2nd German-West African Conference on Sustainable, Renewable Energy Systems SusRes – Kara 2021 Energy Efficiency https://doi.or/10.52825/thwildauensp.v1i.15 © Authors. This work is licensed under a Creative Commons Attribution 4.0 International License Published: 15 June 2021 Minimization of the electric energy in systems using ultra-high density magnetic storage PAKAM Tchilabalo1, A. Adanlété Adjanoh1 1Laboratoire Matériaux et Energie Renouvelable et Environnement (LaMERE), University of Kara, Togo. Abstract. We present an optimization of the thickness of the magnetic layers that serve to record the information of the daily need in order to minimize the useful electrical energy. The study provides details on the energy activation and distribution of the energy barriers in the samples of thickness 𝑡𝐶𝑜 = 0.7, 0.8 𝑎𝑛𝑑 1𝑛𝑚. We find that distribution of the energy barriers Ea, its distribution width 𝜎𝑤, the real activation field μ0Hr are lowest in the sample of thickness 𝑡𝐶𝑜 = 1𝑛𝑚, hence this sample allows to use less electrical energy for information recording. Keywords: Width of distribution of the energy barriers, information recorging, electrical energy minimization. Introduction The evolution of the digital economy and the use of ferromagnetic materials in ultra high density information storage has given rise to interest in these materials in recent decades for researchers. Research on these materials is oriented either towards the understanding of very fundamental mechanisms, or towards important perspectives for applications such as ultra high density storage [1,2]. In fact, the writing of elementary information is traditionally done by applying a magnetic field pulse [3]. The field and energy required to create a first magnetization reversal are called the activation field and activation energy, respectively. But the activation energy is not single in a real sample. In this case the simple activation energy is replaced by a distribution of energy barriers[10]. The lower the distribution of energy barriers, the less electrical energy is needed for the storage of information. Therefore, perfect control and optimization of these parameters controlling the distribution of energy barriers in order to reduce this energy as much as possible, is essential in order to minimize the electrical energy required for this effect. Some works has been devoted to the activation energy [3,4,5,6] but did not discuss the effect of the thickness on the distruibution and the width of the energy barriers in the samples. This paper has the particularity of showing that the thickness of the magnetic layers have an influence on the width of the distribution of energy barrier, hence on electrical energy. Material and Method Sample and Structural Characterizations Si(100) substrate is beforehand cleaned by ultrasounds in an acetone bath. After the cleaning, this substrates is thermally oxidized in a furnace at 1200°C during 2 hours. This time is sufficient for the formation of an oxide layer on the silicon surface substrate. Au/Co/Au films were prepared by electron beam evaporation in an ultrahigh vacuum chamber, with a base pressure about of 10−9 𝑇𝑜𝑟𝑟 and approximately 10−8𝑇𝑜𝑟𝑟 during 129 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” deposition on SiO2, at room temperature. On Au film, cobalt layers with thicknesses (𝑡𝐶𝑜 ) :1, 0.8 and 0.7 nm are then deposited [11]. At finally a second Au layer with a thickness about of 5nm is deposited on top of the cobalt layers. The (111) texture of the Au buffer layer suggests, in each case, a possible epitaxial growth of the cobalt layer with the Hexagonal Close-Packed (0001) structure [7,8,9]. Megnetic investigation Magnetic hysteresis loops, at a field sweep rate of 𝑑𝜇0𝐻 𝑑𝑡 = 1.2 𝑚𝑇, were recorded at room temperature (RT) by polar magneto-optical Kerr effect magnetometry (PMOKE) using a He- Ne laser (𝜆= 633 𝑛m ). On the hysteresis loops we measured the coercive fields 𝜇0𝐻𝑐 and the nucleation fields 𝜇0𝐻𝑛. Table 1. shows magnetic quasi statistic parameters deduced from the hysteresis loops of the three samples [4]. Magnetization Reversal  Average activation energy The energy needed to reverse magnetization can be expressed in the following way [3,5] : W(H) = �̅�𝑎 − MsVB(μ0H) (1), and the time 𝑡1/2 corresponding to the time at the end of which the sample is demagnetized, is expressed following Arrhenius law : t1/2 = t0exp ( �̅�𝑎 − MsVB(μ0H) KBT ) (2) Where �̅�𝑎 is average activation energy at zero field, thermal energy required to initiate the magnetization reversal in the absence of the field, 𝑀𝑠 is the saturation magnetization and 𝑉𝐵 is the Barkhausen volume (the magnetization volume that reverses during a single activation event). The fitting of expérimental dots of 𝑡1/2 vs μ0H and their ajustement by eq (2) allows to have the values of t0, �̅�𝑎 and MsVB for differents samples represented on figure 1. And in table 2 [4]. 𝒕𝑪𝒐 (nm) 0.7 0.8 1 𝛍𝟎𝑯𝒄(mT) 31.60 29.20 26.50 𝛍𝟎𝑯𝒏(mT) 27.4 24.9 23 Table 1. Data obtained from the quasi-static characterizations at 300 K 130 Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” 𝐭𝐂𝟎(𝒏𝒎) 0.7 0.8 1 𝐭𝟎(𝒔) 10 4 104 104 �̅�𝒂 (𝒎𝒆𝑽) 146.12 329.2 138.4 𝐌𝐬𝐕𝐁(𝟏𝟎 −𝟐𝟏 𝑱/𝒎𝑻) 2.15 4.05 3.35  Width of the distribution of the energy barriers According to the work of A. Adanlété Adjanoh, R. Belhi [10,11], the weakness of �̅�𝑎 confirms the fact that the magnetization reversal in thises samples is mainly done by domain wall motion in the sample. In a real sample the magnetic domains have a dendritic structure as shown in image of fig. 3. This indicates that an activation energy would not be single in the sample. In this case the simple energy barrier is replaced by a distribution of energy barriers, characterized by a width 𝜎𝑤 . Bruno et al. [3] showed that if one assumes a square distribution of the energy barriers, the maximum slope of reduced magnetization m(t)=(M(t)+Ms)/2Ms represented as a function of 𝑙𝑛(𝑡) is inversely proportional to the width 𝜎𝑤 of the distribution of the activation energy barriers: 𝑚(𝑡) = − 𝐾𝐵 𝑇 ∗ ln𝑡 𝜎𝑤 (3) The relaxation curves (𝑡) vs (𝑡) and their fittings using Eq.(3) for the layer of 1nm are presented on fig.2. Figure 1. 𝑡1/2depending on μ0H and it fitting by Arrhenius-Néel law Eq. (2), for the three samples Table 2. Data from the fitting byArrhenius-Néel law 131 Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” Results and discussions Width of the distribution of the energy barriers By analyzing the shapes of the curves and their fittings we can write this : 𝐹𝑜𝑟 𝑙𝑛𝑡 𝜖 ] − ∞, 0]; 𝑚(𝑡) = 𝑐𝑡𝑒 = 1 (4) 𝐹𝑜𝑟 𝑙𝑛𝑡 𝜖 [0, 𝑏]; 𝑚(𝑡) = 𝛼𝑙𝑛𝑡 + 𝛽 (5) With 𝛼 and b values depending on the applied field and 𝛽 a constant. At the start of the reversal, the magnetization keeps its saturation value for a period of time (Eq.1), after this demagnetization is almost linear with a negative slope which depends on the field (μ0H) applied. Using the linear fittings and Eq.(5), We determine the value of 𝛽 = 1 . 𝜎𝑤 Depends on applied field [13]. Then 𝛼 Inversely proportional to 𝜎𝑤 . Let’s take 𝛼 = − 𝐾𝐵𝑇 𝜎𝑤 , a negative slope due to decreases in the lines; we can then rewrite the eq. (5) as following: 𝑚(𝑡) = − 𝐾𝐵𝑇𝑙𝑛𝑡 𝜎𝑤 + 1 (6) From this relation we can determine the demagnetization time 𝑡1/2 such that 1 2 = − 𝐾𝐵 𝑇𝑙𝑛(𝑡1/2) 𝜎𝑤 + 1 132 Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” Which implies : 𝑡1/2 = exp ( 1 2 𝜎𝑤 𝐾𝐵𝑇 ) (7) Now let us recall the expression of t1/2 that follows Arrhenius' law in Eq. (1): t1/2 = t0exp ( �̅�𝑎−MsVB(μ0H) KBT ) Whith �̅�𝑎 the average of activation energy. By equalizing the two relations (1) and (7) we end up with the expression for the width of the energy barrier: 𝜎𝑤 = 𝜎𝑤0 − 2μ0𝑀𝑆 𝑉𝐵 𝐻 (8) With 𝜎𝑤0 = 2(�̅�𝑎 + 𝐾𝐵 𝑇𝑙𝑛𝑡0) , (9) corresponding to the width of the distribution of the energy barriers at zero field. This relation (Eq.(8)) shows that 𝜎𝑤 decreases as the applied field increases, which is in perfect agreement with the experimental measurement of 𝜎𝑤 in the sample of 1nm thick. With Eq. (7), we can calculate the value of 𝜎𝑤0 for the three samples. We notice that by using 𝑡0 = 10 4 we get high values of 𝜎𝑤0 compared to those measured experimentally [10]. This leads us to think about the real value of 𝑡0 in a real sample. Taking into account the dendritic form of the domains observed experimentally, the magnetization reversal curves for theses samples can be described by the compressed exponential form [11]: 𝑚(𝑡) = 𝑒𝑥𝑝 [− ( 𝑅𝑡 𝜏(𝑘) ) 𝛽 ] (10) Where R is the nucleation rate and 𝜏(𝑘) a parameter inversely proportional to 𝑘 which designates the competition between the nucleation and the propagation of magnetic domains and β a fractional exponent between 1 and 3. From the relation (10) we deduce another expression of 𝑡1/2 : 𝑡1/2 ≈ 𝜏(𝑘)(𝑙𝑛2) 1 𝛽 𝑅𝑜 exp ( Ea̅̅̅̅ −MsVB(μ0H) KBT ) (11) 133 Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” Figure 3. Width of the distributionof the energy barriers in each sample of thickness 𝒕𝑪𝒐 Hence by identification of Eq.(11) with Eq.(1), we get the prefactor as 𝑡0 ≅ 𝜏(𝑘)(𝑙𝑛2)1/𝛽 𝑅𝑜 . Using this expression of 𝑡0 with the values of its parameters measured [11] and recorded in table.3: 𝐭𝐂𝐨 (nm) 0.7 0.8 1 𝛃 1.41 1.73 1.49 𝐑𝐨(𝐒−𝟏) 2x10−5 3x10−5 8.63x10−6 𝛕(𝐤) 5.5x10−4 8.7x10−4 2.4x10−4 We obtain the values of the width at zero field 𝝈𝒘𝟎 recorded in the table .4 𝒕𝑪𝒐 (nm) 0.7nm 0.8nm 1nm 𝝈𝒘𝟎 (𝒎𝒆𝑽) 435.01 799.84 420.63 We notice that these values are in perfect agreement with the values found by linear fitting in the 1nm thick layer and are low compared to that found for in multilayers (𝑃𝑡𝐶𝑜)3 [6]. And that the value of the width of the distribution of the energy barrier, when no field is applied, is generally low in all thicknesses and the lowest value is obtained in this thickness of 1nm as shown fig.3. This means that it is easier to reverse the magnetization in the thickness of 1nm than 0.7nm and 0,8nm ; which makes it possible to save energy in the latter. The high value within 0.8nm can be explained by a high defect rate in this sample. These defects slow down the magnetization reversal process [10] ; hence this increases the width of the distribution of the energy barries in the sample. Table 4. Values of the Width of the distribution of energy barriers in each sample Table 3. Data of the parameters of magnetization reversal compressed exponential form 0 200 400 600 800 1000 0,7nm 0,8nm 1nm 𝝈𝒘O(meV) tc o 134 Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” Activation Energy barries in a real sample Activation fields in a real sample is the field μ0Hr that must be applied to completely remove the width of the energy barrier distribution, i.e. to cancel the width of the barrier in a sample. From this definition we can then write : σw0 − 2μ0MSVBHr = 0 (12) We find respectively μ0Hr = 16.19mT, μ0Hr = 15.80mT and μ0Hr = 10.04mT for the thickness tCo = 0.7nm, 0.8nm and 1nm. These values compared to those of the coersive field μ0Hc in table 1., are lower in the three cases, what shows that the magnetization reversal is well initiate in the real sample before it is demagnetized. The lowest value of μ0Hr is found in the sample thickness tCo = 1nm. It shows that magnetization reversal (the writing of elementary information) would not need enough electrical field ; therefore this sample will need less electrical energy. Distribution of energy barries The distribution of energy barries can be framed as follows [13]: �̅�𝑎 − σw0 2 ≤ 𝐸𝑎 ≤ �̅�𝑎 + σw0 2 (13) where �̅�𝑎 is the average activation energy in the sample, assumed to be equal to that found in table.2 . Using the Eq.(13) and Eq.(10), we get the following relation : −KBTlnt0 ≤ Ea ≤ 2xE̅a + KBTlnt0 (14) On Fig 4. We show the distribution graph of the energy barrier in each sample. We find respectively the margins : −72.38 𝑚𝑒𝑉 ≤ 𝐸𝑎 ≤ 362,62 𝑚𝑒𝑉, −70,72 ≤ 𝐸𝑎 ≤ 729.12 𝑒𝑡 − 71.91 ≤ 𝐸𝑎 ≤ 348.71 for thicknesses tCo = 0.7nm, 0.8nm, 1nm. It is clear here Figure 4. Distribution graph of the energy barrier in each sample -200 -100 0 100 200 300 400 500 600 700 800 0,7nm 0,8nm 1nm E a (m e V ) tco 135 Pakam et al. | TH Wildau Eng. Nat. Sci. Proc.1 (2021) “SusRES 2021” too that the distribution margin of the energy barrier in the sample of thickness tCo = 1nm is smaller. This shows that reversing the magnetization in the sample tCo = 1nm will require less electrical energy ; so less electrical energy for information storage. Conclusion We have shown through this article the effect of the thickness of the magnetic layers of cobalt on the distribution of the energy barrier and therefore on the saving of electrical energy in the storage of information in these media. We theoretically calculated, the distribution of the energy barrier Ea, its distribution width 𝜎𝑤 and the real activation field μ0Hr, and saw that all are different and weak in each thickness tCo = 0.7nm, 0.8nm and 1nm. Moreover, the smallest value of these parameters are found in the layer of thickness tCo = 1nm. Therefore, this state that the writing a bit of information in this thickness of 1nm would require less magnetic field. Hence the storage of information in cobalt thickness of 1nm would require less electrical energy. References [1] Pommier J, Meyer P, Pénissard G, Ferré J, Bruno P, Renard D. Magnetization reversal in ultrathin ferromagnetic films with perpendicular anistropy: Domain observations. Physical Review Letters. 1990 Oct 15;65(16):2054-2057. https://doi.org/10.1103/physrevlett.65.2054 [2] Shen JX, Kirby RD, Wierman K, Shan Z‐, Sellmyer DJ, Suzuki T. Magnetization reversal and defects in Co/Pt multilayers. 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Proc.1 (2021) “SusRES 2021” Magnetism and Magnetic Materials. 2011 03;323(5):504-508. https://doi.org/10.1016/j.jmmm.2010.10.002 137 15_15-Pakam_etal_Conference paper-23-1-6-20210506 Introduction Material and Method Sample and Structural Characterizations Megnetic investigation Magnetization Reversal Results and discussions Width of the distribution of the energy barriers Activation Energy barries in a real sample Distribution of energy barries Conclusion References Leere Seite