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.