Micromagnetic Study on the Magnetization Reversal of ...

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

198 December 2018 Vol. 22 No. 4

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

Dede Djuhana1*, Dita Oktri1, and Candra Kurniawan1,2

1. Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia2. 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. Thehexagonal shape of the BFO film was modeled with thicknesses of 5, 10, and 15 nm and a diameter size ranging from50 to 100 nm. It was found that the coercivity field HC and the saturation field HS of the BFO film decreased as thediameter size increased and thickness decreased. It was observed that the nucleation field HN increased as the diametersize increased. An analysis of energies showed that the demagnetization energy was dominantly influenced by thediameter and thickness in comparison to the anisotropic energy. From the hysteresis curve, the switching time was alsoinvestigated. Interestingly, the switching time was faster for the thinner BFOs with a diameter under 70 nm. Forparticles larger than 70 nm in diameter, the switching time showed fluctuation irrespective of the BFO thickness. Basedon these results, a diameter size of 70 nm is proposed as the critical size for producing the equal time for switchingdomain polarity.

Abstrak

Studi Mikromagnetik Proses Pembalikan Magnetisasi pada Lapisan Tipis Barium Heksaferit (BaFe12O19). Padapenelitian ini, telah dilakukan investigasi terhadap mekanisme pembalikan magnetisasi berbasis kurva histeresis darilapisan tipis Barium Heksaferit (BFO) menggunakan simulasi mikromagnetik melalui pengamatan magnetisasi terhadaparah 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 koersif HC dan medansaturasi HS dari lapisan BFO mengecil sebanding dengan peningkatan ukuran diameter dan penurunan ketebalan. Dapatdiamati medan nukleasi HN meningkat sebanding dengan peningkatan ukuran diameter. Analisis energi menunjukkanbahwa energi demagnetisasi dipengaruhi secara dominan oleh diameter dan ketebalan dibandingkan dengan energianisotropik. Dari kurva histerisis, dianalisis juga adanya waktu pembalikan. Hal menarik teramati bahwa waktupembalikan terjadi lebih cepat pada BFO yang lebih tipis dengan diameter di bawah 70 nm. Pada ukuran diameterpartikel 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 padaproses 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 materialsthat 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 witha P63/mmc space group that has high uniaxial magneticanisotropy energy [2, 4, 5]. On the other hand, goodchemical stability, high temperature and corrosionresistances, and high mechanical hardness make BFO anattractive material to exploit further potential applications[6, 7]. Based on author’s knowledge, most of the previous

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Makara J. Sci. December 2018 Vol. 22 No. 4

studies involving BFO materials have focused on thematerial preparation methods, influence of dopants, andmacroscale magnetic properties stimulated by practicalapplications [8–10].

There are many popular methods to produce BFOparticles such as using solid state reaction, mechanicalalloying, coprecipitation, sol-gel, and hydrothermalmethods [11–13]. In recent years, some efforts havebeen made toward the growth of nanostructure BFO thinfilm of BFO due to its potential application in ultrahighdensity magnetic recording [14]. While methods havebeen effective in producing bulk quantities of single-phase BFO particles, discussions about the growth ofnanostructure grains and the properties of single-domainparticles of Barium ferrites are lacking. The magneticconfiguration of individual nanostructures has also beenrarely discussed, although several facilities, such asLorentz microscopy, magnetic force microscopy, scanningtunneling microscopy, and Kerr microscopy, have beenemployed to study local magnetic behaviors [15, 16].The limited resolution of those experimental facilitiesmade the observations of the magnetic configuration innanoscale insufficient. Alternatively, a simulation approachusing the micromagnetic method can be performed toanalyze a specific behavior of local magnetization basedon the Landau-Lifshitz-Gilbert equation [17]. Accordingto most studies, the micromagnetic method is powerfulfor the study of next generation ultrahigh densitymagnetic recording materials, including spintronicsdevelopments, due to the continuum approach thatbridges the molecular and macroscopic analysis of theferromagnetic system [18, 19].

This study investigated the magnetization behavior of asingle BFO thin film in the presence of an externalmagnetic field in order to obtain its hysteresis curves forboth in-plane and out-plane directions at a size intervalranging from 50 to 100 nm. Our previous study hasshown that the critical size of a single hexagonal BFOnanostructure was around 430 nm, which agrees withthe analytical Kittel formula [20, 21]. This means thatthe simulations in the present study are in the regime ofsingle-domain particles. The influence of hexagonal sizeon the coercivity, anisotropic field, nucleation field, andswitching time, along with domain configuration arediscussed in detail.

Materials and Methods

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

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

15 nm. Material parameters, such as saturation mag-netization, Ms = 275 kA/m, magnetocrystalline anisotropyconstant, K1 = 96 kJ/m3, and exchange constant, A = 2 ×10-11 J/m, were used in this simulation [23]. Thedamping constant α was fixed at 0.1 and the cell sizewas 2.5×2.5×5 nm3 taking into consideration that the

exchange length of BFO 20/2 sex MAl was around

6.5 nm [4,19]. The initial spin configuration of BFOwas set to random, as shown in Fig. 1(b), and thetemperature was 0 K. Then, the magnetic field wasapplied from -1000 mT to +1000 mT in x direction (Hx)and z direction (Hz) in order to observe magnetizationbehavior on the hard and easy axes direction,respectively.

Results and Discussion

The hysteresis curve of the BFO film diameter andthickness variation is displayed in Figure 2(a–c). Thehysteresis curve closely showed a rectangular patterncorresponded to its easy axis direction. Interestingly thedomain structures only exhibited single-domain struc-ture magnetization and followed the Stoner-Wohlfarthprediction [24]. This was understandable because thedimensions of the simulated BFO were below the criti-cal size, which was around 525 nm [20, 21, 25], and thesingle-domain structure was easily formed. Then, thecoercivity field was observed from the z direction mag-netization for the diameter and thickness variation, asdepicted in Figure 2(d). The coercivity field (Hc) de-creased as the diameter size of BFO increased, while itincreased as the thickness increased. The decreasing ofHc was found to be linear with the increasing diameter.The coherent rotation of magnetization along the easyaxis contributed to the smoothly decreasing coercivityfield as the diameter increased. The value of Hc wasaround 400–520 mT, which was approximately close tothe results of Zhang’s work at low temperature [26].The reduction of Hc in hexaferrite nanostructures hasalso been observed experimentally by some researchers.

200 Djuhana, et al.


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

due to the particle size increase. Our results similarlyshowed that the thicker BaFe12O19 film has a largercoercivity value, which particularly occurred in the sin-gle-domain particle size regime.

Concerning easy axis magnetization, we observed thesaturation field (Hs) in relation to easy axis magnetiza-tion, as given in Figure 3(a), for the diameter and thick-ness variation. The saturation field decreased as the di-ameter increased, whereas it increased as the thicknessincreased. 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 (HS); (b) The Energy Density Consisting of the Demagnetization Energy (Circle) and theAnisotropy Energy (Diamond) Corresponds to the Diameter and Thickness Variation

followed the coercivity field. In this sense, the particledimension and ratio influenced intrinsic magnetic prop-

erties, such as the saturation field. It is known that atlarger volume of the film uses a larger amount of energy



equally with the given magnetic field. However, oursimulation found that the thickness of the film morestrongly affected the Hs values than the film diameter,thus the ratio of the film became important as shown inFigure 3(a). The energy densities of BFO, such as thedemagnetization and anisotropy energies, were alsoanalyzed. The energies are represented in Figure 3(b)through the diameter and thickness variation. Interest-ingly, it was also observed that the demagnetizationenergy decreased as the diameter of the BFO thin filmincreased, while the anisotropy energy was relativelyconstant as the diameter and thickness increased. There-fore, the demagnetization energy was highly affected bythe thin film geometry over the anisotropic energy, asshown in the Figure 3(b). This result, according towhich the demagnetization energy is affected by chang-ing the BFO dimension agrees with the report byGoolaup [25]. As indicated in Figure 3, the saturationfield and the demagnetization energy were related to thechanges in diameter. The demagnetization energy origi-nated from the demagnetization or magnetostatics fieldin the magnetic system [4].

Furthermore, the BFO hysteresis curve in x directionwas also produced, as shown in Figure 4 for the diame-ter and thickness variation. The hysteresis curve showeda typical S-curve for all the diameter and thickness vari-ations, as usually found in the hard axis magnetizationdirection. 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 justas it was reported in Permalloy (Py) [28, 29]. It wasshown that HN changed as the diameter and thicknessincreased. For the cases in which the thicknesses were t= 5 nm and t = 10 nm, the nucleation field tend to in-crease as the diameter increased. However, for thicknesst = 15 nm, the nucleation field showed small fluctuationfrom 50 nm to 70 nm, and above 70 nm it became con-stant. This result was obtained irrespective to changes inthe diameter. Based on the energy analysis shown inFigure 3(b), the anisotropy energy of the 10 nm and 15nm thicknesses were lower for d = 60 in comparison tothe thickness of 5 nm. These characteristics contributedto the total energy that affected the slightly reduced nu-cleation field. In comparison to the thickness 5 nm, theanisotropy energy was insensitive to diameter. There-fore, the total energy was only contributed to by thedemagnetization energy that monotonously increasedthe nucleation field.

Figure 5 shows the domain structure evolution of theBFO thin film, which was applied using a quasi-staticfield in the x direction for the case d = 100 nm with respectto the thicknesses t = 5, 10, and 15 nm. The saturationmagnetization was obtained by giving an external mag-netic field around 1000 mT and denoted by position 1 (xpositive) 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 VariedThicknesses 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 stillmaintained a single-domain structure and the vectormagnetization direction also changed, as presented atpositions 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 struc-ture again at zero magnetic field (positions 3 and 6) withthe vector magnetization preferred to the easy axis mag-netization for all thicknesses. These results showed thatthe magnetization rotation during the domain switchingprocess was coherent and in agreement with the theoret-ical and experimental prediction [30, 31].

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

polarization, such as positive to negative polarization. Itwas observed that the switching time increased as thediameter size increased. Interestingly as can be seen inFigure 6, the switching time increased as the thicknessincreased, until the diameter was around 70 nm. Abovethe 70 nm diameter, the switching time showed a fluctu-ation that was irrespective to the BFO thickness. It wasalso found the relatively equal switching time occurredat the diameter 70 nm for all thicknesses. This meansthat the 70 nm diameter size of the BFO thin film wasthe critical size for switching domain polarity. Abovethe 70 nm diameter, the switching process could be af-fected by incoherent rotation and domain wall motion[32]. These results suggest that the switching time in thehard-magnetic orientation was also influenced by thenucleation field HN. In comparison to Figure 4(d), theswitching time tended to produce the same characteris-tics. For the thickness of 5 nm, an increase of the filmdiameter also increased the switching time significantly.



Figure 6. Switching Time Observation of the BFO ThinFilm in Response to the Diameter Size andThickness Variation

However, for the thicknesses of 10 nm and 15 nm, theswitching time increased only slightly and correspondedwith the insensitive trend of the nucleation field for thesame film size.

Conclusion

In this paper, we investigated the magnetic hysteresiscurve characteristics of Barium Hexaferrite (BFO) nanothin film by micromagnetic simulation methods. Thehexagonal shape of the BFO film was simulated usingvaried the thicknesses of 5, 10, and 15 nm and adiameter size ranging from 50 to 100 nm. This diametersize interval was below the single-domain critical size.It was observed that the coercivity of the hexaferritethin film slightly decreased as the diameter sizeincreased. However, the coercivity increased as thethickness increased. For the hard axis orientationmagnetic field, it was found that the nucleation field HN

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

values were increased as the diameter increased. Thisshows that the demagnetization energy values weredominantly influenced by diameter and thickness size incomparison to anisotropic energy values. Therefore, theincrease in the saturation field was contributed to byincreasing the demagnetization energy as the BFOthickness increases. Interestingly, it was also shown thatthe switching time is faster for a thinner BFO of adiameter that is under 70 nm. For a particle larger than70 nm in diameter, the switching time showedfluctuation that seemed to be irrespective of the BFOthickness. Therefore, the diameter size of 70 nm isproposed as the critical size for producing the equaltime for switching domain polarity.

Acknowledgments

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

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