• International Journal of Technology (IJTech)
  • Vol 12, No 3 (2021)

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

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

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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

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
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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.

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


     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, Ni0.8Fe0.2 (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.


    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.


        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.


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