Design and Micromagnetic Simulation of Fe / L 10-FePt / Fe Trilayer for Exchange Coupled Composite Bit Patterned Media at Ultrahigh Areal Density

Exchange coupled composite bit patterned media (ECC-BPM) are one candidate to solve the trilemma issues, overcome superparamagnetic limitations, and obtain ultrahigh areal density. In this work, the ECC continuous media and ECC-BPM of Fe/L1 0 -FePt/Fe trilayer schemes are proposed and investigated based on the Landau-Lifshitz-Gilbert equation.The switching field, Hsw, of the hard phase in the proposed continuous ECC trilayer media structure is reduced below the maximum write head field at interlayer exchange coupling between hard and soft phases,A ex, higher than 20 pJ/m and its value is lower than that for continuous L1 0 -FePt single layer media and L1 0 -FePt/Fe bilayer. Furthermore, theHsw of the proposed ECC-BPM is lower than the maximum write head field with exchange coupling coefficient between neighboring dots of 5 pJ/m and A ex over 10 pJ/m. Therefore, the proposed ECC-BPM trilayer has the highest potential and is suitable for ultrahigh areal density magnetic recording technology at ultrahigh areal density. The results of this work may be gainful idea for nanopatterning in magnetic media nanotechnology.


Introduction
An ultrahigh areal density of magnetic recording media over 1 Tb/in 2 and overcoming the superparamagnetic limit of conventional perpendicular magnetic recording are required for the development of hard disk drive technology.Magnetic recording media must have smaller magnetic grains, higher magnetocrystalline anisotropy constant,  u , and lower exchange coupling [1].The high  u is the cause of increasing coercivity,  c , of the media; however, it may be over the maximum write field of about 24-25 kOe of heads because the saturation magnetization,  s , of the write head material is limited [2].These problems are called the magnetic recording trilemma [3].There are three conditions of the trilemma that limits areal density growth of magnetic recording technology: (i) the write head field can record data on the media, (ii) the bits must be thermally stable, and (iii) the number of grains per bit is sufficient to obtain the high signal to noise ratio.
From the above writing head field problem, several future magnetic recording technologies are proposed to reduce switching field,  sw , to the maximum write head field or lower.Heat-assisted magnetic recording technology allows a reduced  c of the media during the writing process [4].The  sw of the media under a microwave-assisted field in microwave-assisted magnetic recording technology is lower [5].The magnetization reversal of the media is excited by the microwave field.The tilted media were proposed to reduce  sw and areal density achieved was 62% higher than that of a perpendicular media with 45 ∘ easy-axis-tilted media under the same thermal stability and recording process [6].In addition, the exchange coupled composite (ECC) media proposed by Victora and Shen and the exchange spring and exchange coupled graded media proposed by Suess provide 2 Advances in Materials Science and Engineering better thermal stability, writability, and improved signal to noise ratio [1,7].The  sw of the media is reduced with the same thermal stability.Due to these media comprising soft and hard magnetic materials, the soft phase helps to reverse the magnetization of the hard phase.Therefore, the  sw of the media can be reduced.
At ultrahigh density magnetic recording, the magnetic transition noise also becomes a significant problem.However, this problem is completely eliminated by bit patterned media (BPM) because of the separation of bits by nonmagnetic material [8].Therefore, it is the candidate for magnetic recording technology to overcome the superparamagnetic limit at areal density of 1 Tb/in 2 .Recently, the concepts of ECC-BPM of [Co/Pd] 5 /Pd/[Co/Ni] 3 /Co multilayer have been introduced, showing that  sw can be reduced by inserting a Pd layer while maintaining thermal stability [9].The ECC-BPM and graded BPM media for L1 0 -FePt material are investigated with  u of 1-4 MJ/m 3 [10].After that the structure of high  u of L1 0 -FePt and low  u of a Co/Pd-Co/Ni multilayer with various the interlayer exchange couplings between hard and soft phases,  ex , can reduce the  c [11].In addition, both the  c and saturation field are reduced by 50% owing to exchange coupling between L1 0 -FePt and the Fe interface after the postannealing process [12].
To achieve the reduction of  sw below the maximum write head field at ultrahigh areal density, ECC media of Fe/L1 0 -FePt/Fe trilayer structure for BPM are proposed and investigated in this work.Exchange coupling coefficient between neighboring dots,  dot , for the structure becomes a challenge due to magnetic bits being close to other bits [13].Magnetic flux from individual bit will disturb neighboring bits.Therefore, the  ex and  dot on the  sw of the hard layer, its hysteresis loop, magnetization reversal, and magnetic energy are investigated by the object oriented micromagnetic framework (OOMMF) program [14] based on the Landau-Lifshitz-Gilbert (LLG) equation [15].

Micromagnetic Simulation and Modeling
The LLG equation is used to describe the magnetization dynamics of magnetic particles, as shown in the following [15,16]: where  is the gyromagnetic ratio, ⃗ ( ⃗   , ) is the magnetization vector of the magnetic particles, ⃗  eff ( ⃗   , ) is the effective field vector, as illustrated in (2), and  is the Gilbert damping constant.For the first term, the magnetization is affected by the ⃗  eff ( ⃗   , ), so the magnetization rotates around ⃗  eff ( ⃗   , ) with the precession torque term.For the second term, the magnetization is damped to the ⃗  eff ( ⃗   , ) called the damping torque term.The ⃗  eff ( ⃗   , ) in the LLG equation includes anisotropy, demagnetization, exchange, and external (Zeeman) fields that result from the derivative of the total magnetic energy density, , with respect to ⃗ ( ⃗   , ).The  includes anisotropy, demagnetization, exchange, and Zeeman energy densities [15,16]: ECC media comprise soft and hard magnetic materials and L1 0 -FePt is used for the hard magnetic material of the recording layer because it has a high  u .The ideal  u value is about 7 MJ/m 3 [17] and can be achieved with a minimum stable grain size of about 2.81 nm, but that value will be difficult to produce by the magnetron sputtering method.Therefore, we use  u of 2.8 MJ/m 3 [16,18] for this work and the minimum stable grain size increases to 3.59 nm [16].Fe material is used for the soft magnetic material because of epitaxial growth [19].The  s of soft and hard phases is 1200 and 500 kA/m, respectively [18,20].The  u of the soft phase is 100 J/m 3 [18,21].The exchange coupling constant of soft and hard phases is 28 and 12 pJ/m, respectively [18,21].The  ex and  dot are varied to investigate the effects of exchange coupling behavior on the reduction of  sw .In the present work,  sw is defined as the applied magnetic field that completely reverses the magnetization in the hard phase.The continuous media have width and length of 250 nm.The thickness of L1 0 -FePt hard phase,  FePt , is 10 nm.The Fe soft phase thickness,  Fe , of the ECC bilayer is 10 nm and the proposed ECC trilayer continuous media are 5 and 10 nm.For the proposed ECC-BPM, the dot dimension is 10 nm × 10 nm with the same  FePt and  Fe of the continuous media.The dot spacing is 2.5 nm to achieve an ultrahigh areal density, as shown in Figure 1.The mesh size of the finite difference time domain calculation is 2.5 nm × 2.5 nm × 2.5 nm by OOMMF program based on the LLG equation.

Fe/L1 0 -FePt/Fe Trilayer Structure for Continuous Media.
To demonstrate the advantage and performance of the proposed ECC trilayer structure, a comparison between the bilayer and the proposed ECC trilayer is investigated.The effective  Fe for the trilayer structure is 5 and 10 nm to reduce  sw below the maximum write head field.Figure 2 shows the dependence of normalized  sw (divided by  sw of single layer continuous media) on  ex for bilayer and trilayer.The  sw of the continuous single layer medium is independent of  ex and constant at 1 while the normalized  sw of the bilayer and trilayer continuously decreases.The normalized  sw of the bilayer decreases faster than that of the proposed trilayer media with increasing  ex from 0 to 9 pJ/m, but it is not in the writing head field region.For  ex of 12.5-30 pJ/m, the  sw of the trilayer media continuously decreases below the maximum write head field and its value is lower than the  sw of the bilayer media.This result indicates that the proposed ECC trilayer media can reduce the  sw lower than the bilayer media because of the double interface area [22].
Reduction of the  sw corresponds to calculation of energy barrier height; both of them decrease with increasing

Write head field region
A ex (pJ/m) FePt (10 nm) Fe (10 nm)/FePt (10 nm) Fe (5 nm)/FePt (10 nm)/Fe (5 nm) Fe (10 nm)/FePt (10 nm)/Fe (10 nm) exchange energy per unit area [23] or  ex .Energy barrier of the hard magnetic phase,  B-H , in the proposed trilayer structure is calculated by the Stoner-Wohlfarth model as given in the following: where  H is  u of hard magnetic materials,  H is the thickness of hard phase,  is external magnetic field,  is exchange coupling constant,  H is  s of hard magnet, and  K-H (= 2 H / H ) is the anisotropy field of hard phase.We have also found that a hard phase of the proposed ECC media trilayer structure has a lower energy barrier than the bilayer structure with high thermal stability.Moreover, the exchange energy density at full reversal (not shown here) of the ECC bilayer and trilayer rapidly increases at  ex of 8-12.5 pJ/m for bilayer and trilayer ( Fe = 5 nm) and 8-15 pJ/m for trilayer ( Fe = 10 nm).Therefore, the  sw in these ranges suddenly reduces.For  ex over 15 pJ/m, the  sw is almost constant according to the exchange energy.These results indicate that  ex is important for ECC media in reducing the  sw below the maximum write head field at ultrahigh recording density.Thus, the proposed ECC trilayer continuous media structure has more potential  sw reduction than the ECC bilayer continuous media at the same  Fe for ultrahigh density magnetic recording technology.

Fe/L1
0 -FePt/Fe Trilayer Structure for BPM.The proposed ECC-BPM structure with  Fe of 5 and 10 nm, as shown in Figure 1, is expected to achieve the goal of reducing  sw below the maximum write head field at ultrahigh areal density.The  sw of the bit patterned dots is normalized by the  sw of the single layer without  dot , as shown in Figure 3.It significantly decreases because of the  dot and  ex .The values of  sw of ECC-BPM trilayer and bilayer tend to decrease unlike the BPM single layer.This indicates that the  ex influence on the ECC structure is highly significant for BPM.Although there is no  dot in the trilayer structure, the  sw can be kept within the maximum head field region at very high  ex .Under the influence of  ex and  dot , the  sw of the ECC-BPM trilayer with  Fe of 10 nm is the lowest.ECC-BPM bilayer ( Fe = 10 nm) and trilayer ( Fe = 5 nm) can reduce the  sw close to the maximum write head field.However, the ECC-BPM trilayer with  Fe of 10 nm is the most effective in reducing  sw below the maximum write head field.This indicates that the  dot also affects the reduction of  sw .Therefore, this structure has benefit for magnetic recording technology to solve the magnetic recording trilemma issues at ultrahigh areal density.
Figure 4 shows the hysteresis loops and magnetic domain of the ECC-BPM bilayer and the proposed trilayer.The bilayer and the first trilayer structure denoted by trilayer 1 have  ex and  dot of 10 pJ/m and the second trilayer structure denoted by trilayer 2 has  ex of 10 pJ/m and without  dot .There are different steps in the hysteresis loop shapes.Principally, the reasons are that (i) magnetization reversal of soft and hard phases is separate and the soft phase reverses early because the magnetic properties of the soft magnetic material allow the magnetization to reverse easily and after that the hard phase will reverse and (ii) exchange coupling between interface of soft and hard phases is not enough [1,24,25].Therefore, magnetization reversal of soft and hard phases is separate.The proposed trilayer 1 has a sharp loop and no step because of its structure and the existence of  ex and  dot .
Magnetization reversal processes in Figures 4(a)-4(c) and 4(d)-4(f) are shown without and with an applied external magnetic field,  ex , of −18 kOe, respectively.Without  ex , the magnetization of soft phases in trilayer 2 and bilayer structures begins to reverse but the hard phase magnetization still remains in the + direction (pointing up).When  ex increases in the − direction (pointing down), the magnetic domain wall moves to the interface between soft and hard phases.All magnetization of soft phases will be reversed but hard phase magnetization is still in the same direction, as shown in Figures 4(d proposed trilayer structure can reduce the  sw below the maximum write head field.

Conclusions
The proposed Fe/L1 0 -FePt/Fe ECC trilayer structure for continuous media and BPM was investigated by a micromagnetic model.The proposed trilayer continuous media has lower  sw than that of bilayer and the maximum write head field at  ex over 20 pJ/m.For the proposed ECC-BPM structure, the  ex and  dot have more influence on the reduction of  sw .

Figure 2 :
Figure 2: Normalized  sw and  ex of single layer continuous media, ECC bilayer, and proposed ECC trilayer.

AFigure 3 :
Figure 3: Dependence of normalized  sw on  dot with various  ex .