Minimization of the electric energy in systems using ultra-high density magnetic storage

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.


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.

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 and approximately 10 −8 during deposition on SiO2, at room temperature. On Au film, cobalt layers with thicknesses ( ) :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 0 = 1.2 , were recorded at room temperature (RT) by polar magneto-optical Kerr effect magnetometry (PMOKE) using a He-Ne laser ( = 633 m ). On the hysteresis loops we measured the coercive fields 0 and the nucleation fields 0 . Table 1. shows magnetic quasi statistic parameters deduced from the hysteresis loops of the three samples [4].

 Average activation energy
The energy needed to reverse magnetization can be expressed in the following way [3,5] : (1), and the time 1/2 corresponding to the time at the end of which the sample is demagnetized, is expressed following Arrhenius law : Where ̅ is average activation energy at zero field, thermal energy required to initiate the magnetization reversal in the absence of the field, is the saturation magnetization and is the Barkhausen volume (the magnetization volume that reverses during a single activation event). The fitting of expérimental dots of 1/2 vs μ 0 H and their ajustement by eq (2)  According to the work of A. Adanlété Adjanoh, R. Belhi [10,11], the weakness of ̅ 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 . 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 ( ) is inversely proportional to the width of the distribution of the activation energy barriers: The relaxation curves ( ) vs ( ) and their fittings using Eq.

Width of the distribution of the energy barriers
By analyzing the shapes of the curves and their fittings we can write this : With and b values depending on the applied field and 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 (μ 0 H) applied.
Using the linear fittings and Eq.(5), We determine the value of = 1 .
Depends on applied field [13]. Then Inversely proportional to . Let's take = − , a negative slope due to decreases in the lines; we can then rewrite the eq. (5) as following: From this relation we can determine the demagnetization time 1/2 such that Which implies : Now let us recall the expression of t 1/2 that follows Arrhenius' law in Eq. (1): Whith ̅ 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: corresponding to the width of the distribution of the energy barriers at zero field.
This relation (Eq.(8)) shows that decreases as the applied field increases, which is in perfect agreement with the experimental measurement of in the sample of 1nm thick. With Eq. (7), we can calculate the value of 0 for the three samples. We notice that by using 0 = 10 4 we get high values of 0 compared to those measured experimentally [10].
This leads us to think about the real value of 0 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]: Where R is the nucleation rate and ( ) a parameter inversely proportional to 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 1/2 : . Using this expression of 0 with the values of its parameters measured [11] and recorded in 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 ( ) 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.

tco Activation Energy barries in a real sample
Activation fields in a real sample is the field μ 0 H r 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 : We find respectively μ 0 H r = 16.19mT, μ 0 H r = 15.80mT and μ 0 H r = 10.04mT for the thickness t C o = 0.7nm, 0.8nm and 1nm. These values compared to those of the coersive field μ 0 H c 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 μ 0 H r is found in the sample thickness t C o = 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]: where ̅ is the average activation energy in the sample, assumed to be equal to that found in  Ea(meV) tco too that the distribution margin of the energy barrier in the sample of thickness t C o = 1nm is smaller. This shows that reversing the magnetization in the sample t C o = 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 E a , its distribution width and the real activation field μ 0 H r , and saw that all are different and weak in each thickness t C o = 0.7nm, 0.8nm and 1nm. Moreover, the smallest value of these parameters are found in the layer of thickness t C o = 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.