Micromagnetic Simulation of Domain Structure Transition in Ferromagnetic Nanospheres under Zero External Field

Title: Micromagnetic Simulation of Domain Structure Transition in Ferromagnetic Nanospheres under Zero External Field

Authors
Authors and Affiliations

Dede Djuhana, Candra Kurniawan, Dong-Hyun Kim, Agus Tri Widodo

Corresponding email: dede.djuhana@sci.ui.ac.id

Published at : 19 Jul 2021
Volume : IJtech Vol 12, No 3 (2021)
DOI : https://doi.org/10.14716/ijtech.v12i3.4278

Cite this article as:
Djuhana, D., Kurniawan, C., Kim, D., Widodo, A.T., 2021. Micromagnetic Simulation of Domain Structure Transition in Ferromagnetic Nanospheres under Zero External Field. International Journal of Technology. Volume 12(3), pp. 539-548

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Dede Djuhana	Department of Physics, Faculty Mathematics and Natural Science (FMIPA), Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia
Candra Kurniawan	1.Department of Physics, Faculty Mathematics and Natural Science (FMIPA), Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia 2. Research Center for Physics, Indonesian Institute of Scien
Dong-Hyun Kim	Department of Physics, Chungbuk National University, Cheongju 28644, South Korea
Agus Tri Widodo	Department of Physics, Faculty Mathematics and Natural Science (FMIPA), Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia

Email to Corresponding Author

Abstract

Micromagnetic Simulation of Domain Structure Transition in Ferromagnetic Nanospheres under Zero External Field

In this work, we investigated the domain structure transition in ferromagnetic nanospheres at the ground-state conditions under zero external magnetic field by micromagnetic simulation. Four basic ferromagnetic materials, nickel (Ni), permalloy (Py), iron (Fe), and cobalt (Co), with variation in diameters from 20 to 100 nm were modeled in the simulation. It was observed that a transition of domain structure occurs from a single-domain to a multi-domain structure at a specific diameter based on the magnetization energy profile. Interestingly, a vortex–core orientation in the multi-domain regime was related to the magnetocrystalline axis of the material, which first aligns with the hard-axis direction, and then changes to the easy-axis direction for low-anisotropy materials (Ni, Py, and Fe). In contrast, only hard-axis orientation exists for high-anisotropy materials (Co). Furthermore, it is also observed that the transition of domain structure was related to the critical diameter. Below the critical diameter, a single-domain structure is exhibited in which the demagnetization energy was larger than the exchange energy. A multi-domain structure emerged above the critical diameter where the exchange energy was larger than the demagnetization energy. The comparable values of critical diameter were also calculated based on the Kittel and Brown equations. The results of the critical diameter from the micromagnetic simulation agreed with the theoretical calculations. Therefore, an interpretation of these magnetization dynamics is an important step in the material selection for granular magnetic-based storage.

Keywords

Critical Diameter; Domain Structure; Micromagnetic; Multi-Domain; Single Domain

Introduction

The technological advancement of magnetic storage media was enhanced by an improved understanding of dynamic magnetization in ferromagnetic materials. Some potential application research of magnetic recordings, such as magnetic random-access memory (MRAM), magnetic logic, microwave oscillators, and magnetic nanosensors, has grown extensively in recent years (Udhiarto et al., 2014; Sun et al., 2015; Joshi, 2016; Bhatti et al., 2017; Sbiaa and Piramanayagam, 2017). Magnetic storage technologies, such as granular magnetic recording media, have rapidly developed over the last 20 years. The important key of these technologies was understanding magnetization structure and reversal for individual grains or elements (Ali et al., 2018; Mu et al., 2019).

Recently, investigation of three-dimensional magnetic nanostructures has attracted much attention due to fundamental interest in magnetic properties as well as possible magnetic device applications (Manke et al., 2010; Streubel et al., 2015; Nur Fitriana et al., 2017; Sanz-Hernández et al., 2017; Suzuki et al., 2018; Fischer et al., 2020). In particular, micromagnetic simulations for three-dimensional magnetic nanostructures have been adopted to explain experimental results, in which the detailed domain structures at various magnetic states can be visualized (Aharoni, 2001; Fidler et al., 2002; Evans et al., 2014; Vousden et al., 2016; Leliaert and Mulkers, 2019). Micromagnetic simulation is a mezoscopic scale modeling, which can be solved using a finite difference or finite element discretization approach (Miltat and Donahue, 2007; Schrefl et al., 2007; Haryanto et al., 2017). Numerous studies have been reported that have investigated the domain structure in cube (Hertel and Kronmüller, 1999; Hertel and Kronmüller, 2002; Lu and Leonard, 2002; Piao et al., 2010), sphere (Boardman et al., 2004; Kákay and Varga, 2005; Yani et al., 2018; Usov and Nesmeyanov, 2020), cylinder (Piao et al., 2013; Fernandez-Roldan et al., 2019), and pyramidal shapes (Knittel et al., 2010). Among these, the case of nanospheres has steadily gained interest since it gives exciting features such as transitional domain structure from single-domain (SD) to multi-domain (MD), the critical size effect, and the possible magnetic vortex structure in spheres (Russier, 2009; Kurniawan et al., 2020). However, the ground state condition of a spherical-shaped magnetic nanoparticle around the domain structure transition with visual magnetization observation was rarely been studied.

In this work, micromagnetic simulation was utilized to explore the domain structure transition in ferromagnetic nanospheres at the ground-state conditions without an external magnetic field. The ferromagnetic materials consisting of Ni, Ni_0.8Fe_0.2 (Py), Fe, and Co have been investigated with the variation in diameters ranging from 20 to 100 nm. A transitional behavior of the domain structure from SD to MD has been observed with critical conditions. The vortex structure was formed in an MD state with the vortex-core orientation toward the crystalline easy and hard axes of the materials. We have also calculated a critical diameter based on the analysis of magnetization energy around the transition with a comparable result to the theoretical Kittel and Brown equations.

Conclusion

In conclusion, we have systematically observed the transition of the domain structure of Ni, Py, Fe, and Co sphere models using micromagnetic simulation at ground-state conditions without an external magnetic field. The transition domain structure from SD to MD was analyzed based on the magnetization energies, namely the demagnetization and exchange energy. The MD is first recognized when the demagnetization energy decreases while the exchange energy increases. A VW structure is formed in the MD regime, and the core orientation of the VW structure has two orientations, HAO and EAO. It is found that the HAO and EAO of the VW structure relate to the crystal plane direction. The critical diameter at the transition from SD to MD was also determined. Interestingly, the simulation results show good agreement compared with the theoretical Kittel and Brown equations. Therefore, an interpretation of the magnetization dynamic is an important step in the material selection for magnetic granular-based storage.

Acknowledgement

This work is fully supported by Hibah Penelitian Dasar Unggulan Perguruan Tinggi (PDUPT) year 2020 from the Ministry of Research, Technology, and Higher Education of the Republic of Indonesia with the contract number NKB-202/UN2.RST/HKP.05.00/2020. We also thank DRPM Universitas Indonesia for facilitating this research.

References

Aharoni, A., 2001. Micromagnetics: Past, Present and Future. Physica B: Condensed Matter, Volume 306(1–4), pp. 1–9

Ali, S.R., Naz, F., Akber, H., Naeem, M., Ali, S.I., Basit, S.A., Sarim, M., Qaseem, S., 2018. Effect of Particle Size Distribution on Magnetic Behavior of Nanoparticles with Uniaxial Anisotropy. Chinese Physics B, Volume 27(9), 097503-1–097503-5

Allenspach, R., 2007. Magnetic Properties of Systems of Low Dimensions. Handbook of Magnetism and Advanced Magnetic Materials, Kronmüller, H., Parkin, S. (Eds.), John Wiley & Sons, Ltd, Chichester, UK

Betto, D., Coey, J.M.D., 2014. Vortex State in Ferromagnetic Nanoparticles. Journal of Applied Physics, Volume 115(17), 17D138, https://doi.org/10.1063/1.4867597

Bhatti, S., Sbiaa, R., Hirohata, A., Ohno, H., Fukami, S., Piramanayagam, S.N., 2017. Spintronics Based Random Access Memory: A Review. Materials Today, Volume 20(9), pp. 530–548

Boardman, R.P., Fangohr, H., Cox, S.J., Goncharov, A.V., Zhukov, A.A., de Groot, P.A.J., 2004. Micromagnetic Simulation of Ferromagnetic Part-Spherical Particles. Journal of Applied Physics, Volume 95(11), pp. 7037–7039

Brown, W.F., 1968. The Fundamental Theorem of Fine?Ferromagnetic?Particle Theory. Journal of Applied Physics, Volume 39, pp. 993–994

Coey, J.M.D., 2007. Magnetism and Magnetic Materials. Cambridge University Press

Donahue, M.J., 2012. Micromagnetic Investigation of Periodic Cross-Tie/Vortex Wall Geometry. Advances in Condensed Matter Physics, Volume 2012, pp. 1–8

Donahue, M.J., McMichael, R.D., 2007. Micromagnetics on Curved Geometries using Rectangular Cells: Error Correction and Analysis. IEEE Transactions on Magnetics, Volume 43(6), pp. 2878–2880

Donahue, M.J., Porter, D.G., 1999. OOMMF User’s Guide, Version 1.0, Interagency Report NISTIR 6376. National Institute of Standards and Technology, Gaithersburg, MD

Evans, R.F.L., Fan, W.J., Chureemart, P., Ostler, T.A., Ellis, M.O.A., Chantrell, R.W., 2014. Atomistic Spin Model Simulations of Magnetic Nanomaterials. Journal of Physics: Condensed Matter, Volume 26(10), pp. 1–23

Fangohr, H., 2009. OVF2VTK: Tool for Conversion of OOMMF to VTK Files [WWW Document]. Available Online at https://fangohr.github.io/software/ovf2vtk/index.html

Fernandez-Roldan, J.A., De Riz, A., Trapp, B., Thirion, C., Vazquez, M., Toussaint, J.-C., Fruchart, O., Gusakova, D., 2019. Modeling Magnetic-Field-Induced Domain Wall Propagation in Modulated-Diameter Cylindrical Nanowires. Scientific Reports, Volume 9(5130), pp. 1–12

Fidler, J., Schrefl, T., Tsiantos, V.D., Scholz, W., Suess, D., 2002. Micromagnetic Simulation of the Magnetic Switching Behaviour of Mesoscopic and Nanoscopic Structures. Computational Materials Science, Volume 24(1-2), pp. 163–174

Fischer, P., Sanz-Hernández, D., Streubel, R., Fernández-Pacheco, A., 2020. Launching a New Dimension with 3D Magnetic Nanostructures. APL Materials, Volume 8, pp. 010701-1

– 010701-12

Getzlaff, M., 2008. Fundamentals of Magnetism. New York: Springer Science & Business Media

Gilbert, T.L., 2004. Classics in Magnetics: A Phenomenological Theory of Damping in Ferromagnetic Materials. IEEE Transactions on Magnetics, Volume 40(6), pp. 3443–3449

Guimarães, A.P., 2009. Principles of Nanomagnetism, NanoScience and Technology. Berlin Heidelberg: Springer

Haryanto, Y., Gan, B.S., Maryoto, A., 2017. Wire Rope Flexural Bonded Strengthening System on RC-Beams: A Finite Element Simulation. International Journal of Technology, Volume 8(1), pp. 132–144

Hertel, R., Kronmüller, H., 2002. Finite Element Calculations on the Single-Domain Limit of a Ferromagnetic Cube: A Solution to µMAG Standard Problem No. 3. Journal of Magnetism and Magnetic Materials, Volume 238(2-3), pp. 185–199

Hertel, R., Kronmüller, H., 1999. Computation of the Magnetic Domain Structure in Bulk Permalloy. Physical Review B, Volume 60(10), pp. 7366–7378

Joshi, V.K., 2016. Spintronics: A Contemporary Review of Emerging Electronics Devices. Engineering Science and Technology, an International Journal, Volume 19(3), pp. 1503–1513

Kafrouni, L., Savadogo, O., 2016. Recent Progress on Magnetic Nanoparticles for Magnetic Hyperthermia. Progress in Biomaterials, Volume 5, pp. 147–160

Kákay, A., Varga, L.K., 2005. Monodomain Critical Radius for Soft-Magnetic Fine Particles. Journal of Applied Physics, Volume 97, 083901, https://doi.org/10.1063/1.1844612

Kittel, C., 1949. Physical Theory of Ferromagnetic Domains. Reviews of Modern Physics, Volume 21, pp. 541–583

Knittel, A., Franchin, M., Fischbacher, T., Nasirpouri, F., Bending, S.J., Fangohr, H., 2010. Micromagnetic Studies of Three-Dimensional Pyramidal Shell Structures. New Journal of Physics, Volume 12, pp. 1–23

Kurniawan, C., Widodo, A.T., Kim, D.H., Djuhana, D., 2020. Micromagnetic Investigation of Magnetization Reversal in Sphere-Shaped Ferromagnetic Nanoparticle. Key Engineering Materials, Volume 855, pp. 237–242

Leliaert, J., Mulkers, J., 2019. Tomorrow’s Micromagnetic Simulations. Journal of Applied Physics, Volume 125, pp. 180901-1– 180901-9

López-Urías, F., Torres-Heredia, J.J., Muñoz-Sandoval, E., 2005. Magnetization Patterns Simulations of Fe, Ni, Co, and Permalloy Individual Nanomagnets. Journal of Magnetism and Magnetic Materials, Volume 294(2), pp. e7–e12

Lu, M., Leonard, P.J., 2002. Micromagnetic Simulation of Magnetization Reversal Processes in Ferromagnetic Cubes from Quasisaturation State. Journal of Physics: Condensed Matter, Volume 14, pp. 8089–8101

Manke, I., Kardjilov, N., Schäfer, R., Hilger, A., Strobl, M., Dawson, M., Grünzweig, C., Behr, G., Hentschel, M., David, C., Kupsch, A., Lange, A., Banhart, J., 2010. Three-Dimensional Imaging of Magnetic Domains. Nature Communications, Volume 1(125), pp. 1–6

Miltat, J.E., Donahue, M.J., 2007. Numerical Micromagnetics: Finite Difference Methods. Handbook of Magnetism and Advanced Magnetic Materials, Helmut Kronmuller and Stuart Parkin (eds.), Volume 2: Micromagnetism, John Wiley & Sons, Ltd., pp. 1–23

Mu, C., Jing, J., Dong, J., Wang, W., Xu, J., Nie, A., Xiang, J., Wen, F., Liu, Z., 2019. Static and Dynamic Characteristics of Magnetism in Permalloy Oval Nanoring by Micromagnetic Simulation. Journal of Magnetism and Magnetic Materials, Volume 474, pp. 301–304

Nur Fitriana, K., Hafizah, M.A.E., Manaf, A., 2017. Synthesis and Magnetic Characterization of Mn?Ti Substituted SrO.6Fe_2?xMn_x/2Ti_x/2O₃ (x = 0.0–1.0) Nanoparticles by Combined Destruction Process. International Journal of Technology., Volume 8(4), pp. 644–650

Piao, H.-G., Djuhana, D., Shim, J.-H., Lee, S.-H., Jun, S.-H., Oh, S.K., Yu, S.-C., Kim, D.-H., 2010. Three-Dimensional Spin Configuration of Ferromagnetic Nanocubes. Journal of Nanoscience and Nanotechnology, Volume 10(11), pp. 7212–7216

Piao, H.-G., Shim, J.-H., Djuhana, D., Kim, D.-H., 2013. Intrinsic Pinning Behavior and Propagation Onset of Three-Dimensional Bloch-Point Domain Wall in a Cylindrical Ferromagnetic Nanowire. Applied Physics Letters, Volume 102(11), 112405, https://doi.org/10.1063/1.4794823

Russier, V., 2009. Spherical Magnetic Nanoparticles: Magnetic Structure and Interparticle Interaction. Journal of Applied Physics, Volume 105(7), 073915, https://doi.org/10.1063/1.3093966

Sanz-Hernández, D., Hamans, R.F., Liao, J.-W., Welbourne, A., Lavrijsen, R., Fernández-Pacheco, A., 2017. Fabrication, Detection, and Operation of a Three-Dimensional Nanomagnetic Conduit. ACS Nano, Volume 11(11), pp. 11066–11073

Sbiaa, R., Piramanayagam, S.N., 2017. Recent Developments in Spin Transfer Torque MRAM. Physica Status Solidi RRL - Rapid Research Letters, Volume 11(12), 1700163, https://doi.org/10.1002/pssr.201700163

Schrefl, T., Hrkac, G., Bance, S., Suess, D., Ertl, O., Fidler, J., 2007. Numerical Methods in Micromagnetics (Finite Element Method). In: Handbook of Magnetism and Advanced Magnetic Materials, Kronmüller, H., Parkin, S. (Eds.), John Wiley & Sons, Ltd, Chichester, UK, p. hmm203

Skomski, R., 2001. Micromagnetic Spin Structure. In: Spin Electronics, Lecture Notes in Physics, Ziese, M., Thornton, M.J. (Eds.), Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 204–231

Skomski, R., 2003. Nanomagnetics. Journal of Physics: Condensed Matter, Volume 15(20), pp. R841–R896

Streubel, R., Kronast, F., Fischer, P., Parkinson, D., Schmidt, O.G., Makarov, D., 2015. Retrieving Spin Textures on Curved Magnetic Thin Films with Full-Field Soft X-ray Microscopies. Nature Communications, Volume 6(7612), pp. 1–11

Sun, L., Wong, P.K.J., Zhang, W., Zhai, Y., Niu, D.X., Xu, Y.B., Zou, X., Zhai, H.R., 2015. Micromagnetic Simulation on the Interelement Coupling of High-Density Patterned Film. IEEE Transactions on Magnetics, Volume 51(11), pp. 1–4

Suzuki, M., Kim, K.-J., Kim, S., Yoshikawa, H., Tono, T., Yamada, K.T., Taniguchi, T., Mizuno, H., Oda, K., Ishibashi, M., Hirata, Y., Li, T., Tsukamoto, A., Chiba, D., Ono, T., 2018. Three-Dimensional Visualization of Magnetic Domain Structure with Strong Uniaxial Anisotropy Via Scanning Hard X-ray Microtomography. Applied Physics Express, Volume 11(3), pp. 036601-1–036601-4

Udhiarto, A., Tamam, M.A., Nuryadi, R., Hartanto, D., 2014. Design and Simulation of Two Bits Single-Electron Logic Circuit using Double Quantum Dot Single Electron Transistor. International Journal of Technology, Volume 5(2), pp. 152–158

Usov, N.A., Nesmeyanov, M.S., 2020. Multi-Domain Structures in Spheroidal Co Nanoparticles. Scientific Reports, Volume 10(10173), pp. 1–9

Vaz, C.A.F., Bland, J.A.C., Lauhoff, G., 2008. Magnetism in Ultrathin Film Structures. Reports on Progress in Physics, Volume 71(5), pp. 1–78

Vousden, M., Bisotti, M.-A., Albert, M., Fangohr, H., 2016. Virtual Micromagnetics: A Framework for Accessible and Reproducible Micromagnetic Simulation. Journal of Open Research Software, Volume 4(1), pp. 1–7

Yani, A., Kurniawan, C., Djuhana, D., 2018. Investigation of the Ground State Domain Structure Transition on Magnetite (Fe₃O₄). In: Proceedings of the 3^rd International Symposium on Current Progress in Mathematics and Sciences 2017 (ISCPMS2017), Bali, Indonesia, p. 020020.

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