Magnetic clustering, thermal stability, and recording performance on perpendicular media with multilayered magnetic anisotropy field (Hk)-gradient CoPtCr-oxide/Cap layers with various Ru-oxide layer thicknesses (tRu-oxide) on top of Ru/NiW layers are investigated. With increasing tRu-oxide from 0 to 1.3 nm, Hc and Hs are enhanced but Hn is reduced. Magnetic correlation length (Dn) extracted from a set of major and minor loops significantly decreases but intrinsic switching field distribution remains unaffected. A short-time switching field (Ho) proportional to Hk increases linearly while KuV/kT remains unchanged. Similar KuV/kT is explained by compensation of the reduced Dn with the enhanced Ku induced by a thin Ru-oxide. However, thermal decay rate degrades from 0.06 to 0.32%/decade, which correlates well with Hn. Similar values of initial minor loop slopes indicate no change in magnetic switching behavior. A 1 nm-thick Ru-oxide layer as a well-defined granular template significantly improves recording performance: narrower MCW at 10 T by 8 nm and higher SNR at 2 T by 1.4 dB are observed even at lower OW by 8 dB compared to the media without Ru-oxide. All the recording parameters as a function of Dn correlate well.