A perpendicular magnetic recording medium adapted for high recording density and high data recording rate comprises a non-magnetic substrate having at least one surface with a layer stack formed thereon, the layer stack including a perpendicular recording layer containing a plurality of columnar-shaped magnetic grains extending perpendicularly to the substrate surface for a length, with a first end distal the surface and a second end proximal the surface, wherein each of the magnetic grains has: (1) a gradient of perpendicular magnetic anisotropy field Hk extending along its length between the first end and second ends; and (2) predetermined local exchange coupling strengths along the length.