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Microwave assisted magnetic recording (MAMR) on bit-patterned media (BPM) with areal recording density over 5 Tbit/in2 was investigated using micromagnetic simulation and an analytical method. It was found that a planar magnetic anisotropy material is indispensable for a narrow spin torque oscillator to obtain in-plane oscillation with the required frequency. It was also found that the MAMR on BPM with an areal recording density of 6.2 Tbit/in2 can be obtained by superimposing the write magnetic field gradient from main pole and the effective assist field gradient from field generation layer. These head and media requirements are likely to be achieved by improving the present technology.