Exchange spring magnet
The magnetostatic energy is the energy stored in the field generated by a material's magnetic moments. The magnet's field reaches its maximum intensity if all the magnetic moments orient in one direction; this is what occurs in a hard magnet. In order to prevent building up the magnetic field, sometimes magnetic moments tend to form loops. That way, the energy stored in the magnetic field can be constrained; this is what occurs in a soft magnet. What determines whether a magnet is hard or soft is the dominant term of its magnetic energy. For hard magnets, the anisotropy constant is relatively large, making the magnetic moments align with easy axis. The opposite case applies to soft magnets, in which the magnetostatic energy is dominant.
Nonelectrostatic electric fields
To understand the origin, let us consider a wire loop, placed in magnetic field. According to Faraday's law of induction, if the magnetic flux is changed through the loop, an emf will be induced in this. The magnetic flux may be changed by changing the area of the loop or by changing the magnetic field. Why a changing magnetic field produces current in the loop? The loop contains electrons, which don't feel magnetic field, but if the magnetic field changes, they feel it. It is customary to think that if in a given region magnetic field changes with time, an electric field is induced in this region, which causes motion of electrons in the loop. But, an electric field can be there even if we don't place a loop. So, the complete discussion will be that if the magnetic field is changing, the electric field will appear, circulating the changing magnetic field.