A film 12 with perpendicular magnetic anisotropy and a protective film 13 are formed over a single-crystal substrate 11. This substrate is made of either a single crystal having a hexagonal crystal structure and a plane (0001) in parallel with the substrate plane or a single crystal having a cubic crystal structure and a plane (111) in parallel with the substrate plane, and the film is epitaxially grown such that its easy axis of magnetization is perpendicular to the substrate plane. As a result, the film can have its perpendicular orientation and perpendicular magnetic anisotropy improved to effect a perpendicular magnetic recording of high density thereby to provide the perpendicular magnetic recording media, of which the film has a remarkably enhanced orientation.