A perpendicular magnetic recording medium, comprising: (a) a non-magnetic substrate having a surface; and (b) a layer stack formed over the substrate surface, comprising in overlying sequence from the substrate surface: (i) a magnetically soft underlayer; (ii) an interlayer structure for crystallographically orienting a layer of a perpendicular magnetic recording material formed thereon; and (iii) at least one crystallographically oriented magnetically hard perpendicular recording layer; wherein the magnetically soft underlayer is sputter-deposited at a sufficiently large target-to-substrate spacing and at a sufficiently low gas pressure selected to provide the underlayer with a smooth surface having a low average surface roughness Ra below about 0.3 nm, as measured by Atomic Force Microscopy (AFM).