A nanocrystalline alloy ribbon has an alloy composition represented by FeCuxBySizAaXb where 0.6≦x<1.2, 10≦y≦20, 0<z≦10, 10≦(y+z)≦24, 0≦a≦10, 0≦b≦5, with the balance being Fe and incidental impurities, 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, all numbers being in atomic percent. The ribbon has a local structure having nanocrystals with average particle sizes of less than 40 nm dispersed in an amorphous matrix, the nanocrystals occupying more than 30 volume percent of the ribbon and has a radius of ribbon curvature of at least 200 mm.