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A description of the development of a family of high-squareness low-stress-sensitivity Permalloys of controlled coercive force for application as the soft magnetic element in the piggyback twister-type memory is given. Since both the hard- and soft-magnetic elements are wrapped simultaneously around the conductor core, the magnetic properties of both elements must be optimized by a single post-wrap annealing treatment. Previous work on a Co-Fe-Au alloy as the hard magnetic element has led to an annealing temperature range of 800-900°C, which must now be adopted for the treatment of the soft magnetic element as well. From published data on the compositional dependence of magnetocrystalline anisotropy and saturation magnetostriction in Ni-Fe-Mo alloys, an optimum composition, 6 percent Mo-80.5 percent Ni-13.5 percent Fe was first devised for which , and Oe after post-wrap annealing. By adding small amounts of Be (0.4-0.7 percent) or Zr (0.2-0.4 percent), the coercive force can be controlled to any value up to 3 Oe as a result of precipitation. At the same time, low stress sensitivity was retained and squareness improved.