Ferronagnetic materials vary in "hardness". A ideally "soft" magnetic material would follow the applied magnetization: Turn on the current in the surrounding coil (or other method of applying a magnetic field), the magnetization appears - the directions of the unpaired electron's "spins" go from random to a few more pointed along the applied field than against it. Increase the current, the magnetization increases in proportion - up to a limit where its magnetization will not increase any further, because all the unpaired electrons have their spins pointed the same way - the "little magnet" electrons are all aligned. Turn down the current and the magnetization decreases in proportion. Take the current away and they are back to a completely random (or a structure, like tiny "domains" - regions where the electrons point the same way - that averages out to random), and the material is unmagneitized. The material follows the magnetic field - magnifying it proportionally (compared to an equivalent volume of vacuum or a non-magnetic material with only paired electrons) because the field from the aligned electron spins adds to that of the applied magnetic field, and may be as much as hundreds of times stronger.
In a "hard"(er) magnetic material the orientation of the spins of the unpaired electrons is not freely moving, but sticky. They stay in their current orientation until the applied field reaches a threshold. Then they "flip" to align with it (pulling a bit of energy from it in the process and turning it into heat as the electron settles into its new, now-lower-energy, orientation). Take away the applied field and they (or some of them) tend to stay in the new orientation until enough field is applied in the opposite direction to flip them the other way. Take away all externally applied fields and at least some of the electrons don't flip back to averaging-random orientations. The higher the threshold, and the more electrons that maintain alignment (despite thermal vibration and structural factors tending to re-randomize them) creating a "residual" magnetization once the , the magnetically "hard"er the material. The harder the material, the more energy required to magnetize it or change its magnetization.
The materials we deal with are not ideal. But they are either very (but not ideally) soft, which we use to make flux paths to concentrate (and thus greatly magnify) magnetic flux, or very hard, to make permanent magnets to apply flux without spending electrical energy driving current through the resistance of a magnetizing coil.
Where the magnetic field is changing you use the (magnetically) softest material practical, to avoid throwing away energy every time it changes. (You also cut it into thin plates, varnished to provide a little insulation and stacked up so they're never crosswise to the changing field, to avoid the other big source of losses - eddy currents.)
Neodymium alloys - at least those you're likely to have access to - are a VERY hard magnetic material. The issue with them is not their permeability, it's their extreme fields necessary to magnetize them in the firsrt place. For neodymium magnets it's done at the factory, by discharging capacitors through a coil consisting essentially of a few turns of copper pipe, creating hysterically high currents for the nanoseconds necessary to flip the electrons. Then they stay magnetized (if not mishandled) for somewhere from years to geologic time. It's really impractical to use them for an electromagnet core - the currents needed to affect their magnetization would melt the coil in a fraction of a second.
On the other hand, they are what made small windmills practical. The lower the wind, the slower the blades and shaft turn, and the stronger a magnetic excitation field you need to generate a given amount of power. If you're using an electromagnet to provide the field, you need a lot of power to overcome the resistive losses in the copper - and more power input as the wind gets lower, when you need your dwindling output for more important things. Electromagnet excitation puts your cutin wind speed, not at the point where the mill is providing enough power to start using it, but where it produces enough MORE power than the excitation consumes to have a surplus.
But permanent magnets don't require continuous excitation. They're excited ONCE, at the factory, by a giant pulse of magnetic field lasting less than a milisecond, and never need magnetization power again. Instead of spending tens of bucks once, and electrical power forever, for silicon-steel cores and copper wire, you spend a couple hundred bucks once for pre-magnetized rare earth alloys (and the electronic or design wizardry necessary to make use of the unregulated voltage produced when you can't adjust the alternator's excitation), and you get to consume essentially all the power turned into electricity by the machine.