Multi-segmented nanowires for vortex magnetic domain wall racetrack memory

M Al Bahri, M Al Hinaai, and T Al Harthy

Department of Basic Sciences,A’Sharqiyah University,Post Box 42,PC 400,Ibra,Oman

Keywords: micromagnetic simulation, vortex domain wall racetrack memory, multi-segmented magnetic nanowire,spin transfer torque

1.Introduction

Future storage memory novel properties, such as low power consumption, high speed for reading and writing of the stored information, storage of multi-bit per cell and spin-transfer torque driving have been the subject of recent developments.[1-7]Racetrack memory is one application of future storage memory.[8,9]Thus, several studies have focused on studying the current induced domain wall(DW)motion to improve critical issues like the DW’s heat fluctuation.[10,11]Other studies have examined the DW speed and how to improve the DW speed reduction related to various parameters,such as the Walker field.[12-15]However, other researchers have concentrated on using different ways to trap the DW at certain positions within devices.[16-23]Triangular notches are the most common DW trapping methods, although this has some limitations: for example,their shape facilitates the VW structural transformation.However, the notching process is complex and costly,especially for devices with ten-nanometer widths and nonuniform pinning.[24-28]The manipulation of driven DW using spin currents is the key for future spintronics storage devices.Herein, the challenge is maintaining the DW’s structure during the dynamics and pinning process for the construction of racetrack memory, especially with magnetic vortex racetrack memory.[29-32]In this work,we propose a VW storage memory using offset magnetic nanowires.The proposed scheme consists of two nanowire segments with an offset area in the center, as shown in Fig.1(a).Using this offset device with nanoscale dimensions will help to lower the power consumption.Furthermore, the design of the offset area as the overlapping between two nanowire edges will help to pin the VW precisely by adjusting the length of the offset area (l) and its depth (d).Moreover, the offset area is free of the sharp edges in its center.This helps to protect the VW structure from transformations during its pinning and depinning process,which extends the memory life.In addition,with the offset nanowire,the VW speed could be controlled by altering the geometry of the offset area, such aslandd.Unlike the spin valve,the offset device can play a role in storing more than one bit per cell by increasing the number of junctions in one cell,as shown in Fig.1(b).In this work,with this proposed scheme,the structural stability of the VW during the dynamics and pinning process is examined due to magnetic properties such as saturation magnetization (Ms).A study of the VW speed is subsequently carried out based on the current density and the geometry of the offset area.

Finally, a multi-segmented magnetic nanowire is designed to increase the storage density with four junctions to obtain six states per cell(three bits),as shown in Fig.1(b).

Fig.1.(a) The offset magnetic nanowire.(b) The multi-segmented magnetic nanowire for high storage density.

2.Modeling

The dynamics of VWs with tail to tail ( TT) configurations in offset nanowire are carried out using a framework of OOMMF codes at 0 K[33]based on the Landau-Liftshitz-Gilbert (LLG) equation with a spin-transfer torque(STT)term,according to the Zhang and Li model[34,35]

We consider the fact that the magnetic properties are used for in-plane magnetic materials,such as permalloy,CO90Fe10and Ni81Fe19.[36]The damping coefficientαis fixed to 0.01,the nonadiabatic constantβis chosen as 0.04 for all simulations and the exchange stiffness isA=1.3×10-11J/m[37]andu=(gPµB/(2eMs))J.[38]

Offset magnetic nanowires with the geometries ofL(2000 nm)×w(200 nm)×t(30 nm) are considered in this study.These dimensions are chosen due to the availability of the VW depending on nanowire sizes.[39,40]A cubic cell size(mesh size) of 5×5×5 nm3is selected, and is sufficiently smaller than the exchange length(≈5.3 nm).

At the nanowire center, an offset junction is created by shifting one part vertically in they-direction with vertical length (d) and horizontal length (l) in thex-direction.Figure 2(a)shows the initial state with the dimensions of the offset magnetic nanowire.

Fig.2.(a) An OOMMF image of magnetic offset magnetic nanowire dimensions with an initial state where all spins are configurated to the positive x-direction(mx=+1).(b)An OOMMF image of VW motion in offset nanowire under a value of current density(J=2×1011 A/m2).

The offset nanowire is connected with a nucleation pad with dimensions of length 2000 nm and width 1000 nm.Initially,the current density is applied in the positivex-direction to saturate the magnetization in this direction (red color),as in Fig.2(a).Then, the current density with a value of 2×1011A/m2is used to create VWs with tail to tail magnetization at the nucleation pad,and one of them is propagated in the offset magnetic nanowire[Fig.2(b)].

3.Results and discussion

Different parameters, such as the high stability, fast access,and large density of VW racetrack magnetic storage devices, have been investigated in this study using offset magnetic nanowires.

3.1.VW structural stability

One parameter for the construction of a stable VW magnetic racetrack memory is the VW structural stability during its dynamics in magnetic nanowires.[41]Thus, the effects of magnetic properties,such asMsand offset area dimensions,on VW structural stability before reaching the offset area are studied first.Simulations are formed using offset nanowires with fixedl=50 nm and varyingd(50 nm,100 nm,150 nm).It is found that by increasing the values of the offset area depth(d),the VW loses its structural stability and converts to TW early during its dynamics before reaching the offset area.Thus,increasing the values ofMshelps to maintain the VW structure.With the magnetic nanowire with offset area(l=50 nm andd=50 nm),it is seen that the VW has less structural stability withMs≤700 kA/m in its dynamics toward the offset area and it converts to a transverse domain wall (TW).However, the VW becomes stable in its structure withMsvalues of≥800 kA/m and no structural changes are observed.For example, with anMsof 500 kA/m, the VW converted to TW after 1 ns of starting its motion,as shown in Fig.3(b),while its structure is stable for 2.5 ns withMsof 600 kA/m,as illustrated in Fig.3(c).As theMsis increased to 700 kA/m[Fig.3(d)],it can be seen that the VW maintains its structure for 6.5 ns until it reaches the offset area,before transforming to a TW within the constricted region.However,the VW has high stability in its structure withMs≥800 kA/m and has pinned at the offset area as a VW,as illustrated in Fig.3(e).To better understand how theMsaffects VW structural stability in offset nanowire(d=50 nm andl=50 nm),Fig.3(f)presents the plot of normalized magnetization in thex-direction(mx)versus time for different values ofMs.The circled dashed area indicates the time of switching of the VW to TW during the VW dynamics(i.e.,Ms=500 kA/m and 600 kA/m).In contrast,by increasing theMsto values of≥700 kA/m, the VW becomes more stable and its graph becomes smooth, without any indication of the transformation type[Ms=700 kA/m and 800 kA/m].

A VW transformation results from competition between exchange energy,which keeps the magnetic field surrounding the core and the easy axes’energy,which keeps the DW magnetization on the easy axes as a TW.To understand the effect ofMson VW transformation,exchange energy is plotted against time for two values ofMs, as shown in Fig.3(g).It is found that the VW has higher exchange energy when increasing theMs.As a result,there is an improvement in the VW structure stability.For more confidence that the VW has more structural stability with increasingMsvalues, more investigations are carried out using offset nanowire with area dimensions of(l=50 nm andd=100 nm);it is seen that the VW changes its type to TW,as observed for the nanowire with dimensions of(l=50 nm andd=50 nm)forMs=500 kA/m and 600 kA/m[Figs.4(b)and 4(c)].However, forMs=700 kA/m, the VW converts after 3.5 ns to TW before reaching the offset area,as shown in Fig.4(d).More structural stability is observed with 700 kA/m

When increasing the depth of the offset area tod=150 nm,the VW becomes less stable and needs to use values ofMs≥1000 kA/m to maintain its structure until it is trapped by the offset area.Figures 5(b)-5(d) show the VW transformation under the values ofMs≤700 kA/m with the same VW transformation time as in the nanowires with (l=50 nm andd=50 nm)and(l=50 nm andd=100 nm).However,in this nanowire of offset dimensions (l=50 nm andd=150 nm),the VW remains stable in its structure until it is pinned at the offset area with onlyMsvalues of 1000 kA/m and higher(Ms≥1000 kA/m), as illustrated in Fig.5(f).Figure 5(g)shows themxversus time for different values ofMs.As can be seen, the VW switching varies depending on theMsvalues.However, with theMsof 1000 kA/m, the curve actually becomes smooth without any sign of VW switching.

Fig.5.(a)An OOMMF image of VW dynamics in offset nanowire with an offset area of(l=50 nm andd=150 nm).(b)-(d)OOMMF images of the VW converting to TW with values ofMs≤700 kA/m.(e)The VW transforms to TW at the offset area with 700 kA/m

Fig.6.The VW structure stability time dependence of Ms in different nanowire structures of offset areas.

For a better understanding of the effect of increasingdon the VW structural stability time, the VW structure stability time is plotted againstMsfor several nanowire structures[Fig.6].It can be observed that there is no effect of any variations indon VW structural stability time for values ofMs≤600 kA/m, and the transformation takes place before the VW reaches the offset area at the same time in different nanowires.However, the effect ofdon VW switching becomes obvious when the VW reaches the offset area forMs≥700 kA/m.Herein,it is found that the VW structural stability time decreases when increasingdfor the sameMsvalue.For an instant,the VW switches to TW withMsof 800 kA/m after 10 ns in magnetic nanowire withd=100 nm, while it undergoes transformation after 8 ns and 6 ns in nanowire with offset areas ofd= 150 nm and 200 nm, respectively.Moreover,it is noted from the graph that an increasingdleads to a linear relationship between the VW stability time andMs.

3.2.VW speed

The effect of increasingdon VW stability time leads to the investigation of the effect of the variation ofdon VW motion.Thus,the influence of increasingdon VW speed is studied.Here, theMsof 1100 kA/m is used to maintain the VW structure during its motion until it gets pinned at the offset area.Figure 7(a) shows the plot of VW velocity dependence on current density in nanowires with different values ofd.It is noted that the VW velocity changes linearly with current density and this agrees with the equation

whereJis the current density,gis the Lande factor,Pis the spin polarization,eis the carrier charge,µBis the Bohr magneton,βis the non-adiabatic parameter andαis the Gilbert damping factor.[38]

In addition, it is found that VW dynamics increase by increasing the offset area geometryddue to the decrease in the easy axis’s energy in positivex-axes, which means that the VW magnetization switches from the positivex-axes direction to the negative will be faster and, therefore, the VW moves faster.For example, with a current density value of 6×1011A/m2, the VW moves with the speed of 250 m/s in a nanowire with an offset area ofd=50 nm, while it moves with 280 m/s in the offset nanowire withd=100 nm and with 310 m/s in the nanowire withd=150 nm.

Figures 7(b)-7(e)show snapshot images of the VW at different positions in nanowires ofd(50 nm,100 nm,150 nm and 200 nm) under a driven current density of 1.2×1012A/m2at the same time of 1.65 ns from the start of its motion.It is observed that by increasingd, the VW has crossed farther distances at this time (1.65 ns).Thus, the VW is closer to the offset area in the nanowire withdof 200 nm [Fig.7(e)].For future VW memory,the VW should move with a speed of 100 m/s and higher.Using offset nanowire, we achieve the result that the VW moves with a speed of 500 m/s, which is desirable for fast writing and reading of stored information.Meanwhile, in the literature, they have only achieved 200 m/s.[32]More efficient results for increasing the VW velocity by manipulating the offset geometry are obtained via reduction of the VW thermal fluctuations by driving VWs at low current densities.

Fig.7.(a)The plot of VW velocity as a function of current density in offset nanowire with different values of d.OOMMF images of the VW position at the time of 1.65 ns and in the offset nanowire with l=50 nm and(b)d=50 nm,(c)100 nm,(d)150 nm and(e)200 nm.

3.3.VW pining at offset area

For high performance of the VW magnetic racetrack memory, the VW should be pinned at the offset area.This pinning strength depends on the offset area dimensions(landd) and the development of magnetic properties, suchMsandKu.Thus, the depinning current density (Jd) over the offset area geometry (landd) is investigated.It is found that the depinning current density increases linearly withd[Fig.8(a)],while it decreases with increasingl,as shown in Fig.8(b).

Fig.8.VW depinning current density versus(a)d with fixed l to 50 nm and(b)l with fixed d to 50 nm.The magnetic properties of the investigated material are Ku=0.5×105 J/m3 and Ms=1100 kA·m.

Furthermore,depinning current density(Jd)values based onMsandKuare investigated using different offset area dimension values(landd).Figure 9 shows the graph ofJdversusdfor different values ofMsandKu.In these graphs, it is obvious thatJdincreases when theMsorKuvalues increase.It is worth noting thatJdhas linear behavior withdfor different values ofMsandKu, which would add critical improvements for high VW storage memory with a long lifetime.

For example, in the nanowire with offset area dimensions of (l=50 nm andd=100 nm),Jdis 7.5×1012A/m2for theMsof 1100 kA/m, while it is 11×1012A/m2and 15×1012A/m2for theMsof 1150 kA/m and 1200 kA/m,respectively[Fig.9(a)].The effects ofKuon VW pinning with varyingdare the same as forMs.The results are plotted in the graph ofJdversusKu,as shown in Fig.9(b).To get a better understanding of the effects oflonJd(the offset nanowire junctions),nanowires are proposed with fixed values ofd(50 nm)and the values oflare varied by 50 nm.Figure 9(c)shows the plot ofJddependence onlfor different values ofMs, showing that theJddecreases with increasinglvalues and the same results are observed with different values ofKu[Fig.9(d)].These results have confirmed that the pinning potential of the offset nanowire has increased by improving the values ofMsandKu.

Fig.9.(a)The plot of Jd as a function of(a)d for three values of Ms,(b)d for three values of Ku,(c)l for three values of Ms and(d)l for three values of Ku.

3.4.VW multi-bit per cell

A critical parameter for future VW storage memory is to increase the storage density to more than one bit per cell.For this implementation,the offset nanowire is designed with four junctions by increasing the values ofdfrom left to right and keepinglfixed (50 nm).To maintain the VW structural stability,theMsis kept to 1100 kA/m.The possibility of storing six states using the offset nanowire with four junctions is also investigated.It is noted from Fig.10 that six states are obtained, and Fig.10(a).shows a plot of themxdependence of current density for the six states.Figure 10(b)shows the first state where all spins pointed to the positivex-direction while increasing the current density to 1×1012A/m2; the VW is created and moves to become pinned at the first junction to represent the second state[Fig.10(c)].Once the current density is increased to reach the value of 2.5×1012A/m2, the VW leaves the first junction and moves to the second one and gets trapped there.This represents the third state and so on,until the VW moves to the end of the nanowire, as shown in Fig.10(g).

Fig.10.The six states of multi-segmented magnetic nanowires with L=1000 nm, w=200 nm and t =30 nm.The magnetic properties are Ms =1100 kA/m and 0.5×105 J/m3.(b)The first state and(c)the second state,where the VW is pinned at the first junction(d=50 nm).(d)The third state,where the VW is pinned at the second junction(d=100 nm).(e)The fourth state,where the is VW pinned at the third junction(d=150 nm).(f)The fifth state,where the VW is pinned at the fourth junction(d=200 nm),and(g)the sixth state,where the VW moves to the end of the nanowire.

4.Conclusion

In summary,several properties of VW magnetic racetrack memory were investigated using offset magnetic nanowires for future high speed,high density and long lifetime storage memory.It was found that VW transformation could be controlled by increasing theMs.ForMsvalues of≥800 kA/m,the VW structure was stable during its dynamics and depinning process, which helps to maintain the long lifetime of the storage devices.Using offset magnetic nanowires, a VW maximum speed of 500 m/s has been achieved to implement fast access memories.We found that the VW speed could be controlled by adjusting the offset area dimensions (landd) and the driven current density.Six stable states were achieved using multisegmented nanowires with four junctions.The VW pinning through the junction depends on the junction sizes (landd)and magnetic properties (MsandKu).It was observed thatJdincreases with increasingdor magnetic properties and decreases with increasinglor magnetic properties.