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Exchange spring media are proposed for magnetic-recording systems consisting of a hard/soft bilayer. By varying the fraction of thickness for the hard and soft layer and by varying their saturation polarizations, the media properties can be optimized in order to achieve high thermal stability without increase of coercive field. In grains with identical size and coercivity, an optimized bilayer reaches an energy barrier exceeding those of optimized single-phase media by more than a factor of two. Thus, exchange spring media allow to reduce the grain diameter by more than a factor of 1/√2. Additionally, the lower angular dependence of coercivity of exchange spring media improves the signal-to-noise ratio (SNR) by a factor of 2.5.