= Magnetic sublattice
A <magnetic sublattice> groups sites with a common ordered <magnetic moment> in a description of <magnetic order>. In the simplest two-sublattice description, assign <magnetizations> $\mathbf M_A$ and $\mathbf M_B$ per total specimen <volume>, so that
$$
\mathbf M=\mathbf M_A+\mathbf M_B,\qquad
\mathbf L=\mathbf M_A-\mathbf M_B.
$$
Here $\mathbf L$ is one normalization of the <staggered magnetization>; conventions may include a factor $1/2$. Using the same total <volume> for both contributions is essential. Equal <magnetic moment> per site does not imply equal sublattice contributions if the site populations differ.
\Image[/magnetic-sublattice-order-comparison.png]
{title=<Ferromagnetism>, <antiferromagnetism>, and <ferrimagnetism>: order and the net <magnetic moment>}
{description=Original counting diagrams with six sites in equal <volumes>. Arrows are <magnetic moments>, not trajectories. The stipulated site contributions are $+m_0,+m_0$ for <ferromagnetism>, $+m_0,-m_0$ for <antiferromagnetism>, and $+2m_0,-m_0$ for <ferrimagnetism>. The two colors identify A and B sites. This schematic is not a measured material or the <crystal structure> of <manganese(II) oxide>.}
In this six-site example, three A sites and three B sites give total <magnetic moments> $6m_0$, $0$, and $3m_0$, respectively, along the chosen axis. The antiferromagnetic case has $\mathbf M=0$ but $\mathbf L=6m_0\widehat{\mathbf z}/V$. Cancellation of the sum leaves the alternating information intact.
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