# Writer Performance Optimization with Shingled Rounded Corner and Exchange Coupled Composite Media
## 2 Model Parameters and Methodology  
### Design of Trapezoidal Shingled Writer  
The experimental model applies the frequently used trapezoidal shingled writer to investigate the rounded corner effect. The shingled writer consists of a tapered pole tip, return yoke, half wrap-around shield, and soft magnetic underlayer (SUL) which functions as a mirror for the shingled writer to increase the field gradient. The finite element micromagnetic method (FEM) is introduced to mesh the shingled writer into tetrahedral elements [14], and the edge length of pole tip part is 1 nm, which is sufficient to emulate the relaxation process of the magnetic writer. The height of the pole tip is 80 nm. The write corner angle (\(\alpha\)) and tip tapered angle are set as 78\({}^{\circ}\) and 45\({}^{\circ}\), respectively. The height of the half wrapped-around shield is 15 nm and the shield tapered angle is 30\({}^{\circ}\). The width of the narrow end (\(T_{\text{s}}\)) and the length (\(T_{L}\)) of the pole tip (shown in Figure 1b) are set as 14 nm and 34 nm, respectively. The writer-media spacing is maintained at 5 nm. During simulation, the shingled rounded corner writer with various rounded angles (\(\theta\)), corner lengths (\(L\)), and shield gaps (\(SG\)) are designed to analyze the effect of the rounded corner on the write performance. The detailed structure of the shingled writer was discussed in our previous work [13].  
The magnetic parameters of the shingled writer are set as follows according to [13; 15]: the saturation magnetization (\(M_{\text{s}}\)), exchange coupling constant and anisotropy constants (\(K_{u}\)) of the main pole are 1910 emu/cm\({}^{3}\), 1.0 \(\times\) 10\({}^{-6}\) erg/cm and 3 \(\times\) 10\({}^{4}\) erg/cm\({}^{3}\), respectively. The shield is half wrapped around to produce a steeper field gradient in the cross-track direction. The \(M\)s of shield is 800 emu/cm\({}^{3}\), the exchange coupling, and \(K_{u}\) are the same as the shingled writer. The damping factor is 0.1 for the recording simulation. The width of the tip broad end (\(T_{w}\)) is varied to obtain reasonable writing capability of the shingled writer.  
Figure 2 shows the effective write field and field gradient as a function of the width of the tip broad end (\(T_{w}\)) without a rounded corner. As illustrated, the effective write field increases as the width becomes longer, but it reaches a comparatively large value and grows slowly if the width exceeds about 48 nm. The effective write field does not grow unrestricted with the increasing width. This is because the effective write field is mainly determined by the writing corner in the SMR system, and when the width is larger than a certain value (i.e., 50 nm in our simulation), the newly added portion of the pole tip is further away from the writing corner, which makes the impact of the write field negligible. The write field gradient peaks at the width of 40 nm, which avoids ATE and reduces the bit error rate of adjacent tracks. In this situation (\(T_{w}\) = 40 nm), the effective write field is 17.6 kOe and the maximum field gradient is 470 Oe/nm.  
Figure 2: Effective write field and cross-track field gradient of shingled writer depends on the width of broad end (without rounded corner).