Q:

Changing current and magnetic materials in an inductor to genereate eddy currents

I come from a biomedical background which has primarily focused on inductors as an element of a transcranial magnetic stimulator. The way this method works is that a copper coil receives pulses of electric current which generates a changing magnetic field. This changing magnetic field is great for getting past the skull and into the brain, where it generates a reverse-direction electric current, used to treat various diseases and malflictions. We don't call these coils "inductors" nor do we call these neural stimulations "eddy currents". But that's probably what you know them as. 
I know that typically, inductors use ferromagnets as a core, because they have a much higher saturation level than other materials, leading to higher inductance. However, I have just read that for magnetic stimulation, it is better to use ferrimagnets because they are non-conductive. The book implies that Eddy currents generated in the core of a conductive ferromagnet would weaken the induced electric current in the brain. Is this really true? This is just just conservation of energy I guess? The book seems to assume that there is a layer of insulation between the copper coil and the conductive ferromagnetic center.
Say you have a copper wire that's immersed in a ferromagnetic material - no insulation between the wire and the material. Does the same result apply? Is it because ferromagnets are insulative relative to copper, meaning they won't pick up much current from the actual pulse, but will only pick up the eddy currents? 
Now for my real question. Imagine you had a magical material that was uniformly conductive and uniformly ferrimagnetic. Not a conductive wire in a magnetic substance, but a uniformly conductive and magnetizable material, which I guess was also highly conductive like copper. How would the inductance, or induced current, change here?

A:

Ferrites are non-conductive ferrimagnetic materials with high permeability and high resistance; that makes them very good as the core of an inductor when you want to minimize losses due to eddy currents (conduction in the core).  
Large transformers may use laminated ferromagnetic metals (conductors) - you want to use the metals because they are cheap, you laminate (that is, split it into thin sheets of metal that are electrically insulated from each other) in order to disrupt eddy currents / prevent large loops of current from flowing. This helps reduce losses in the core, and thus makes the transformer / inductor more efficient.

Now for my real question. Imagine you had a magical material that was uniformly conductive and uniformly ferrimagnetic. Not a conductive wire in a magnetic substance, but a uniformly conductive and magnetizable material, which I guess was also highly conductive like copper. How would the inductance, or induced current, change here?

A conductive core will generate losses (heat) and reduce the flux linkage (Lenz's law: the current will flow to oppose the changing flux). In the case of a perfect (super) conductor, this effect is such as to prevent any magnetic flux from existing inside (up to certain saturation effects). Whether that material is ferri- or ferro-magnetic will not change the result: if it's a perfect conductor, there will be no flux change inside.

