As a necessary condition, ferromagnetism in elements requires the existence of unpaired electrons. However, all elements with unpaired electrons are not ferromagnetic, e.g., metals such as aluminium or copper are either paramagnetic or diamagnetic. Why don't all elements with unpaired electrons become ferromagnetic? In addition to unpaired electrons, what extra conditions need to be satisfied for elements to exhibit ferromagnetism (or exchange interaction)?
Paramagnetic materials can also act as ferromagnetic at very low temperatures where there isnt enough heat to reorientate the electrons magnetic field randomly.What I do not know is if magnetic domains , regions inside ferromagnetic materials cooled beliw Curie temperature where the magnetic fields of nearby atoms are alligned, can exist in paramagnetic materials at very low temperatures.As other answers have already stated , ferromagnetism is a QM effect , due to lone electrons and Hund's rule(All lone electrons in an atom have the same spin).Actually I suggest you look at this:https://en.m.wikipedia.org/wiki/Ferromagnetism Under the influence of a magnetic field all the electrons allign their magnetic fields to the direction of the external magnetic field causing attraction between the material and the external magnetic field.In ferromagnetic materials this allignment remains even if the external magnetic field is later gone.
PS By the way Mr.Szendrei has given an excellent answer.I dont know why it was downvoted
Ferromagnetism is a purely QM phenomenon.
It needs two things:
the alignment of the individual elementary dipoles, electrons, this is what you call the alignment of the spins, now spin has two components:
magnetic dipole moment of the electron
orbital angular momentum of the electron
Pauli exclusion principle
When two nearby atoms have unpaired electrons, whether the electron spins are parallel or antiparallel affects whether the electrons can share the same orbit as a result of the quantum mechanical effect called the exchange interaction.
This is in connection to the Pauli exclusion principle, which says that two electrons with the same spin cannot be in the same spatial state, orbital.
Electrons that repel, can move further apart, by aligning their spins. This way the spins of these electrons tend to line up. This is the exchange energy.
Please see from wiki:
his energy difference can be orders of magnitude larger than the energy differences associated with the magnetic dipole-dipole interaction due to dipole orientation, which tends to align the dipoles antiparallel. In certain doped semiconductor oxides RKKY interactions have been shown to bring about periodic longer-range magnetic interactions, a phenomenon of significance in the study of spintronic materials. The materials in which the exchange interaction is much stronger than the competing dipole-dipole interaction are frequently called magnetic materials. For instance, in iron (Fe) the exchange force is about 1000 times stronger than the dipole interaction.
So the answer to your question is that other then spin, there is magnetic dipole moment, orbital angular momentum, and exchange energy.