A super-paramagnetic cladding layer formed on from 1 to 3 sides of a conductive line in a magnetic device is disclosed. The cladding layer is made of "x" ML/SL stacks in which x is between 5 and 50, SL is an amorphous AlO.sub.x seed layer, and ML is a composite with a soft magnetic layer comprised of discontinuous particles less than 2 nm in size on the seed layer and a capping layer of Ru, Ta, or Cu on the soft magnetic layer. Fringing fields and hysteresis effects from continuous ferromagnetic cladding layers associated with switching the magnetic state of an adjacent MTJ are totally eliminated because of the super-paramagnetic character of the soft magnetic layer at room temperature. The soft magnetic layer has near zero magnetostriction, very high susceptibility, and may be made of Ni.sub..about.80Fe.sub..about.20, Ni.sub..about.30Fe.sub..about.70, Co.sub..about.90Fe.sub..about.10, or CoNiFe.