 Ferrimagnetism

Ferrimagnetism has opposing, generally unequal ordered magnetic sublattices, with net magnetization $|M_A-M_B|$ in a collinear model. Louis Néel used it to explain magnetic oxides.^[ref]

The counting example in magnetic sublattice gives $3(2m_0)-3(m_0)=3m_0$. Unequal populations also suffice: four sites carrying $+m_0$ and two carrying $-m_0$ give $2m_0$, even with identical individual magnitudes. Thus one must compare total sublattice contributions per common volume, rather than merely asking whether two atomic species carry different magnetic moments.

Both ferromagnetism and ferrimagnetism can produce a macroscopic magnet. Their internal organization differs: the latter retains opposing contributions. This makes ferrimagnetism a useful bridge between net magnetization and microscopic magnetic order: reducing one opposing contribution can increase the net sum, even though the total sum of moment magnitudes decreases.

Ferrimagnetism is a type of magnetic ordering that occurs in certain materials, where the magnetic moments of atoms or ions align in opposite directions but unequal magnitudes. This results in a net magnetic moment even though the opposing moments partially cancel each other out. In ferrimagnetic materials, typically found in certain types of oxides (like magnetite, Fe3O4), there are two different types of magnetic ions or sublattices with unequal magnetic moments.