Step 1: Magnetic properties arise from the presence of unpaired electrons, usually in transition metal ions.
Step 2: \(SiO_2\), \(MgO\), and \(Na_2O\) are diamagnetic (no unpaired electrons).
Step 3: \(Mn_3O_4\) (Hausmannite) contains \(Mn^{2+}\) and \(Mn^{3+}\) ions, both of which have unpaired electrons in their \(d\)-orbitals, making it paramagnetic or ferrimagnetic at low temperatures.