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A magnetic core includes a nanocrystalline alloy ribbon having a composition represented by FeCuxBySizAaXb, where 0.6≤x<1.2, 10≤y≤20, 0≤(y+z)≤24, and 0≤a≤10, 0≤b≤5, all numbers being in atomic percent, with the balance being Fe and incidental impurities, and where A is an optional inclusion of at least one element selected from Ni, Mn, Co, V, Cr, Ti, Zr, Nb, Mo, Hf, Ta and W, and X is an optional inclusion of at least one element selected from Re, Y, Zn, As, In, Sn, and rare earth elements. The nanocrylstalline alloy ribbon has a local structure such that nanocrystals with average particle sizes of less than 40 nm are dispersed in an amorphous matrix and are occupying more than 30 volume percent of the ribbon.