The recording medium according to the invention has a magnetic recording layer, an exchange coupling layer and an enhancement or bias layer with an anisotropy orthogonal to the recording layer. The enhancement layer is designed to have no significant remanent magnetization and preferably to saturate under the write head. The enhancement layer creates an exchange field normal to the anisotropy of the recording layer and has the effect of rotating the magnetization of the recording layer and lowering the required switching field, i.e., the coercivity. The invention can be embodied in a longitudinal recording medium or a perpendicular recording medium. The exchange coupling can either ferromagnetic or antiferromagnetic. The bias layer has a high KuV and anisotropy and is designed to have high thermal stability and minimize the rotation of magnetization with the head field.