The Landau theory of second-order phase transitions has been applied to magnetic phase transitions. The magnetic space group of disordered structure, , transitions to the magnetic space group of the ordered phase, .  is a subgroup of , and keeps only the symmetries which have not been broken during the phase transition. This can be tracked numerically by evolution of the order parameter, which belongs to a single irreducible representation of .
Important magnetic phase transitions include the paramagnetic to ferromagnetic transition at the Curie temperature and the paramagnetic to antiferromagnetic transition at the Néel temperature. Differences in the magnetic phase transitions explain why FeO, MnCO, and CoCO are weakly ferromagnetic, whereas the structurally similar CrO and FeCO are purely antiferromagnetic. This theory developed into what is now known as antisymmetric exchange.
A related scheme is the classification of Aizu species which consist of a prototypical non-ferroic magnetic point group, the letter "F" for ferroic, and a ferromagnetic or ferroelectric point group which is a subgroup of the prototypical group which can be reached by continuous motion of the atoms in the crystal structure.