The differences between this material and the 'soft iron' used in many of Ed's experiments are many, but the two primary things to note are:
Paramagnetism:
1. Internal magnetism is linear
2. Internal magnetism is lost when the external field is removed.
Ferromagnetism:
1. Internal magnetism is recursive, very non-linear
2. Internal magnetism persists after external field is removed.
The linear aspect of paramagnetic materials is rather important, because it stipulates that you can never get an internal field greater than the external field, they are typically 1:1.
With ferromagnetic soft iron, this isn't the case. The resultant field can actually be stronger than the H field used to create it, however the curve does flatten out at the saturation point after the H field is removed. But while it is in place, the combined field can be stronger.
This means that conventional magnetic flux will not remain in the toroid ring of hematite after the external field is removed. Theoretically, all of the energy used to align the domains in the paramagnetic material, is returned to the source when the field is allowed to collapse, less that energy converted to heat (or other EM radiation). This is the principle of ferrite core transformers.
However, let us imagine that some of that charge energy is not converted to heat, and is not dissipated. Consider the possibility that these little domains that have been physically repositioned, end up resonating back and forth after they are let loose. Imagine, that instead of getting warm, the ring gets cool and these domains all start interacting with each other in a supportive way while using external thermal energy to keep the process going. Now imagine, that once setup in this resonant manner, the "output" is some higher energy emission, say in the THz range - small bursts of energy when ever the domains reach some maximum threshold. Then, if this worked, the only way to stop it would be to chill it, take away the energy that keeps it going. Thus charging it while it is hot, or striking it to make it ring at a specific frequency while it is hot, may cause it to go into this perpetual process of converting external thermal energy to some other form of EM energy.

I'm not saying that this is what's happening with the rings being experimented with - but I am saying that it could be a scientific explanation if all the conditions were right. Understanding how a single atom transfers thermal energy to its neighbors is important to comprehending how this could take place.



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