A magnet core has a linear B-H loop, a high modulability with alternating current and direct current, a relative permeability of more than 500 but less than 15,000, and a saturation magnetostriction lambdas of less than 15 ppm, and is made of a ferromagnetic alloy, at least 50 percent of which consist of fine crystalline parts having an average particle size of 100 nm or less (nanocrystalline alloy) and which is characterized by formula FeaCobNicCudMeSifBgXh, wherein M represents at least one of the elements V, Nb, Ta, Ti, Mo, W, Zr, Cr, Mn, and Hf, a, b, c, d, e, f, g are indicated in atomic percent, X represents the elements P, Ge, C and commercially available impurities, and a, b, c, d, e, f, g, h satisfy the following conditions: 0