A horizontal magnetic recording medium that has as its magnetic film a granular film with grains of a chemically-ordered FePt or FePtX (or CoPt or CoPtX) alloy in the tetragonal L10 structure uses an etched seed layer beneath the granular film. The granular magnetic film reveals a very high magnetocrystalline anisotropy within the individual grains. The film is produced by sputtering from a single alloy target or cosputtering from several targets. The granular structure and the chemical ordering are controlled by means of sputter parameters, e.g., temperature and deposition rate, and by the use of the etched seed layer that provides a structure for the subsequently sputter-deposited granular magnetic film. The structure of the seed layer is obtained by sputter etching, plasma etching, ion irradiation, or laser irradiation. The magnetic properties, i.e., Hc and areal moment density Mrt, are controlled by the granularity (grain size and grain distribution), the degree of chemical ordering, and the addition of one or more nonmagnetic materials, such as Cr, Ag, Cu, Ta, or B. The resulting granular magnetic film has magnetic properties suitable for application in high-density, horizontal magnetic recording media.