# Writer Performance Optimization with Shingled Rounded Corner and Exchange Coupled Composite Media
## 3 Results and Discussion  
### The Rounded Corner  
The rounded corner writer is modeled as shown in Figure 1c. The shape of the rounded corner is characterized by the rounded angle (\(\theta\)) and corner length (\(L\)). The rounded corner greatly influences the field distribution of the shingled writer and also changes the field gradient at the writing corner. A tiny loss of the tapered structure caused by manufacturing deviation may have little influence on the edge field to recording bit, but it could cause the fluctuation of the stray field and thus lead to adjacent track erasure. Therefore, the parameter \(\theta\) and \(L\) are varied to generate different rounded corner structures to analyze their impact on the write performance of the recording system.  
The tip broad end width of the shingled writer is fixed as 40 nm according to Figure 2. \(\theta\) is ranged from 10\({}^{\circ}\) to 50\({}^{\circ}\), and \(L\) varies from 1 nm to 6 nm to construct different rounded corner shapes. The write field gradient changes with different \(\theta\) and \(L\), which is shown in Figure 5. As illustrated, the shingled rounded corner writer can attain the maximum field gradient when \(L\) is 3 nm, and the field gradient peaks when the rounded angle is 40\({}^{\circ}\) for all corner length cases. The larger field gradient results in a larger field margin, which is the difference between the write field of recording cells and the erasing field of adjacent track erasure cells. As a result, the peak of field gradient is about 552 Oe/nm (with \(\theta\) = 40\({}^{\circ}\) and \(L\) = 3 nm). In this case, the field margin is the largest, which helps to reduce the possibility of erasing neighboring cells and avoiding adjacent track encroachment. It is worth noting that a larger field gradient results in a smaller ATE field, which is most affected by the writer stray field and determines the bit error rate of the adjacent track. Thus, the maximum field gradient in cross-track direction is calculated to avoid track erasure and attain a better write performance.  
Figure 4: Bit error rate versus switching field of recording media.  
Figure 6 shows the combined write-in error probability versus different rounded corner cases. As illustrated, a moderate corner length (\(L\) = 3 nm) is recommended to achieve a satisfactory system BER. Furthermore, a relatively large rounded angle (\(\theta\) = 40\({}^{\circ}\)) is helpful to achieve the lowest combined write-in error rate. According to the calculation, the combined write-in error rate of \(L\) = 3 reduces by 31% compared with that of \(L\) = 1 nm when \(\theta\) = 40\({}^{\circ}\). The recording system achieves the best write performance at \(\theta\) = 40\({}^{\circ}\) and \(L\) = 3 nm with the combined write-in error rate of 3.9 \(\times\) 10\({}^{-4}\). Meanwhile, the BER of the recording cell and the adjacent cell are \(P_{reconling\_hit}\) = 1.4 \(\times\) 10\({}^{-4}\), \(P_{erasure}\) = 2.5 \(\times\) 10\({}^{-4}\), respectively.  
Figure 7 compares the skew angular dependence of EBW between a normal shingled writer and a rounded corner writer (\(\theta\) = 40\({}^{\circ}\) and \(L\) = 3 nm). The results show that the EBW increases with the skew angle, and the EBW of the rounded corner writer is smaller than the normal writer when the skew angle increases from \(-\)20\({}^{\circ}\) to 8\({}^{\circ}\), because the effective write field with a rounded corner is slightly smaller than the normal writer. Meanwhile the write field gradient with rounded corner decreases more sharply than the normal writer when the skew angle is greater than 8\({}^{\circ}\), which brings a severer fringing field, and correspondingly the EBW of the rounded corner writer increases more sharply.  
Figure 5: Write field gradient with different rounded angle (\(\theta\)) and corner length (\(L\)).  
Figure 6: Combined write-in error rate with different rounded angle (\(\theta\)) and corner length (\(L\)).