A perpendicular magnetic recording disk has a graded-anisotropy recording layer (RL) formed of at least two ferromagnetically exchange coupled CoPtCr-oxide magnetic layers (MAG1 and MAG2) with two nucleation films (NF1 and NF2) between the magnetic layers. NF1 is a metal film, preferably Ru or a Ru-based alloy like RuCr, sputter deposited on MAG1 at low pressure to a thickness between about 0.1-1.5 nm. NF2 is a metal oxide film, preferably an oxide of Ta, sputter deposited on NF1 at high pressure to a thickness between about 0.2-1.0 nm. MAG2 is sputter deposited over NF2. NF1 and NF2 provide a significant reduction in average grain size in the RL from a graded-anisotropy RL without nucleation films between MAG1 and MAG2, while also assuring that MAG1 and MAG2 are strongly exchange coupled.