A shingled recording head design is proposed that makes use of a saturation magnetization gradient to focus flux into the corner of the writing pole. This design yields field gradients of 800 Oe/nm and can write more than 2.5 Tbits/in2 of user data onto a 10 nm thick ECC recording layer with 6 nm Voronoi grains. Maximum user densities are predicted to be over 4.66 Tbits/in2 with 8 nm grains and 12 Tbits/in2 with 5 nm grains using a perfect read and write scheme at a 1:1 bit aspect ratio. For read back, three contact dual differential MR head designs that have two independent free layers with magnetization pointing oppositely are examined for the purpose of extending magnetoresistive technology. The differential head shows good cross track resolution that will be advantageous at the low bit aspect ratios likely for two-dimensional magnetic recording. Results show that an array of three dual differential heads can successfully resolve an 8 nm track surrounded by adjacent tracks that have pseudo random bit sequences written to them, even though each head is wider than the track.