The magnetic systems of superconducting wires and tapes, consisting of a magnesium diboride (MgB_2) superconducting core surrounded by a ferromagnetic iron (Fe) sheath, have been investigated. The interaction of the superconductor with the soft magnetic environment has been experimentally shown to lead to significant enhancement of dissipation-free super-current densities. The maximum densities of the super-currents can exceed the critical current densities obtained in the same 'bare' wire (with its iron sheath removed) by more than one order of magnitude under the same experimental conditions. This current density enhancement is referred to as the overcritical state, which has been observed over a wide range of magnetic fields applied transversely to the wire. No overcritical currents are observed for the longitudinal field orientation. The irreversibility field is shown to be considerably suppressed by the influence of the iron sheath for both field orientations. Different geometries of the wire cross section have been investigated.
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