= Antiferromagnetism
{wiki}
= Antiferromagnet
{synonym}
= Antiferromagnetic
{synonym}
<Antiferromagnetism> is ordered compensation of <magnetic moments>. In the collinear two-sublattice model, $\mathbf M_A=-\mathbf M_B\ne0$: net <magnetization> vanishes but <staggered magnetization> remains. <Louis Néel> developed this possibility.<Magnetism and the local molecular field by Louis Néel>[§5, pp.324–326: opposing ordered sublattices]{ref}
For an original local <energy> check, perturb the antiparallel pair in <exchange interaction> by writing $\theta=\pi-\delta$. Then
$$
E=-JS^2\cos\delta=-JS^2+\frac12JS^2\delta^2+O(\delta^4).
$$
For $J>0$, a small relative rotation costs positive <energy>. This verifies a pair's preference; it does not prove a bulk ordering <temperature>. A whole <crystal> must satisfy many bonds simultaneously, and <thermal fluctuations> and quantum effects matter. The <Heisenberg antiferromagnet> and <antiferromagnetic Ising model> specify different assumptions about those collective degrees of freedom.
Why is the distinction useful? A measurement of zero <magnetization> cannot decide between an ordered alternating arrangement, a disordered ensemble, and oppositely magnetized <magnetic domains>. A spatial probe such as <magnetic neutron diffraction> tests the pattern directly. The <manganese monoxide neutron diffraction experiment> is a particularly clear example: the order adds a new periodic scattering signal even though the net <magnetic moment> cancels.
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