A perpendicular magnetic recording writer with an all wrap around (AWA) shield design wherein one or more of the leading shield, trailing shield, and side shields comprises a magnetic hot seed layer made of a >19 kG to 24 kG material that adjoins a gap layer, and a side of the hot seed layer opposite the gap layer adjoins a high damping magnetic layer made of a 10-16 kG material (or a 16-19 kG material in the trailing shield) having a Gilbert damping parameter a >0.04. In one embodiment, the high damping magnetic layer is FeNiRe with a Re content of 3 to 15 atomic %. The main pole leading and trailing sides may be tapered. Side shields may have a single taper or dual taper structure. Higher writer speed with greater areal density capability is achieved.