185
Polyakova, O.P., Akimova, M.L., Polyakova, P.A.: Remagnetization of a fractal magnetic structure. Bull. Russ. Acad. Sci.: Phys. (2020). https://doi.org/10.3103/S106287382002029X
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. J. Phys. Conf. Ser. (2020). https://doi.org/10.1088/1742-6596/1658/1/012050
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. Bull. Russ. Acad. Sci.: Phys. (2021). https://doi.org/10.3103/S1062873821090252
Zigert, A.D., Dunaeva, G.G., Sdobnyakov, N.Yu.: Fractal analysis of the maze-like domain structure of ferrite-garnet films in the process of magnetization. Phys. Chem. Aspects Stud. Clusters, Nanostruct. Nanomater. (2021). https://doi.org/10.26456/pcascnn/2021.13.134
Vakhitov, R.M., Magadeev, E.B., Yumaguzin, A.R., Solonetskii, R.V.: Stable states of magnetic inhomogeneities localized in the region of defects. Phys. Solid State. (2015). https://doi.org/10.1134/S106378341508034X
Khmelevskaya, V.S., Kulikova, N.V., Bondarenko, V.V.: Fractal structures formed in metals irradiated by ion and laser beams. Tech. Phys. Lett. (2005). https://doi.org/10.1134/1.2001073
Lisovskii, F.V., Lukashenko, L.I., Mansvetova, E.G.: Thermodynamically stable fractal-like domain structures in magnetic films. J. Exp. Theor. Phys. (2004). https://doi.org/10.1134/1.1765181
Otsu, N.: A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern.: Syst. (1979). https://doi.org/10.1109/TSMC.1979.4310076
Gwyddion – Free SPM (AFM, SNOM/NSOM, STM, MFM, …) data analysis software. http://gwyddion.net. Accessed 26 January 2022
DigitalSurf. https://www.digitalsurf.com. Accessed 26 January 2022
Ivanov, D.V., Antonov, A.S., Semenova, E.M., et al.: Determination of the fractal size of titanium films at different scales. J. Phys. Conf. Ser. (2021). https://doi.org/10.1088/1742-6596/1758/1/012013
Feder J.: Fractals: Springer New York, New York (1988)
Torkhov A.N., Bozhkov V.G., Ivonin I.V., Novikov V.A.: Determination of the fractal dimension for the epitaxial n-GaAs surface in the local limit. Semiconductors (2009). https://doi.org/10.1134/S1063782609010084
Han, B.-S., Li, D., Zheng, D.-J., Zhou, Y.: Fractal study of magnetic domain patterns. Phys. Rev. B (2002). https://doi.org/10.1103/PhysRevB.66.014433
Maslovskaya, A.G., Barabash, T.K.: Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation. J. Phys.: Conf. Ser. (2018). https://doi.org/10.1088/1742-6596/973/1/012038
Hapishah, A.N., Hamidon, M.N., Syazwan, M.M., Shafiee, F.N.: Effect of grain size on microstructural and magnetic properties of holmium substituted yttrium iron garnets (Y1.5Ho1.5Fe5O12). Results Phys. (2019). https://doi.org/10.1016/j.rinp.2019.102391
Liu, J., Wilson, J., Davis, C.L., Peyton, A.: Magnetic characterisation of grain size and precipitate distribution by major and minor BH loop measurements. J. Magn. Magn. Mater. (2019). https://doi.org/10.1016/j.jmmm.2019.02.088
Bathany, C., Romancer, M.L., Armstrong, J.N., Chopra, H.D.: Morphogenesis of maze-like magnetic domains. Phys. Rev. B (2010). https://doi.org/10.1103/PhysRevB.82.184411
Komogortsev, S.V., Iskhakov, R.S., Fel’k, V.A.: Fractal dimension effect on the magnetization curves of exchange-coupled clusters of magnetic nanoparticles. J. Exp. Theor. Phys. (2019). https://doi.org/10.1134/S1063776119040095
Ivanova, A.I., Semenova, E.M., Zhdanova, O.V., Rostova, T.V., Grechishkin, R.M.: Colloid-SEM method for the investigation of magnetic domain structures. Micron (2020). https://doi.org/10.1016/j.micron.2020.102899
Acknowledgements
This work is dedicated to the memory of R. M. Grechishkin (1941–2020).
Funding
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).
Author information
Authors and Affiliations
Contributions
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.
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/s10948-022-06301-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10948-022-06301-w