Makara Journal of Science Makara Journal of Science

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Makara Journal of Science Makara Journal of Science

Volume 22

Issue 4 December Article 7

12-20-2018

Micromagnetic Study on the Magnetization Reversal of Barium Micromagnetic Study on the Magnetization Reversal of Barium Hexaferrite (BaFe12O19) Thin Film

Hexaferrite (BaFe12O19) Thin Film

Dede Djuhana

Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia, [email protected]

Dita Oktri

Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia

Candra Kurniawan

1. Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia. 2. Research Center for Physics, Indonesian Institute of Sciences (LIPI), Tangerang Selatan 15314, Indonesia.

Follow this and additional works at: https://scholarhub.ui.ac.id/science Recommended Citation

Recommended Citation

Djuhana, Dede; Oktri, Dita; and Kurniawan, Candra (2018) "Micromagnetic Study on the Magnetization Reversal of Barium Hexaferrite (BaFe12O19) Thin Film," Makara Journal of Science: Vol. 22 : Iss. 4 , Article 7.

DOI: 10.7454/mss.v22i4.9986

Available at: https://scholarhub.ui.ac.id/science/vol22/iss4/7

This Article is brought to you for free and open access by the Universitas Indonesia at UI Scholars Hub. It has been accepted for inclusion in Makara Journal of Science by an authorized editor of UI Scholars Hub.

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Micromagnetic Study on the Magnetization Reversal of Barium Hexaferrite Micromagnetic Study on the Magnetization Reversal of Barium Hexaferrite (BaFe12O19) Thin Film

(BaFe12O19) Thin Film

Cover Page Footnote Cover Page Footnote

This study is supported by theHibah Publikasi Internasional Terindeks untuk Tugas Akhir Mahasiswa (PITTA) Universitas Indonesia with contract No:2245/UN2.R3.1/HKP.05.00/2018.

This article is available in Makara Journal of Science: https://scholarhub.ui.ac.id/science/vol22/iss4/7

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Makara Journal of Science, 22/4 (2018), 198-204 doi: 10.7454/mss.v22i4.9986

198 December 2018Vol. 22No. 4

Micromagnetic Study on the Magnetization Reversal of Barium Hexaferrite (BaFe

12

O

19

) Thin Film

Dede Djuhana

^1*

, Dita Oktri

¹

, and Candra Kurniawan

^1,2

1. Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia 2. Research Center for Physics, Indonesian Institute of Sciences (LIPI), Tangerang Selatan 15314, Indonesia

*E-mail: [email protected]

Received October 21, 2018 | Accepted December 28, 2018

Abstract

This study investigates a magnetization reversal mechanism based on the hysteresis curve of Barium Hexaferrite (BFO) thin film by micromagnetic simulation through parallel and perpendicular magnetization directions along the axes. The hexagonal shape of the BFO film was modeled with thicknesses of 5, 10, and 15 nm and a diameter size ranging from 50 to 100 nm. It was found that the coercivity field HCand the saturation field HSof the BFO film decreased as the diameter size increased and thickness decreased. It was observed that the nucleation fieldHNincreased as the diameter size increased. An analysis of energies showed that the demagnetization energy was dominantly influenced by the diameter and thickness in comparison to the anisotropic energy. From the hysteresis curve, the switching time was also investigated. Interestingly, the switching time was faster for the thinner BFOs with a diameter under 70 nm. For particles larger than 70 nm in diameter, the switching time showed fluctuation irrespective of the BFO thickness. Based on these results, a diameter size of 70 nm is proposed as the critical size for producing the equal time for switching domain polarity.

Abstrak

Studi Mikromagnetik Proses Pembalikan Magnetisasi pada Lapisan Tipis Barium Heksaferit (BaFe12O19).Pada penelitian ini, telah dilakukan investigasi terhadap mekanisme pembalikan magnetisasi berbasis kurva histeresis dari lapisan tipis Barium Heksaferit (BFO) menggunakan simulasi mikromagnetik melalui pengamatan magnetisasi terhadap arah sejajar dan tegak lurus bidang aksis. Bentuk heksagonal dari lapisan BFO dimodelkan dengan variasi ketebalan 5, 10, dan 15 nm dan rentang ukuran diameter dari 50 sampai 100 nm. Ditemukan bahwa medan koersifHCdan medan saturasiHSdari lapisan BFO mengecil sebanding dengan peningkatan ukuran diameter dan penurunan ketebalan. Dapat diamati medan nukleasi HN meningkat sebanding dengan peningkatan ukuran diameter. Analisis energi menunjukkan bahwa energi demagnetisasi dipengaruhi secara dominan oleh diameter dan ketebalan dibandingkan dengan energi anisotropik. Dari kurva histerisis, dianalisis juga adanya waktu pembalikan. Hal menarik teramati bahwa waktu pembalikan terjadi lebih cepat pada BFO yang lebih tipis dengan diameter di bawah 70 nm. Pada ukuran diameter partikel lebih besar dari 70 nm, terjadi fluktuasi nilai waktu pembalikan tidak tergantung terhadap ketebalan BFO.

Berdasarkan hasil tersebut, diameter partikel 70 nm dapat menjadi ukuran kritis terjadinya waktu yang sama pada proses pembalikan polaritas domain.

Keywords: micromagnetics, magnetization reversal, hysteresis, barium hexaferrite

Introduction

Magnetoplumbite-type Barium ferrite (BaFe12O19, BFO) is one of the well-known permanent magnet materials that has been widely applied to sensors, toys, motors, microwave absorbers, and magnetic storage media [1-3].

A BFO with a hexagonal close packed (HCP) crystal

structure consists of 64 ions per primitive unit cells with a P63/mmc space group that has high uniaxial magnetic anisotropy energy [2, 4, 5]. On the other hand, good chemical stability, high temperature and corrosion resistances, and high mechanical hardness make BFO an attractive material to exploit further potential applications [6, 7]. Based on author’s knowledge, most of the previous

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studies involving BFO materials have focused on the material preparation methods, influence of dopants, and macroscale magnetic properties stimulated by practical applications [8–10].

There are many popular methods to produce BFO particles such as using solid state reaction, mechanical alloying, coprecipitation, sol-gel, and hydrothermal methods [11–13]. In recent years, some efforts have been made toward the growth of nanostructure BFO thin film of BFO due to its potential application in ultrahigh density magnetic recording [14]. While methods have been effective in producing bulk quantities of single- phase BFO particles, discussions about the growth of nanostructure grains and the properties of single-domain particles of Barium ferrites are lacking. The magnetic configuration of individual nanostructures has also been rarely discussed, although several facilities, such as Lorentz microscopy, magnetic force microscopy, scanning tunneling microscopy, and Kerr microscopy, have been employed to study local magnetic behaviors [15, 16].

The limited resolution of those experimental facilities made the observations of the magnetic configuration in nanoscale insufficient. Alternatively, a simulation approach using the micromagnetic method can be performed to analyze a specific behavior of local magnetization based on the Landau-Lifshitz-Gilbert equation [17]. According to most studies, the micromagnetic method is powerful for the study of next generation ultrahigh density magnetic recording materials, including spintronics developments, due to the continuum approach that bridges the molecular and macroscopic analysis of the ferromagnetic system [18, 19].

This study investigated the magnetization behavior of a single BFO thin film in the presence of an external magnetic field in order to obtain its hysteresis curves for both in-plane and out-plane directions at a size interval ranging from 50 to 100 nm. Our previous study has shown that the critical size of a single hexagonal BFO nanostructure was around 430 nm, which agrees with the analytical Kittel formula [20, 21]. This means that the simulations in the present study are in the regime of single-domain particles. The influence of hexagonal size on the coercivity, anisotropic field, nucleation field, and switching time, along with domain configuration are discussed in detail.

Materials and Methods

To produce the hysteresis curve of the BFO film, micromagnetic simulation was performed using public software, the Object Oriented Micro-Magnetic Framework (OOMMF) based on the Landau-Lifshitz-Gilbert (LLG) equation [18-22]. A hexagonal shape BFO film was used as illustrated in Figure 1(a), with respect to the diameter size and thickness variation. The diameter size varied from 50 to 100 nm and the thicknessestwere 5, 10, and

Figure 1. (a) The Hexagonal Shape BFO Model, which the Magnetic Field was Applied in x Direction (Hx) and z Direction (Hz); (b) the Initial Magnetization is set to Random with the Color Bar Representing the Magnetization Direction

15 nm. Material parameters, such as saturation magnetization,Ms= 275 kA/m, magnetocrystalline anisotropy constant,K1= 96 kJ/m³, and exchange constant,A= 2 × 10^-11 J/m, were used in this simulation [23]. The damping constant α was fixed at 0.1 and the cell size was 2.5×2.5×5 nm³ taking into consideration that the exchange length of BFO l_ex 2A/₀M_s² was around 6.5 nm [4,19]. The initial spin configuration of BFO was set to random, as shown in Fig. 1(b), and the temperature was 0 K. Then, the magnetic field was applied from -1000 mT to +1000 mT in x direction (Hx) and z direction (Hz) in order to observe magnetization behavior on the hard and easy axes direction, respectively.

Results and Discussion

The hysteresis curve of the BFO film diameter and thickness variation is displayed in Figure 2(a–c). The hysteresis curve closely showed a rectangular pattern corresponded to its easy axis direction. Interestingly the domain structures only exhibited single-domain structure magnetization and followed the Stoner-Wohlfarth prediction [24]. This was understandable because the dimensions of the simulated BFO were below the critical size, which was around 525 nm [20, 21, 25], and the single-domain structure was easily formed. Then, the coercivity field was observed from the z direction magnetization for the diameter and thickness variation, as depicted in Figure 2(d). The coercivity field (Hc) decreased as the diameter size of BFO increased, while it increased as the thickness increased. The decreasing of Hc was found to be linear with the increasing diameter.

The coherent rotation of magnetization along the easy axis contributed to the smoothly decreasing coercivity field as the diameter increased. The value of Hc was around 400–520 mT, which was approximately close to the results of Zhang’s work at low temperature [26].

The reduction of Hc in hexaferrite nanostructures has also been observed experimentally by some researchers.

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200 Djuhana, et al.

The study by Mosleh et al. [27] showed that an annealing temperature could have an increasing effect on Hc

due to the particle size increase. Our results similarly showed that the thicker BaFe12O19 film has a larger coercivity value, which particularly occurred in the single-domain particle size regime.

Concerning easy axis magnetization, we observed the saturation field (Hs) in relation to easy axis magnetization, as given in Figure 3(a), for the diameter and thickness variation. The saturation field decreased as the diameter increased, whereas it increased as the thickness increased. The decreasing trend of the saturation field

Figure 2. The Hysteresis BFO Curve in the z Direction Magnetic Field with Respect to the Thickness Variation (a) t = 5 nm, (b) t = 10 nm, (c) t =15 nm, and (d) the Coercivity Field to Diameter and Thickness Variation. Symbols (*) and (**) Relate to the Domain Structure in Positive and Negative Magnetization, Respectively

Figure 3. (a) The Saturation Field (H_S); (b) The Energy Density Consisting of the Demagnetization Energy (Circle) and the Anisotropy Energy (Diamond) Corresponds to the Diameter and Thickness Variation

followed the coercivity field. In this sense, the particle

dimension and ratio influenced intrinsic magnetic properties, such as the saturation field. It is known that at larger volume of the film uses a larger amount of energy

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equally with the given magnetic field. However, our simulation found that the thickness of the film more strongly affected the Hsvalues than the film diameter, thus the ratio of the film became important as shown in Figure 3(a). The energy densities of BFO, such as the demagnetization and anisotropy energies, were also analyzed. The energies are represented in Figure 3(b) through the diameter and thickness variation. Interest- ingly, it was also observed that the demagnetization energy decreased as the diameter of the BFO thin film increased, while the anisotropy energy was relatively constant as the diameter and thickness increased. There- fore, the demagnetization energy was highly affected by the thin film geometry over the anisotropic energy, as shown in the Figure 3(b). This result, according to which the demagnetization energy is affected by chang- ing the BFO dimension agrees with the report by Goolaup [25]. As indicated in Figure 3, the saturation field and the demagnetization energy were related to the changes in diameter. The demagnetization energy origi- nated from the demagnetization or magnetostatics field in the magnetic system [4].

Furthermore, the BFO hysteresis curve in x direction was also produced, as shown in Figure 4 for the diameter and thickness variation. The hysteresis curve showed a typical S-curve for all the diameter and thickness vari- ations, as usually found in the hard axis magnetization direction. An interesting aspect of the hysteresis curve

in the x direction was in respect to the nucleation field (HN), where the magnetic field abruptly decreased just as it was reported in Permalloy (Py) [28, 29]. It was shown that HN changed as the diameter and thickness increased. For the cases in which the thicknesses weret

= 5 nm andt= 10 nm, the nucleation field tend to increase as the diameter increased. However, for thickness t= 15 nm, the nucleation field showed small fluctuation from 50 nm to 70 nm, and above 70 nm it became constant. This result was obtained irrespective to changes in the diameter. Based on the energy analysis shown in Figure 3(b), the anisotropy energy of the 10 nm and 15 nm thicknesses were lower ford= 60 in comparison to the thickness of 5 nm. These characteristics contributed to the total energy that affected the slightly reduced nucleation field. In comparison to the thickness 5 nm, the anisotropy energy was insensitive to diameter. There- fore, the total energy was only contributed to by the demagnetization energy that monotonously increased the nucleation field.

Figure 5 shows the domain structure evolution of the BFO thin film, which was applied using a quasi-static field in the x direction for the cased= 100 nm with respect to the thicknesses t = 5, 10, and 15 nm. The saturation magnetization was obtained by giving an external magnetic field around 1000 mT and denoted by position 1 (x positive) and position 4 (x negative) with the single- domain structure. Then, the domain structure started to

Figure 4. The BFO Hysteresis Curve in the x Direction Magnetic Field with Respect to the Thickness Variation (a)t= 5 nm, (b)t= 10 nm, (c)t= 15 nm, and (d) the Nucleation field (HN) in Relation to the Diameter and Thickness Variation

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Figure 5. The Magnetic Domain Structures during Magnetization Reversal Process in x Direction Magnetic Field with Varied Thicknesses of (a) 5 nm, (b) 10 nm, and (c) 15 nm

change after the magnetic field was applied in the oppo- site direction. It was found that the domain structure still maintained a single-domain structure and the vector magnetization direction also changed, as presented at positions 2 and 5 around the field magnitude of 340 mT (t= 5 nm), 380 mT (t= 10 nm), and 420 mT (t= 15 nm).

Interestingly, the domain showed a single-domain structure again at zero magnetic field (positions 3 and 6) with the vector magnetization preferred to the easy axis magnetization for all thicknesses. These results showed that the magnetization rotation during the domain switching process was coherent and in agreement with the theoretical and experimental prediction [30, 31].

Besides the coercivity, nucleation, and saturation field, the switching time of BFO thin film was also determined based on the hysteresis curve in x direction magnetic field. The switching time was defined by the time needed to switch the domain magnetization from a different

polarization, such as positive to negative polarization. It was observed that the switching time increased as the diameter size increased. Interestingly as can be seen in Figure 6, the switching time increased as the thickness increased, until the diameter was around 70 nm. Above the 70 nm diameter, the switching time showed a fluctuation that was irrespective to the BFO thickness. It was also found the relatively equal switching time occurred at the diameter 70 nm for all thicknesses. This means that the 70 nm diameter size of the BFO thin film was the critical size for switching domain polarity. Above the 70 nm diameter, the switching process could be affected by incoherent rotation and domain wall motion [32]. These results suggest that the switching time in the hard-magnetic orientation was also influenced by the nucleation field HN. In comparison to Figure 4(d), the switching time tended to produce the same characteristics. For the thickness of 5 nm, an increase of the film diameter also increased the switching time significantly.

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Figure 6. Switching Time Observation of the BFO Thin Film in Response to the Diameter Size and Thickness Variation

However, for the thicknesses of 10 nm and 15 nm, the switching time increased only slightly and corresponded with the insensitive trend of the nucleation field for the same film size.

Conclusion

In this paper, we investigated the magnetic hysteresis curve characteristics of Barium Hexaferrite (BFO) nano thin film by micromagnetic simulation methods. The hexagonal shape of the BFO film was simulated using varied the thicknesses of 5, 10, and 15 nm and a diameter size ranging from 50 to 100 nm. This diameter size interval was below the single-domain critical size.

It was observed that the coercivity of the hexaferrite thin film slightly decreased as the diameter size increased. However, the coercivity increased as the thickness increased. For the hard axis orientation magnetic field, it was found that the nucleation fieldHN

values are changed as the BFO diameter and thickness increased. For thicknesses of 5 and 10 nm, the HN

values were increased as the diameter increased. This shows that the demagnetization energy values were dominantly influenced by diameter and thickness size in comparison to anisotropic energy values. Therefore, the increase in the saturation field was contributed to by increasing the demagnetization energy as the BFO thickness increases. Interestingly, it was also shown that the switching time is faster for a thinner BFO of a diameter that is under 70 nm. For a particle larger than 70 nm in diameter, the switching time showed fluctuation that seemed to be irrespective of the BFO thickness. Therefore, the diameter size of 70 nm is proposed as the critical size for producing the equal time for switching domain polarity.

Acknowledgments

This study is supported by the Hibah Publikasi Internasional Terindeks untuk Tugas Akhir Mahasiswa (PITTA) Universitas Indonesia with contract No:2245/

UN2.R3.1/HKP.05.00/2018.

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