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The progression toward gigahertz data rates in magnetic recording has introduced considerable challenges to soft magnetic materials design. The difficulties lie in satisfying two sets of conflicting demands: 1) simultaneously achieving soft magnetic properties, high saturation magnetization, and a high resistivity, with the latter required to limit eddy-current losses and 2) balancing the inherent tradeoff between bandwidth and permeability imposed by the direct and inverse dependences, respectively, of these two parameters on the anisotropy field. This paper describes a new soft magnetic composite system that meets these requirements: a metal/native-oxide multilayer (MNOM) film consisting of nanogranular high-moment CoxFe100-x layers separated by ultrathin magnetic native oxide layers. The high-resistivity magnetic oxide layers isolate the metallic layers electrically, while coupling them magnetically and minimizing the decrease in volume-averaged saturation magnetization that exists in traditional metal/nonmagnetic oxide composites. In addition, the "exchange-averaged" soft magnetic properties of the MNOM composite include an ideal low-dispersion in-plane uniaxial anisotropy whose magnitude varies linearly with the fraction x of Co in the alloy. The resulting anisotropy control, together with the large saturation magnetization, permits the permeability and resonance frequency to be tuned over a wide range to meet specific application requirements.