Non-uniform field and switching criterion

  1. Consider a ferromagnetic (or other ferroic) crystal small enough to be a monodomain. We can switch magnetization with coercive magnetic field. Now what if we attach non-uniform field, which exceeds coercive value only in, for example 40% of a crystal? How much of a volume the field has to exceed coercive value to switch the magnetization in a crystal?
     
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