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Bit patterned media with inclined anisotropy were proposed along with media design with a higher saturation magnetization and a small thickness for the dot. Inclination of the anisotropy axis was found to reduce broadened switching field distribution of the media caused by the magnetostatic interaction between the dots. Recording simulation at an areal density of 2.6 Tbit/in2 using a write field of a shielded planar head exhibited substantially increased write shift margins of 6.5 nm and 10 nm in down- and cross track directions, respectively, for the media with inclined anisotropy when the anisotropy dispersion of the media was as small as 2%. Recording density was expected to be increased beyond 4 Tbit/in2 for the media with additional exchange coupling between the dots.