A perpendicular magnetic recording medium having a substrate, an amorphous soft underlayer of thickness 30 nm or greater, and a granular magnetic recording layer for perpendicular recording is disclosed. The granular magnetic recording layer includes a non-magnetic region between magnetic grains, wherein the non-magnetic region includes metal nitride or metal carbide and provides exchange decoupling between the magnetic grains. The perpendicular recording medium of this invention reduces DC noise and increases media signal-to-noise ratio; it reduces surface roughness, which in turn reduces the head-to-media spacing and the head-to-amorphous soft underlayer spacing.