In the magnetic storage device, magnetization characteristics during write cycles are homogenized, and write cycles are carried out efficiently. In the magnetic storage device, the soft magnetic body is formed so as to cover the line either totally or partially, and the anti-ferromagnetic layer is formed on the outer surface of this soft magnetic body. Furthermore, the magneto-resistive element is disposed in the vicinity of the line. Suppose the case where the exchange coupling energy at the interface between the soft magnetic body and the anti-ferromagnetic layer is J (erg/cm2), the saturation magnetization of the soft magnetic body is Ms (emu/cc), and the coercive force of the soft magnetic body is Hc (Oe). Then, the thickness t (cm) of the soft magnetic body is selected to be such that t