Angular Dependence of Spin Transfer Switching in Spin Valve Nanopillar Based Heusler Alloy

The spin transfer induced magnetization switching in current perpendicular-to-the-plane spin valve nanopillar based Co 2 FeAl 0.5 Si 0.5 Heusler alloy with varying the initial angles of themagnetization of sensing layer, θ 0 , was investigated via macrospin simulations. The effects of an in-plane magnetic field, H i , on the switching behavior were also evaluated. The magnetization switching was excited by spin polarized switching current, I s . The time varying magnetization was computed by the LandauLifshitz-Gilbert-Slonczewski equation, while the spin transfer induced noise was examined by using the power spectral density analysis. It was found that θ 0 should be narrowly initialized since this configuration produces the small noise during the switching. Also, the negative I s produced more uniform switching than the positive I s due to existence of ferromagnetic exchange coupling. WhenH i was presented, the noise generated at low frequencies could be suppressed, and then the switching behavior becamemore uniform. In addition, the results indicated that the noise configuration could be explained by the physical dynamic ofmagnetization behavior. Hence, the spin transfer induced noise needs to beminimized in order to improve the performance of spin transfer torque random access memory for high density recording.


Introduction
In 1996, Slonczewski discovered that a spin polarized current could transfer the angular momentum to the magnetization of ferromagnet by spin transfer torque phenomenon, which has become the major mechanism of spin transfer torque random access memory (STT-RAM) [1,2].Also, the STT-RAM has been extensively proposed to be the memory for high density recording technologies because of its outstanding performances including high operating speed, high reliability, long endurance, nonvolatility, and low writing energy [3][4][5][6].Then, an improvement of the STT-RAM performance by reducing the switching current has been of wide interest in order to minimize the energy consumption and increase the operating speed [5,[7][8][9].In particular, the important factors which directly impact the switching current and the switching behavior were the initial angle between the magnetization of free and pinned layers,  0 , and the external magnetic field [10][11][12].
Nowadays, the ferromagnetic Heusler alloy materials are of wide interest for the spintronic applications due to their various advantages such as high spin polarization, high MR ratio, high Curie temperature, and high magnetic moment [13][14][15][16].Particularly, the spin valve using Co 2 FeAl 0.5 Si 0.5 (CFAS) Heusler alloy as the ferromagnetic electrode presented a high MR ratio of 6.9% with Ag spacer [17].Several researches have focused on an enhancement of MR ratio of CFAS Heusler alloy; however, the spin transfer switching in the spin valve nanopillars based on this alloy has been rarely presented [18].
Hence, the aim of this paper is to investigate the spin transfer induced magnetization switching in the spin valve nanopillar based on CFAS Heusler alloy with varying initial angle,  0 , including the effects of the external

Simulation Model
The simulation model of spin valve nanopillar is an elliptical geometry with a cross section area of 250 × 190 nm 2 , as shown in Figure 1.It consists of the pinned and free layers separated by a nonmagnetic layer which are CFAS (20 nm)/Ag (4 nm)/CFAS (2.5 nm) [18].The magnetization of free and pinned layers is initially aligned along -axis which is its easy axis.Also, the magnetization dynamic under spin polarized current is generally computed by Landau-Lifshitz-Gilbert equation including a spin transfer torque term, written as follows [20]: Equation ( 1) consists of precession term, damping term, and spin transfer torque term, respectively.M and m  are the magnetization of the free layer and the direction of electron polarization, respectively., , and   are gyromagnetic ratio, Gilbert damping constant, and saturation magnetization, respectively.H eff is the effective magnetic field including the anisotropy field, exchange field, demagnetization field, and external field.The spin torque factor,   , is defined as follows: where () is the scalar function written as ,  is the angle between the magnetization of free layer and pinned layers,  is the spin polarization, ℏ = ℎ/2, where ℎ is Planck's constant,  is the spin current density,  is the absolute value of electron charge, and  is the thickness of the free layer.
The CFAS Heusler alloy has the following magnetic parameters [18]:   of 9.0 × 10 5 A/m,  of 0.01,  of 0.76, exchange stiffness constant, , of 2.0 × 10 −11 J/m, and magnetocrystalline anisotropy constant,  1 , of −1.0 × 10 4 J/m 3 .The system was relaxed before the magnetization switching was excited by a constant switching current,   , of two times of the critical current.This was because this magnitude produced a minimum switching energy during the switching process [21].The positive   is generally defined as the electron flowing from the free layer to the pinned layer which causes the magnetization switching from parallel (P) to antiparallel (AP) state.On the other hand, negative   is defined as the electron flowing from the pinned layer to free layer, resulting in the magnetization reversal from AP to P state.In this investigation, the magnetization of free layer was initialized along + and − directions for cases using the positive and negative   , respectively.
In this study, the noise power spectral density (PSD) generated during the switching was investigated with  0 of 0 ∘ to 30 ∘ .Furthermore, in order to evaluate the effects of   on the noise PSD, the constant   of 3,980 A/m (50 Oe) was applied along − and + directions for the cases using the positive and the negative   , respectively.
First of all, the magnetization switching time,  sw , of spin transfer switching with varying  0 was evaluated. sw was defined as the time period of magnetization oscillation starting from the initial state until the magnetization crosses -axis which is perpendicular to the initial easy axis.Then, the noise PSD generated from the spin transfer switching was further considered by using the PSD analysis.
The local PSD of the magnetization dynamic was firstly computed by the discrete Fourier transform of the local time varying magnetization, M ,, (r  ,   ), for each point, r  , and each time,   , as written in the following equation: Accordingly, the overall PSD was calculated by summation of local PSD of the time varying magnetization, given as the following equation [22]:  2(a) and 2(b).These results could be explained by using (1); that is, an increase of  0 yields an enhancement of () which results in a large   .Then, large   further causes a massive spin transfer torque term which leads to a reduction of  sw [20].

Results and Discussions
Likewise, applying   decreases the magnitude of H eff which also reduces the damping term.Then, a small damping term brings about short  sw because the magnetization could be easily switched into the reversal.Additionally, negative   results in shorter  sw than positive   because of an asymmetry of the critical current for switching,   , which is generally proportional to  sw [21].It is indicated that   AP→P is always lower than   P→AP due to an asymmetry of (), as described by Mangin et al. [23].
For the investigation of the noise PSD generated during the switching, the time varying magnetization in  direction is focused.This is because the overall PSD is mainly generated from the magnetization oscillation in  direction which also produces the resonance frequency of the magnetization switching [12].
Figure 3 illustrates the noise PSD generated from positive   (Figure 3(a)) and negative   (Figure 3(b)) with varying  0 .From Figure 3(a), it is shown that the PSD has a minimum value at  0 = 1 ∘ which is indicated as the smallest noise generated in the switching process.After that, the PSD tends to increase by an increment of  0 from 1 ∘ to 20 ∘ and it decreases afterwards when  0 is increased up to 30 ∘ .The changes of PSD configuration could be described by the physical behavior of time varying magnetization.The amplitude of PSD is generally proportional to the magnitude and time periods of the magnetization oscillation, whereas the frequency of PSD depends on the magnetization oscillating frequency.The examples of magnetization switching behavior are displayed in Figures 2(a)-2(f).By a consideration of time varying magnetization, it is found that the PSD generated at low frequency components (less than 4 GHz) mainly result from the magnetization oscillation during the switching period.In this work, the switching period is defined as the period when the magnetization is tiled more than 30 ∘ out of an easy axis approximately.In contrast, the PSD generated at high frequency components (higher than 4 GHz) are generated from the magnetization oscillation at the time period before and after switching period.During the switching period, the magnetization becomes the most unstable because it is highly aligned out of its easy axis which is quite unstable configuration.Then, the noise could be extremely generated during the switching period.The results also show that the PSD at low frequency components are higher than high frequency components, which implies that the noise generated during the switching period plays a significant role in the overall noise PSD.Thus, the changes of the PSD configurations at low and high frequency components are proportional to the variations of magnetization oscillation during the switching period and before and after switching period, respectively.On the other hand, Figure 3(b) shows that the magnitude of the PSD generated by negative   is insignificantly changed with varying  0 .This is because negative   causes slight differences of the magnetization oscillation when  0 is varied, which brings about the little changes of  sw , as can be seen from Figure 2(d) compared to Figure 2(c).Also, negative   results in two obvious peaks of PSD located at low and high frequency components.The low frequency peak is located at about 3 GHz, whereas the high frequency peak is located at about 4.7 GHz.In this case, it is found that the PSD peak at low frequency is induced by the magnetization oscillation during the switching period, whereas the high frequency peak is excited by magnetization oscillation at preswitching and postswitching period.In addition, a comparison between Figures 3(a) and 3(b) indicates that negative   produces the lower and more uniform PSD than positive   .This is because negative   causes the AP to P switching which is more uniform than the P to AP switching induced by positive   , which could be described by the behavior of an exchange coupling interaction.The exchange coupling is an interaction that tries to maintain the stable state between two nearby spins, which can imply the stability of the magnetization orientation between two adjacent layers.Also, this interaction directly affects the exchange energy of ferromagnetic system under the magnetic field as given in the following equation [23,24]: where  = /  is the normalized magnetization vector, V is the volume of material, and  ex = ( ex  2 /) is the exchange stiffness constant, where  is the number of atoms per unit cell,  is the spin,  is the lattice parameter, and  ex is the exchange integral which indicates the types of coupling by its sign.The ferromagnetic coupling occurs with the positive sign of  ex , whereas the antiferromagnetic coupling occurs when the sign of  ex is negative.The exchange energy represents the existent energy of the magnetic domain wall configuration [24].This energy indicates the stability of the magnetization alignment between two adjacent layers stabilized by an exchange force.The maximum stability of two nearby magnetizations occurs with the minimum exchange energy.For the ferromagnetic coupling, the maximum stability occurs when the magnetizations of two adjacent layers are parallel.On the other hand, the maximum stability of the antiferromagnetic coupling occurs when two neighbor magnetizations are antiparallel.In this model, a positive sign of  ex indicates the ferromagnetic coupling which becomes stable when magnetization of free layer and magnetization of pinned layer are parallel.Then, the AP to P switching caused Initial angle,  0 (degree) Switching time,   by negative   could be reached with lower noise and more uniform response than the P to AP switching induced by positive   .Furthermore, Figures 4(a) and 4(b) show the PSD of the magnetization switching including an effect of   with using positive and negative   , respectively.It is found that the PSD produced by positive   is divided into low and high frequency components, as displayed in Figure 4(a).For the low frequency component, the PSD starts to increase from a minimum value at  0 = 1 ∘ .Then, the PSD is continually enhanced when  0 is raised up to 20 ∘ and it is decreased afterwards with increasing  0 to 30 ∘ , which is similar to the changes of PSD for a case without   .Nevertheless, the high frequency component is enlarged only when  0 increases from 1 ∘ to 5 ∘ ; after that it is reduced with increasing  0 .Also, the peak at low frequency is higher than the peak at high frequency, similar to that found in a case without   .Similar to the PSD for a case without applying   , a comparison between Figures 4(a) and 4(b) indicates that the PSD can be reduced by using negative   .In particular, it is discovered that the noise PSD at frequencies lower than 1 GHz is suppressed by applying   , which can be clearly seen from Figure 4(a) compared to Figure 3(a).This is because   forces the magnetization into the reversal which can reduce the switching time and also the switching period, as illustrated in Figures 2(b), 2(d), and 2(f) compared to Figures 2(a), 2(c), and 2(e).As explained in Figure 3, the noise at frequency range between 0 and 4 GHz is mainly induced during the switching period, and then applying   can suppress the noise generated at frequencies less than 1 GHz because some periods of the switching period which produce the noise at this frequency range are reduced.Thus, the magnetization reversal becomes more uniform with two separated peaks when   is presented, which benefits in terms of design because the frequency response of the system is less complicated.From the simulation results,  0 can be set by applying the external magnetic field to the magnetization of free layer in the particular direction.As a result, the magnetization of free layer can be initially aligned along the given direction.Hence, the results suggested that the spin transfer switching should be initialized with  0 = 1 ∘ including the effect of   in order to minimize the instabilities generated during the switching.

Conclusions
The spin transfer induced magnetization switching in spin valve nanopillar with varying  0 , including the effects of   , was investigated.It was found that the magnetization of free and pinned layers initialized with a small  0 results in a small PSD generated during switching.Also, the negative   creates a more uniform reversal than the positive   .In addition, the dependence of the PSD on the physical dynamics of magnetization switching was studied in detail.It was indicated that the magnetization oscillation during the switching period plays the most significant role to the overall PSD.Furthermore, the results confirmed that including an external field,   , can significantly reduce the switching times and the PSD, while at the same time it tends to lead to a more uniform response.As a result of our calculations, the frequency response of the system can be parametrized which can be beneficial to design the spin valves in terms of avoiding the interference from the spin transfer induced reversals.

Figure 1 :
Figure 1: Geometric definition of spin valve nanopillar based on CFAS Heusler alloy.

Figure 2 :
Figure 2: Magnetization switching time,  sw , with varying  0 , resulting from the positive and negative   , including the effects of   .(a) and (b): the magnetization switching behavior resulting from positive   at  0 = 1 ∘ without and with an effect of   , respectively.(c) and (d): the magnetization switching behavior resulting from negative   at  0 = 1 ∘ without and with an effect of   , respectively.(e) and (f): the magnetization switching behavior caused by positive   at  0 = 20 ∘ without and with an effect of   , respectively.
Figure2illustrates  sw with varying  0 , resulting from the positive and negative   , including the effects of   .Figures2(a)-2(f) show the examples of the magnetization switching behavior projected in , , and  directions for each particular point.From the simulation results in Figure2, it is indicated that  sw is reduced either by increasing  0 or applying   .The dependence of  sw on  0 can be clearly seen from a comparison between Figures2(a) and 2(b) and between Figures 2(e) and 2(f).The dependence of  sw on   is shown by a comparison between Figures 2(a), 2(c), and 2(e) and between Figures 2(b), 2(d), and 2(f).Also, negative   causes shorter  sw than positive   , as can be seen from a comparison between Figures 2(c) and 2(d) and between Figures Positive I s with H i Negative I s with H i