A PMR writer is disclosed with an all wrap around (AWA) shield design in which one or more of the leading shield, side shields, and trailing shield (TS) structure (except the hot seed layer) at the air bearing surface (ABS) are comprised of an alloy having a damping parameter α of ≥0.04 to minimize wide area track erasure (WATE). The TS structure comprises two outer magnetic layers with an 8-16 kiloGauss (kG) saturation magnetic moment (Ms) on each side of a center stack with a lower write gap, a middle hot seed layer (Ms of 19-24 kG), and an upper magnetic layer (Ms of 16-24 kG). The hot seed layer, and upper TS magnetic layer promote improved area density capability (ADC). A second TS layer with Ms of 16-24 kG and a full width at the ABS may be formed on the upper magnetic layer.