Ferromagnetism, magnetic domains
Looking back to the beginning of our thought experiment, magnetic fields may only be produced by a current. Taking the definition of current as a flow of electrons, electrons orbiting an atom should create a current and thus a magnetic field! If every atom has electrons is everything magnetic? YES! All matter, including frogs, can express magnetic properties when given enough energy. But not all magnetism is created equally. The reason I can pick up screws with a refriderator magnent and not a frog is the difference between ferromagnetism and paramagnetism. The way to differentiate the two (and a few more types) is through the study of quantum mechanics.
Ferromagnetism will be our focus, since it is the strongest phenomenon and is what we have the most experience with. Further, to relieve us from having to understanding this at the quantum level, we are going to accept that atoms of ferromagnetic materials tend to align their magnetic fields with their neighbors. Though they tend to align, inconsistencies in material and other factors like crystaline structure create magnetic domains.
When magnetic domains are aligned in a random order, neighboring fields cancel each other out resulting in a non-magnetized material. Once in the presence of an strong external field it is possible to re-align these domains. By aligning these domains, the overall field strengthens, creating a magnet!
This re-alignment can be permanent depending on the strength of the field. This is great because we’ll need these in the next section.