There are many different types of magnetic materials:
Ferromagnetic
Diamagnetic
Paramagnetic
Antiferromagnetic
Ferrimagnetic
Super Paramagnetic

Based on your earlier question, I'm guessing you are asking about ferromagnetic properties.

At the macro level, the distinguishing characteristic of ferromagnetic materials is a larger permeability (when magnetized) and the ability to retain magnetized when the magnetizing field is removed.

At the atomic level, the magnetism does originate from the availablity of unpaired electrons in the outer shell.  I can't recall of the atomic radius/center ratio is a factor.

and while the electron configuration is important for the material to be ferromagnetic, in order to be able to make large scale physically useful magnets there must also be a mechanism that leads to anisotropy, so that you can create a preferred orientation.

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