What is the connection between the relativistic explanation for magnetic fields and the phenomenon of natural magnets existing? How does the concept of the relativistic explanation for magnetism— that is, the explanation that considers the reference frame of a moving charge in cooperation with length contraction— overlap with the daily phenomenon we see of natural magnets existing by means of the magnetic domains within a compound being lined up? How does this relativistic explanation give way for compounds with no moving charges (?) producing magnetic fields?
Side question: How do these sorts of compounds arise? Why are the magnetic domains of solid iron, for example, often aligned, while the magnetic domains of, say, solid gold, not often (or never?) being aligned?
Physics experience: I took 3 years of physics in highschool and I am currently in my second year of physics in undergraduate. While I have never officially learned about subjects regarding general and special relativity and quantum mechanics, I have a base understanding of these concepts from outside learning.
 A: The source of the magnetic field of a permanent magnet is permanently moving charge.
Electrons are not really points, but quanta of fields, and fields can be in states that are both stationary (i.e., independent of time) and moving (i.e., with a nonzero, though time invariant, current everywhere). Classically, there is always some friction, but quantum mechanics allows for permanent frictionless motion. Frictionless currents over long distances only exist in superconductors, but frictionless atomic-scale currents are everywhere.
Even electron spin is motion of the field, not spinning of an infinitesimal point. See Hans C. Ohanian, "What is spin?", in Am. J. Phys. 54 (6), June 1986, online here.
The answer to your side question is that iron is ferromagnetic, but I don't understand what makes some materials ferromagnetic and most not.
A: The source of the magnetic field of a permanent magnet is the common alignment of the magnetic dipoles of subatomic particles, mainly electrons.
Electrons are not only electric charges, they are also magnetic dipoles. It does not matter at all for the explanation of the magnetic properties of permanent magnets whether the observation of the magnetic dipole of the electron is considered as an intrinsic property per se or as a consequence of a relativistic self-rotation of the particle.
It is sufficiently and intuitively simple to explain the existence of permanent magnets by the phenomenon of self-holding of co-aligned subatomic particles.
It is observable that any substance becomes magnetic itself under the influence of an external sufficiently strong magnetic field. This is simply based on the influence of the previously more or less chaotic orientation of the magnetic dipoles of the subatomic particles. A substance becomes a permanent magnet when the mutual self-holding of the aligned particles is stronger than the thermal motion destroying them. Each substance has its specific Curri temperature at which the mutual self-holding of the magnetic alignment is destroyed.
It remains to state that for a simple explanation of the phenomenon of permanent magnets no relativistic effects need to be referred to. The reference to the standard model of particle physics, in which the subatomic particles have a defined and constant magnetic dipole (for the electron see its value here), is sufficient for the explanation of the existence of permanent magnets.
