Side fringing fields and write and read crosstalk of narrow magnetic recording heads

In magnetic recording systems the side fringing fields of magnetic recording heads are responsible for crosstalk from adjacent tracks and eventually for partial erasure of adjacent tracks, thereby limiting the attainable track density. In this paper we derive analytical expressions for the magnetic field near the side of a recording head and calculate the cosine transform of the longitudinal field component, with the head side angle and gap length as parameters. The field of a head of zero width is also considered. Due to the side fringing field the written track is somewhat wider than the geometrical head width; the increase in width being approximately proportional to the maximum field strength in the recording medium and the head-to-medium distance. The amplitude u of the read crosstalk signal from an adjacent, infinitesimally narrow track is calculated and it appears that it can be approximated by u/u_{0} = 0.5 \exp (-2\pi x/\lambda) , where u 0 is the on-track signal (with zero head-to-medium spacing), x is the distance between track and head side, and λ is the wavelength. Maximum track densities are calculated for a specified crosstalk-to-signal ratio and a given head width and wavelength. For a wavelength of 10 μm, a head width of 5 μm, and a crosstalk of -20 dB, the track density is limited to about 130 tracks/mm, assuming a track width equal to the head width. When the track is taken to be 5 μm wider than the head to account for the effects of the write process, no guardband at all is needed for -20 dB crosstalk and the limit to the track density is 100 tracks/mn.