Magnetically Soft Materials
Ferromagnetic materials in which the magnetic field can can be easily reversed are said to be magnetically soft. They may have high permeability but very small coercivity, and therefore have very narrow hysteresis loops.
Commercial magnetically soft materials are usually made from alloys of iron and nickel with compositions around Ni80Fe20. Commercial materials have names like 'Permalloy', 'Hymu' and 'Mumetal' and are characterized by high initial permeability and narrow, square hysteresis loops. Myers quotes typical values of remanence at 0.8 times saturation and coercivity about 2 μT.
Magnetically soft materials are used for the cores of transformers to reduce the energy losses associated with the reversing fields of the AC currents. Such cores are used in coils up to radio frequencies to increase the inductance.