MICROMAGNETIC STUDY OF THERMALLY ASSISTED MAGNETIZATION REVERSAL MECHANISM ON PERPENDICULARLY MAGNETIC ANISOTROPY CoXSiYBZ Oleh, Agustina Candra Dewi Permatasari NIM : 192009003
TUGAS AKHIR
Diajukan kepada Program Studi Pendidikan Fisika, Fakultas Sains dan Matematika guna memenuhi sebagian dari persyaratan untuk mencapai gelar Sarjana Pendidikan
Program Studi Pendidikan Fisika
Fakultas Sains dan Matematika Universitas Kristen Satya Wacana Salatiga 2013 i
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Kata Pengantar Puji dan Syukur kepada Tuhan Yesus Kristus Sang Juru Selamat, karena atas berkat dan kasih-Nya yang sungguh luar biasa sehingga penulis dapat menyelesaikan Tugas Akhir dengan baik. Skripsi ini ditulis dan disusun untuk memenuhi sebagian persyaratan memperoleh gelar sarjana pendidikan (S.Pd) Fisika di Universitas Kristen Satya Wacana Salatiga. Dalam penyusunan skripsi ini, tidak lepas dari bantuan dan dukungan berbagai pihak. Atas segala bantuan dan dukungan tersebut, pada kesempatan kali ini penulis mengucapkan terima kasih kepada : 1. Bapak Ferdy S. Rondonuwu, selaku dosen dan wali studi. Terima kasih telah menjadi orangtua saya selama kuliah di Universitas Kristen Satya Wacana, semoga Bapak sekeluarga selalu diberkati. 2. Bapak Nur Aji Wibowo, selaku dosen dan pembimbing 1, yang telah bersedia meluangkan waktu, memberikan tenaga, masukan, dorongan semangat, semua ilmu mengenai tugas akhir ini, serta pembelajaran yang sangat berharga mengenai kedisiplinan waktu maupun target dalam menulis tugas akhir ini sehingga dapat selesai tepat sesuai rencana. Terimakasih Pak, atas semuanya itu. Semoga Tuhan Yesus Kristus selalu beserta Bapak sekeluarga. 3. Bapak Suryasatriya Trihandaru, selaku dosen dan pembimbing 2, terima kasih atas pendalaman yang diberikan untuk tugas akhir ini dan bersedia meluangkan waktu untuk bimbingan di sela-sela kesibukan. 4. Semua Dosen Fisika yang sudah mengajari dan mendidik saya, Ibu Marmi, Pak Adita, Pak Kris, Ibu Shanti, Pak Andre, Ibu Diane, Bu Debora dan Pak Alfa. Terima kasih banyak untuk ilmu yang sangat bermanfaat selama hidup saya, Tuhan Yesus memberkati. 5. Keluargaku tercinta, Bapak, Ibu, kakak dan suaminya, cipat dan gondel. Terima kasih untuk dukungan doa, sharing, semangat, dan bantuan materiil yang diberikan, sehingga penulis dapat menyelesaikan kuliah dan skripsi dengan baik. 6. Keluarga Selfrimus, dimanapun mereka berada. Terima kasih untuk dukungan doa serta motivasi yang sangat kuat untuk lulus bulan Juli. You are the best for me. 7. Laboran-laboran yang selalu direpotkan. Mas Tri, Mas Sigit dan Pak Tafid terimakasih atas kesabaran menghadapi penulis yang banyak maunya dan cerewet. Semoga semuanya selalu diberkati Tuhan Yesus. 8. Buat sahabatku, para MAMEN..Makasih ya Mamen Ayuk, Natalis dan Nimang..serta Mas Roy..kalian teman terbaik bahkan menjadi saudara disaat penulis galau. Begitu banyak cerita tentang kita, dari awal jas almameter kita kenakan, perjalanan selama kuliah yang penuh liku-liku, hingga jas almameter ini akan kita lepas, kita selalu berjuang bersama. I will be miss you all….
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9. Teman-teman Fisika dan Pendidikan Fisika angkatan 2009 yang tidak dapat disebutkan satu-satu. Terimakasih kawan atas semua kisahnya dan menemani penulis hingga skripsi dapat selesai. Tugas akhir yang dibuat ini belumlah sempurna, sehingga kritik dan saran yang membangun sangat dibutuhkan dalam penyempurnaan ke depan.
Salatiga, 27 Juni 2013
Penulis
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MOTTO “Success is a state of mind. If you want success, start thinking of yourself as a success. "
Dipersembahkan kepada : 1.Allah Bapa di surga, Yesus Kristus dan Bunda Maria juru slamatku. 2. Bapak dan Ibuku, orang tua terhebat. 3. Universitas Kristen Satya Wacana. 4. Keluarga kakakku satu-satunya. 5. Keluarga Selfrimus.
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Micromagnetic Study of Thermally Assisted Magnetization Reversal Mechanism on Perpendicularly Magnetic Anisotropy CoXSiYBZ Agustina Candra D.P, Suryasatriya Trihandaru, Nur Aji Wibowo Satya Wacana Christian University, Faculty of Science and Mathematic, 52-60 Diponegoro, Salatiga 50711, Jawa Tengah, Indonesia
[email protected] [email protected] Abstract Micromagnetic simulation for perpendicular magnetic anisotropy CoxSiyBz substance which utilizes thermal activating for several parameter such as anisotropy constant and saturation magnetization parameter has been examined using Landau-Liftshitz Gilbert equation. Perpendicular Magnetic Anisotropy is used to realize storage medium with sizable capacity. However, it has a disadvantage in the need of a large writing field. Providing of heat can be used as a solution to lessen magnitude of writing field. At room temperature, combination value of anisotropy constant and saturation magnetization give impact to energy barrier, switching field and domain wall propagation rate in magnetization reversal. When nano-dot is heated at Curie temperature then cooled abruptly until room temperature, writing field is needed to reverse the magnetization has been successfully reduced up to ~ 90%. Keyword: anisotropy constant, saturation magnetization, probability, domain wall and reversal field.
1. INTRODUCTION The rapid development of Personal Computer (PC) is mainly caused by the human needs of processing data and information using PC. One motivating aspect in the development of PC is the worldwide needs of the existence of a storing media with massive capacity and high speed in reading and writing abilities. In 2006, Perpendicular Magnetic Recording (PMR) was introduced as a new technology of a magnetic recording of hard drive which unitizes Perpendicular Magnetic Anisotropy (PMA) as storing media. This technology offer a bigger capacity, better ability and endurance. In PMR, the magnetic bits direction are perpendicular to its surface. Whereas in the conventional recording technology, Longitudinal Magnetic Recording (LMR) which developed, its magnetic bits was arranged parallel to the surface, so that, a larger area is needed in storing the information [1][2]. However, in PMR technology, a greater energy is required in reversing the direction of magnetized composer bits. A promising alternative solution that can be used to reduce the energy is by giving an amount of heat during the reversing magnetization [3]. The magnetic material’s properties are very influential in the reversal process of magnetization. There are several parameters that can be used in determining the characteristics of the material such as anisotropy constant and saturation magnetization. In this paper, the influence of those parameters in reordering the magnetization at room temperature altogether with thermal activation examined in a simulation of micromagnetic by using the Landau-Liftshitz Gilbert (LLG) Equation.
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2. METHODS Influence of magnetic material properties to the reversal mechanism of magnetization was investigated by modeling ferromagnetic material with perpendicular magnetic anisotropy CoxSiyBz as a perpendicular magnetized nano-dot having 50 50 20 nm3 in dimension.
Figure 1: Nano-dot models which the volume is 50 50 20 nm3 with appropnate coordinate. Chosen magnetic material parameters for CoxSiyBz are 4Ms = 4116,6 G with K = 2 106 erg/cm3 [4]. Magnetization reversal simulation is done by accomplishing the Landau - Liftshitz Gilbert (LLG) Equation. It contains the time derivative of the magnetization on one of side only which is shown in Eq.(1). This equation describes the magnetic material response which is characterized by the magnetization direction if it is induced by a current field [5].
dMi i i i 0 0 2 Mi Heff M Mi Heff dt Ms 1 2 1
(1)
where M as the magnetization, Ms as the saturation magnetization, as the gilbert damping constant (0.3), 0 as the gyro-magnetic ratio (1.7 107/Oe-1.s-1) and Heff as the effective field. The Heff is composed by anisotropy field (Hk), magnetostatic field (HM), the exchange interaction field (Hex), the external field (Hext) and a random stochastic field (HT) if a thermal field activated as seen in Eq.(2) [6]. i i i Hieff Hki HM Hex Hext HTi
(2)
Hex as an exchange stiffness constant function which described in Eq.(3)[7].
Hex
A M 0Ms2
(3)
where A as exchange stiffness constant (1×107 erg/cm), 0 as permeability of vacuum and function of M as shown in Eq.[8]. M
2 2 2 M M Mz x y x 2 y 2 z 2
(4)
The exchange energy between the magnetization i and j in a system of N spin is defined as [9] :
2
Eex
N
i , j ,k 1
2
2
A Mx r My r Mz r
2
(5)
where Mx ,y ,z is the spatial gradient of the magnetization normalized components corresponding to the x, y and z axis. The temperature dependence of exchange stiffness can be formulated in Eq. (6)[10]. M T A(T ) A s M 0 s
2
(0)
(6)
where T as actual room temperature (298 K). Relation between Hk with anisotropy constant is expressed as a function of the unitary vector m can be seen at Eq.(7)[9]. Hk
2K (u.m)u 0 Ms
(7)
M . Ms The effect of temperature toward the anisotropy and saturation magnetization constant is shown in Eq.(8) and (9)[10].
where u is the unit vector, along the direction of the uniaxial easy axis 1 0 0 and m
0 M T K T K s M 0 s
2
(8)
0,5 0 Ms T Ms 1 T / Tc
(9)
where K = anisotropy constant, Ms = saturation magnetization and Tc = curie temperature with the assumed value 373 K. The thermal fluctuation field has zero mean and is assumed to be Gaussian distributed with a variance given by the fluctuation-dissipation theorem as shown in Eq. (10), Eq.(11) and Eq.(12)[11]. HTi t 0
HTi t HTj t '
(10)
ij t t ' 2
2kBT VMs t
(11)
(12)
with t is the delta dirac function, ij is the Kronecker delta, the indices i and j label the unit cell or the vector component, k B = boltzman constant, V = volume of nano-dot (50 50 20 nm3) and t = time increment ( 0, 25 10 12 s).
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3. RESULT/DISCUSSION 3.1 Magnetization Reversal at Room Temperature Nano-dot ferromagnetic with perpendicular anisotropy which analyzed numerically in this research magnetized upward, perpendicularly to its surface along +x (M). In the scheme of micromagnetic simulation of writing process through declining energy barrier mechanism, nano-dot is conditioned at the room temperature and then induced by a bias magnetic field (HB) opposite to its initial magnetization with linearly increasing size from 0 to 20 kOe during 2,5 ns as shown in Figure 2.
2
300 298 296
1 294
T (K)
HB (104 Oe)
T
HB 292 0 0
1
2
290
t (ns)
Figure 2 : Scheme of micromagnetic simulation of the writing process through mechanism of declining energy barrier.
Figure 3: Energy barrier occurred in perpendicular magnetized nano-dot at room temperature (298K).
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In order to reverse the nano-dot magnetization into –x direction (M), bias magnetic field in –x orientation is needed to overcome an energy barrier inside. This energy barrier separates two minimum energy level, which representing the direction of upward and downward magnetization as seen in Figure 3.
Figure 4: Magnetization reversal mechanism occurred in perpendicular magnetized nano-dot at room temperature (298K). Figure 4 shows that the reversal process is represented through the value of Mx/Ms. Mx and Ms are the actual magnetization in the x axis and initial magnetization respectively. For Mx/Ms = 1, magnetization of nano-dot saturated in +x direction. While for Mx/Ms= 0, nano-dot magnetization is perpendicularly oriented to its initial magnetization and/or the number of upward and downward magnetic moment is equal so that they cancel each other. In other words, the nano-dot magnetization exactly will reverse and then this point is called as a switching point, whereas the current magnetic field and time related to this point is called as switching field (Hswt) and switching time (tswt). Explicitly, Hswt and tswt are the minimum bias field and time are needed to switch the magnetization. Mx/Ms= 1 shows that magnetization of the nano-dot is saturated toward the external magnetic field direction.
t = 1,087 ns
t = 1,130 ns
t = 1,222 ns
t = 1,333 ns
t = 1,521 ns
Figure 5 : Visualization of magnetization reversal mechanism with corresponding properties for CoxSiyBz material are 4Ms = 5316,6 G and K = 2 106 erg/cm3 at room temperature ( 298 K)
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Figure 5 visualizes the nano-dot magnetization at room temperature for 4Ms = 5316,6 G and K = 2 106 erg/cm3. Black color illustrate the magnetization which aligned in HB direction, whereas white color shows the initial direction of magnetization. Magnetization reversal of nano-dot occurred through domain wall nucleation from its center, continuing on its edgecenter. This domain walls propagate up to saturated parallel to HB direction. The middle region of the nano-dot is easier to be reversed rather than its edge caused of domination of exchange field in the middle. Whereas at the edge, reversal mechanism are led by anisotropy field. The changing of material characteristic with K variation influences ΔE and Hswt , as seen in Figure 6. Increasing of K causes ΔE and Hswt also accrue. The reason is that increasing of bonding of atomic moment with crystal lattice as a consequence of large K needs a substantial energy to reverse the magnetization. Except K parameter that influences the ΔE and Hswt values, variances of ΔE and Hswt magnitudes also affected by saturation magnetization constant (4Ms), as seen in Figure 7. A substance that has a substantial 4Ms value, it has a tiny ΔE, thus it needs a bit of Hswt .
Figure 6: Raising of energy barrier (ΔE) and switching field (Hswt) towards K value at room temperature (298 K) and for 4Ms = 4116,6 G.
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Figure 7: Decreasing of ΔE and Hswt values towards saturation magnetization on room temperature (298 K) and with K = 2 106 erg/cm3.
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t = 1,917 ns
t = 1,965 ns
t = 2,036 ns
t = 2,114 ns
t = 2,195 ns
Figure 8 : Visualization of reversal magnetization for CoxSiyBz material with 4Ms = 4116,6 G with K = 2,5 106 erg/cm3 at room temperature (298 K).
t = 1,027 ns
t = 1,065 ns
t = 1,132 ns
t = 1,268 ns
t = 1,475 ns
Figure 9 : Visualization of reversal magnetization for CoxSiyBz material with 4Ms = 5516,6 G with K = 2 106 erg/cm3 at room temperature (298 K). Figure 8 and 9 describe visualization of reversal magnetization of ferromagnetic nano-dot at room temperature for two different characteristic materials, i.e. small 4Ms - large K and small K - large 4Ms respectively. Nucleation and propagation profile of domain wall that occurs for both materials are identical, however, rate of domain wall propagation is faster for materials with large 4Ms - small K (5116,6 G and 2 106 erg/cm3) i.e. 1,110 ns. Mean while, for small 4Ms - large K (4116,6 G and 2,5 106 erg/cm3), it require longer time, i.e. 2,045 ns to reverse. 3.2 Magnetization Reversal with Activating Thermal In second part of this paper concerning to investigation of reversal magnetization with support of heat. Meantime, the performed scheme is as follows, nano-dot is heated at Curie temperature, then cooled abruptly in 2,5 ns until reaching the room temperature 298 K under influence of constant HB at +x direction, just as seen in Figure 10. Heating causes both, field and initial magnetization turns to be random, therefore, the calculation should be performed using 50 different random numbers. Probability of magnetization with direction parallel to HB after cooling process for 50 random numbers called is as reversal probability P. As seen in Figure 11, switching probability is a function of bias field. The minimum HB that required to reach the probability equal to 1 called as Threshold Field (HT). A swift cooling, in fact, has not been able to magnetize nano-dot spontaneously at +x direction. As shows in the value of P(HB) = 0 while HB = 0. Furthermore, HB that less than 250 Oe, does not sufficient to magnetize nano-dot in line with its direction. Value of probability become larger when HB is more than 250 Oe, and increases rapidly for interval 550 Oe to 700
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Oe. HT is achieved, when HB as much as 870 Oe, 980 Oe, 910 Oe, 960 Oe, and 970 Oe for each 4Ms consecutively from 5116,6 G to 5516,6 G.
HB Tc
0
1
t (ns)
2
Figure 10 : Simulation scheme on reversal magnetization with support of heat.
Figure 11 : Dependence of P with respect to HB on reversal magnetization scheme with heat activation for five different value of 4Ms. The size of HT towards value of 4Ms tends to fluctuate as seen in Figure 12. Effect of thermally assisted plays a pivotal role in magnetization process during the cooling process, and as a result, the influence of initial nano-dot magnetization is eliminated. Supplying of heat has successfully decreases the reversal field up to ~90% for 4Ms value about 5116,6 G to 5516,6 G. Figure 13 displays the influence of HB on P(HB) for several different K. When HB is less than 150 Oe for all K value of P(HB) = 0. The field that has 150 Oe value considered as a beginning value at which sufficient to magnetize nano-dot at +x direction. The probability increases rapidly at interval HB from 450 until 700 Oe. Nano-dot is completely magnetized at HB direction
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for 50 random numbers when HB reaching 810 Oe, 850 Oe, 980 Oe, 1050 Oe and 1140 Oe for respectively of K from 1,7 106 erg/cm3 to 2,5 106 erg/cm3 .
Figure 12 : Increasing of HT towards 4Ms value by thermal assisting with constant K = 2 106 erg/cm3.
Figure 13 : The dependence of P with respect to HB on reversal magnetization scheme by thermal assisting for K variation.
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Figure 14 : Increasing of HT towards K value by thermal assisting with constant 4Ms = 4116,6 G. During cooling process, the interaction of magnetization towards crystal lattice has a massive contribution in its magnetization reversal. It indicates that the increasing of K needs larger HT. Dependency of K towards HT seen in Figure 14. From Figure 6, it can be seen that for K = 1,7 106 erg/cm3, the field required to reverse the magnetization direction as much as 11.340 Oe. By thermal assisting, this field can be reduced up to ~ 90 %, and it applied for another K. 4. CONCLUSION Previously, there has been a studied about the influence of material characteristic, as indicated at combination value of 4Ms and K and thermally assisted scheme towards the reversal process of magnetization reversal through miromagnetic simulation by solving Landau-Liftshitz Gilbert equation. Both parameters have an important role on reversal magnetization process for a perpendicular anisotropy ferromagnetic nano-dot. Larger K will increase ΔE, and with increasing of ΔE, then larger Hswt will be needed. On the other hand, the greater 4Ms will decrease ΔE, and followed by declining of Hswt. In addition, they also influence domain wall propagation rate. Nano-dot with large 4Ms - small K combination gives a faster domain wall propagation rate comparing to nano-dot with small 4Ms - large K. The interesting part of this research is that the thermally assisted scheme make a good decreasing of reversal field magnitude up to ~ 90% during the ongoing reversal mechanism. 5. REFERENCE [1] R. Wood, Y. Hsu, M. Schultz, “Perpendicular Magnetic Recording Technology”, in Hitachi Global Storage Technologies, White Paper, USA, 2007.
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[2] J.H Judy. Past, “Present and future of perpendicular magnetic recording,” Journal of Magnetism and Magnetic Materials, CCXVL, pp. 235–240, 2001. [3] Sousa RC, Prejbeanu IL, “Non-volatile magnetic random access memories (MRAM),” Comptes Rendus Physique (6), pp.1013-1021, 2005. [4] J. S. Park and H. I. Yim, J. Y. Hwang and S. B. Lee, T. W. Kim, “Perpendicular Magnetic Anisotropy of CoSiB/Pt Multilayers,” Journal of the Korean Physical Society, LVII (6), pp. 1672-1674, 2010. [5] Dmitri V. Berkov, Handbook of magnetism and advance magnetic materials : magnetization dynamics including thermal fluctuation basic phenomenology, fast remagnetization processes and transitions over high energy-barriers, Innovent technology development Germany, 2007. [6] T. Schrelf, J. Fidler, D.Suess, W. Scholz, and V. Tsiantos, Handbook of magnetic materials: micro magnetic simulation of dynamic and thermal effects, Tsihua University Press, 2006. [7] L’ubomir Banas, “Numerical Methods for the Landau-Liftshitz-Gilbert equation,” in Numerical Analysis and Its Applications, pp.158-165, 2005. [8] Y. Nakatani, Y. Uesaka, N. Hayashi, “Direct solution of the Landau-Lifshitz-Gilbert equation for micromag-netics,” Japanese Journal of Applied Physics, XXVIII, pp.2485-2507. [9] D.E.S. Stanescu, Magnetization Dynamics in Magnetic Nanostuctures, Thèse, Docteur De L’universite Joseph Fourier, 2003. [10] Y. Nosaki, Y. Isowaki, A. Hashimoto, B. Purnama, K.Matsuyama, “Numerical analysis of thermally assisted magnetization reversal in rectangular MRAM cell consisted of exchange coupled bilayer,” Journal Magnetic Soc., XXX, pp.574-577, 2006. [11] Lee, K.J, T.D. Lee., “Effect of The Thermal Fluctuation on Switching Field of Deep Submicron Sized Soft Magnetic Thin Film,” Journal of Applied Physics, XCI, pp.7706-7708, 2002.
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Skripsi ini telah dipublikasikan di Internasional Journal of Science and Research (IJSR), Volume2 Issue 5, Halaman 48-52 Mei 2013, India Online ISSN : 2319-7064 dengan judul “Micromagnetic Study of Thermally Assisted Magnetization Reversal
Mechanism on Perpendicularly Magnetic Anisotropy CoXSiYBZ” Alamat jurnal : www.ijsr.net Alamat paper : www.ijsr.net/v2i5.php#.UckTwjtZZnM
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