# Writer Performance Optimization with Shingled Rounded Corner and Exchange Coupled Composite Media
## 2 Model Parameters and Methodology
### Magnetic Configuration of ECC Media  
Compared with the conventional perpendicular media, the ECC media effectively decreases the switching field without a loss in thermal stability. The ECC media structure increases the writability for the shingled writer, which reaches a trade-off between adequate write field and manufacture of the shingled writer. The ECC media is modeled from Voronoi grains with an average diameter of 5 nm, targeting an areal density of 20 T grains per square inch. Each grain consists of a two-layer composite structure, the top layer is the soft magnetic layer, and the bottom layer is the hard magnetic layer. The thickness of the seed layer between the two-layer composite structures is 2 nm. The average relaxation time \(\tau\) is calculated as a function of the energy barrier \(\Delta E\) of ECC magnetic grain according to the Neel-Arrhenius equation [4]. \[1/\tau\ =\ f_{0}e^{-\Delta E/k_{B}T} \tag{1}\]  
where \(k_{B}\) is Boltzmann constant, \(T\) is working temperature (\(T\) = 350 K), and the thermal attempt frequency \(f_{0}\) of two spin model for composite media is set as 1.3 \(\times\) 10\({}^{12}\) Hz for ultra-high recording density [4]. Here, the thermal stability factor (\(\Delta E/k_{B}T\)) is set as 60, aiming at the relaxation time of more than 10 years in the working environment. The energy barrier (\(\Delta E\)) as mentioned in [16] is given by  
\[\Delta E\ =\ (K_{u}^{h}V^{h}+K_{u}^{s}V^{s})(1-\frac{H}{H_{\text{sep}}})^{\gamma} \tag{2}\]  
where \(Ku\) is the anisotropy constant of soft (index \(s\)) and hard (index \(h\)) layers, \(V\) is the volume, \(H\) is the writer field and \(H_{sw}\) is the switching field, \(\gamma\) equals 1.5. In the micromagnetic simulation, \(L1_{0}\)-FePt is used for the hard layer of ECC media due to its high magnetocrystalline anisotropy which could provide sufficient thermal stability [17], and [Co/Ni]\({}_{5}\) is chosen as the soft layer materials, which helps to overcome the limitation of the current magnetic writing field. The magnetic parameters are set as follows according to [13; 18; 19]: \(Ku\) are set as \(K_{\text{FePt}}\) = 1.61 \(\times\) 10\({}^{7}\) erg/cm\({}^{3}\) and \(K_{\text{[Co/Ni]5}}\) = 2.5 \(\times\) 10\({}^{6}\) erg/cm\({}^{3}\), while the thicknesses of hard and soft layers are set to 6 nm and 4 nm to keep \(\Delta E\) = 60\(k_{B}T\), respectively. \(M_{\text{s}}\) is set to \(M_{\text{FePt}}\) = 500 emu/cm\({}^{3}\) and \(M_{\text{[Co/Ni]5}}\) = 750 emu/cm\({}^{3}\). The exchange coupling constants are set as \(A_{\text{FePt}}\) = 1.2 \(\times\) 10\({}^{-6}\) erg/cm and \(A_{\text{[Co/Ni]5}}\) = 1.0 \(\times\) 10\({}^{-6}\) erg/cm; the interlayer exchange coupling constant A\({}_{\text{ex}}\) between hard and soft phases is assumed to be 1.1 \(\times\) 10\({}^{-6}\) erg/cm. The switching field of FePt(6 nm)/[Co/Ni]\({}_{5}\)(4 nm) is 16.44 kOe according to our simulation. The erase band width is not only determined by the write field, but also by the media geometric, magnetic properties, etc. The EBW calculation is applied to continuous magnetic recording media for evaluating the erase band noise. The EBW calculation method provides a fast evaluation criterion for the write performance, which can account for the effects of the rounded corner and adjacent track erasure. For comparison, the EBW as a function of skew angle is investigated for the single-phase media [Co/Ni]\({}_{5}\)(10 nm) and ECC media FePt(6 nm)/[Co/Ni]\({}_{5}\)(4 nm) with the same thickness. As illustrated in Figure 3, the minimum and maximum EBW of FePt/[Co/Ni]\({}_{5}\) are 8.1 nm and 15.8 nm, respectively. In contrast, the EBW of ECC media is far superior to the corresponding EBW of 54.8 nm and 55.5 nm for the single-phase media [Co/Ni]\({}_{5}\). Meanwhile, the EBW of the single-phase media varies insignificantly with the increase of skew angle. Because the switching field of [Co/Ni]\({}_{5}\) (about 6.8 kOe) is much smaller than that of FePt/[Co/Ni]\({}_{5}\) with the same thickness.