a perpendicular magnetic recording medium comprising

a generally planar substrate;

an underlayer of magnetically permeable material on the substrate and having a thickness greater than zero and less than 50 nm, the underlayer being sufficiently thick to provide magnetic permeability μ to the underlayer of greater than 1 and less than 25, the underlayer having a magnetic saturation B_s; and

a magnetic recording layer on the underlayer for enabling the recording of data in magnetized regions along data tracks; and

a perpendicular recording head comprising

a magnetic write pole for applying a generally perpendicular magnetic field to the recording layer for magnetizing regions in the data tracks, the write pole having a substantially planar end facing the recording layer and a trailing edge oriented generally orthogonal to the along-the-track direction;

a trailing shield having a substantially planar end facing the recording layer, a front edge facing the write pole trailing edge and located down-track from the write pole trailing edge, and a throat thickness measured generally orthogonally from the trailing shield's planar end, the trailing shield having a throat thickness and magnetic permeability so as not to be magnetically saturated in the presence of a write field from the write pole and a magnetic saturation B_s greater than the magnetic saturation B_s of the underlayer;

nonmagnetic gap material between the trailing edge of the write pole and the front edge of the trailing shield to define a write gap; and

a magnetic return pole for return of write pole magnetic flux from the magnetically permeable underlayer of the recording medium.